Transport Phenomena in Plasma

Volume Editors/Serial Editors

A. Fridman and Y.I. ChoDepartment of Mechanical Engineering and Mechanics

Drexel University

Philadelphia, Pennsylvania

Coordinating Technical Editor

George A. GreeneEnergy Sciences and Technology

Brookhaven National Laboratory

Upton, New York

Serial EditorAvram Bar-CohenDepartment of Mechanical Engineering

University of Maryland

College Park, Marland

Volume 40

Founding EditorsThomas F. Irvine, Jr.

yState University of New York at Stony Brook, Stony Brook, NY

James P. Hartnetty

University of Illinois at Chicago, Chicago, IL

Amsterdam Boston London New York Oxford Paris

San Diego San Francisco Singapore Sydney Tokyo

Academic Press is an imprint of Elsevier

ACADEMICPRESS

Transport Phenomenain Plasma Advances in Heat Transfer

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PREFACE

For more than 40 years, Advances in Heat Transfer has filled the infor-mation gap between journals and university-level textbooks. The seriespresents review articles on topics of current interest, starting from widelyunderstood principles and bringing the reader to the forefront of the topicbeing addressed. The favorable response of the international scientific andengineering community to the 40 volumes published to date is an indicationof the success of our authors in fulfilling this purpose.

In recent years, the editors have published topical volumes dedicated tospecific fields of endeavor. Examples of such volumes are Volume 22 (Bio-engineering Heat Transfer), Volume 28 (Transport Phenomena in MaterialsProcessing) and Volume 29 (Heat Transfer in Nuclear Reactor Safety). Theeditors have continued this practice of topical volumes with the publicationof Volume 40, which is dedicated to Heat Transfer in Plasma Physics.

The editors would like to express their appreciation to the contributingauthors of Volume 40, who have maintained the high standards associatedwith Advances in Heat Transfer. Finally, the editors would like to acknowl-edge the efforts of the staff at Academic Press and Elsevier, who havemaintained the attractive presentation of the volumes over the years.

xiii

CONTENTS

Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Non-Thermal Atmospheric Pressure Plasma

A. FRIDMAN, A. GUTSOL, Y.I. CHO

I. Non-Thermal Plasma Stabilization at High Pressures . . . . . . . . 1

II. Townsend and Spark Breakdown Mechanisms . . . . . . . . . . . . 4

A. The Townsend Mechanism of Electric Breakdown of Gases . . . . . . . . . . . . 4

B. The Critical Electric Field of Townsend Breakdown . . . . . . . . . . . . . . . . . 6

C. The Townsend Breakdown Mechanism in Large Gaps. . . . . . . . . . . . . . . . 7

D. The Spark Breakdown Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

E. Electron Avalanches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

F. The Streamers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

G. The Meek Criterion of Streamer Formation . . . . . . . . . . . . . . . . . . . . . . . 13

H. The Streamer Breakdown Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

I. The Leader Breakdown Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

III. The Corona Discharge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

A. Overview of the Corona Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

B. Negative and Positive Coronas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

C. Ignition Criterion for Corona in Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

D. Active Corona Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

E. Influence of Space Charge on Electric Field in Corona. . . . . . . . . . . . . . . . 21

F. Current-Voltage Characteristics of a Corona Discharge . . . . . . . . . . . . . . . 22

G. Power Released in a Continuous Corona Discharge . . . . . . . . . . . . . . . . . 23

IV. Pulsed Corona Discharge. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

A. Overview of Pulsed Corona Discharges . . . . . . . . . . . . . . . . . . . . . . . . . . 24

B. Corona Ignition Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

C. Flashing Corona . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

D. Trichel Pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

E. Pulsed Corona Discharges Sustained by Nano-Second Pulse Power Supplies 27

F. Configurations of Pulsed Corona Discharges. . . . . . . . . . . . . . . . . . . . . . . 28

V. Dielectric-Barrier Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . 30

A. Overview of Dielectric Barrier Discharges. . . . . . . . . . . . . . . . . . . . . . . . . 30

B. Properties of Dielectric Barrier Discharges . . . . . . . . . . . . . . . . . . . . . . . . 31

C. Phenomena of Microdischarge Interaction: Pattern Formation . . . . . . . . . . 35

v

D. Surface Discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

E. The Packed-Bed Corona Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

F. Atmospheric Pressure Glow DBD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

G. Ferroelectric Discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

VI. Spark Discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

A. Development of a Spark Channel, a Back Wave of Strong Electric Field and

Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

B. Laser Directed Spark Discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

VII. Atmospheric Pressure Glows . . . . . . . . . . . . . . . . . . . . . . . . . 52

A. Resistive Barrier Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

B. One Atmosphere Uniform Glow Discharge Plasma . . . . . . . . . . . . . . . . . . 55

C. Electronically Stabilized APG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

D. Atmospheric Pressure Plasma Jet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

E. Role of Noble Gases in Atmospheric Glows . . . . . . . . . . . . . . . . . . . . . . . 72

VIII.Microplasmas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

A. Micro Glow Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

B. Micro DBDs for Plasma TV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

C. Micro Hollow Cathode Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

D. Other Microdischarges and Microdischarge Arrays . . . . . . . . . . . . . . . . . . 89

IX. Gliding Discharges (GD) and Fast Flow Discharges. . . . . . . . . 96

X. Plasma Discharges in Water. . . . . . . . . . . . . . . . . . . . . . . . . . 104

A. Needs for Plasma Water Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

B. Conventional Methods for Drinking Water Treatment . . . . . . . . . . . . . . . . 105

C. Water Treatment Using Plasma Discharge . . . . . . . . . . . . . . . . . . . . . . . . 106

D. Production of Electrical Discharges in Water . . . . . . . . . . . . . . . . . . . . . . 109

E. Previous Studies on the Plasma Water Treatment . . . . . . . . . . . . . . . . . . . 111

F. Mechanism of Plasma Discharges in Water. . . . . . . . . . . . . . . . . . . . . . . . 116

G. Process of the Electrical Breakdown in Water. . . . . . . . . . . . . . . . . . . . . . 120

H. New Developments in Plasma Water Treatment at Drexel Plasma Institute . 124

XI. Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Heat Transfer in Plasma Spray Coating Processes

J. MOSTAGHIMI, S. CHANDRA

I. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

II. Plasma Spray Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

A. Direct Current (DC) Plasma Gun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

B. Radio-Frequency Inductively Coupled Plasma (RF-ICP) . . . . . . . . . . . . . . 148

C. Wire-Arc Spraying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

III. Droplet Impact, Spread and Solidification. . . . . . . . . . . . . . . . 150

A. Axi-Symmetric Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

B. Splashing and Break-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

vi CONTENTS

IV. Mathematical Model of Impact . . . . . . . . . . . . . . . . . . . . . . . 156

A. Fluid Flow and Free Surface Reconstruction . . . . . . . . . . . . . . . . . . . . . . 156

B. Heat Transfer and Solidification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

C. Thermal Contact Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

D. Effect of Solidification on Fluid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

E. Numerical Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

F. Simulation of Splat Formation in Thermal Spray . . . . . . . . . . . . . . . . . . . 163

G. Effect of Roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

V. Laboratory Experiments on Droplet Impact . . . . . . . . . . . . . . 173

A. Large Droplets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

B. Small Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

C. Transition Temperature Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

D. Effect of Substrate Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

VI. Thermal Spray Splats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

A. Wire-Arc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

B. Plasma Particle Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

VII. Simulating Coating Formation . . . . . . . . . . . . . . . . . . . . . . . 196

A. Direct Coating Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

B. Stochastic Coating Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

Plasma Spraying: From Plasma Generation to Coating Structure

P. FAUCHAIS, G. MONTAVON

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

II. Plasma Spray Torches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

A. General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

B. Plasma Jet Characterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

C. Direct Current Stick-Type Cathode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

D. Velocity and Temperature Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 223

E. Soft Vacuum or Controlled Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . 230

F. Other d.c. Torches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

III. RF Plasma Spray Torches . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

A. Conventional Torches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

B. Supersonic Torches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

IV. Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

A. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

B. General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

C. RF Plasma Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

D. d.c. Plasmas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

E. In-Flight Particles Interaction with the Plasma Jet . . . . . . . . . . . . . . . . . . . 246

F. Corrections Specific to Plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

G. Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

viiCONTENTS

H. In-flight Particle Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

I. Ensemble of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

V. Coating Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

A. General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

B. Characteristic Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

C. Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

D. Models and Results on Smooth Substrates Normal to Impact

Direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

E. Transition Temperature when Preheating the Substrate . . . . . . . . . . . . . . . 294

F. Models and Measurements on Rough Orthogonal Substrates . . . . . . . . . . . 303

G. Impacts on Inclined Substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

H. Splashing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

I. Parameters Controlling the Particle Flattening . . . . . . . . . . . . . . . . . . . . . . 311

J. Adhesion of Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

K. Splat Layering and Coating Construction. . . . . . . . . . . . . . . . . . . . . . . . . 320

L. Coating Architecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

VI. Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

Heat Transfer Processes and Modeling of Arc Discharges

E. PFENDER, J. HEBERLEIN

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

II. General Features of Thermal Arcs . . . . . . . . . . . . . . . . . . . . . 347

A. Relatively High Current Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348

B. Low Cathode Fall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348

C. High Luminosity of the Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348

III. Thermodynamic and Transport Properties Relevant to ThermalArcs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

A. Equilibrium Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

B. Non-equilibrium Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391

IV. Modeling of Thermal Arcs . . . . . . . . . . . . . . . . . . . . . . . . . . . 412

A. Simple Models Based on LTE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412

B. Models for Non-LTE Arcs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

V. Heat Transfer Processes in Thermal Arcs . . . . . . . . . . . . . . . . 428

A. General Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428

B. Anode Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

C. Cathode Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

VI. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446

viii CONTENTS

Heat and Mass Transfer in Plasma Jets

S.V. DRESVIN, J. AMOUROUX

I. The General Concepts of Convective Heat Transfer . . . . . . . . . 451

A. What is a Convective Heat Transfer? The Newton’s Formula. . . . . . . . . . . 451

B. The Energy Conservation Law at the Solid Wall Interface . . . . . . . . . . . . . 453

C. Similarity Criteria (Numbers): Reynolds and Nusselt’s Numbers. . . . . . . . . 454

D. On the Boundary Layer and Similarity Theory . . . . . . . . . . . . . . . . . . . . . 457

E. Boundary Layer Thickness Evaluation and the First Possibility of Expressing

the Heat Transfer Coefficient with Flow Parameters . . . . . . . . . . . . . . . . . 459

F. The Full Energy of The Oncoming Flow: The Stanton’s Number . . . . . . . . 461

G. The Prandtl and Peklet Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

H. The Equations of the Laminar Boundary Layer . . . . . . . . . . . . . . . . . . . . 465

I. Estimation of the Thermal Boundary Layer Thickness . . . . . . . . . . . . . . . . 469

J. The Approximate Expression for the Convective Heat Transfer Coefficient

as Function of Medium and Flow Parameters . . . . . . . . . . . . . . . . . . . . . . 470

K. The Exact Calculation of the Heat Transfer Coefficient a (Laminar Thermal

Boundary Layer at the Plane Plate) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472

L. Heat Transfer Formulas for Sphere, Cylinder and Plate . . . . . . . . . . . . . . . 476

II. The Convective Heat Transfer in Plasma. . . . . . . . . . . . . . . . . 482

A. The Key Concepts and Its Considerations . . . . . . . . . . . . . . . . . . . . . . . . 482

B. Experimental Studies of Heat Transfer in Plasma . . . . . . . . . . . . . . . . . . . 492

C. Comparison and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523

Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

ixCONTENTS

ARTICLE IN PRESS

Non-Thermal Atmospheric Pressure Plasma

A. FRIDMAN, A. GUTSOL and Y.I. CHO

Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia,

PA 19104

I. Non-Thermal Plasma Stabilization at High Pressures

Plasma-chemical and plasma-processing systems are traditionally dividedinto two major categories: thermal and non-thermal ones [1]. Thermalplasma of arcs or radio-frequency (RF) discharges is associated with Jouleheating and thermal ionization that enables to deliver high power (to over50MW per unit) at high operating pressures. However, low excitationselectivity, very high gas temperature, quenching requirements and electrodeproblems result in limited energy efficiency and applicability of thermalplasma sources. Non-thermal plasma is usually very far from thermo-dynamic equilibrium: while temperature of electrons reaches 1–3 eV andprovides intensive ionization, gas as whole remains cold. Non-thermalplasma offers high selectivity and energy efficiency of plasma-chemicalreactions; it is able to operate effectively at low temperatures, in contactwith fragile and delicate materials and does not require any quenching. Thusit is the non-thermal plasma, which this chapter is to be focused on.

Electric energy of plasma sources is initially absorbed by electrons, andthen transferred from the electrons to the neutral gas. If the rate of energytransfer from the plasma electrons to the neutral gas is significant, butcooling of the gas is not effective, then the plasma becomes thermal. If therate of energy transfer from the plasma electrons to the neutral gas is limi-ted, and/or cooling of the gas is fast and effective, then the electron temper-ature significantly exceeds that of neutrals (TecT0) and the plasma becomesnon-thermal and strongly non-equilibrium. Most of the conventional non-thermal plasma discharges are organized at low pressures, where the neutralgas cooling by the walls is much faster. Such low-pressure non-thermalplasma discharges can be represented by traditional glow, inductively (ICP)and capacitively (CCP) coupled RF discharges, and are widely used inmodern electronics and reviewed particularly in Ref. [1,2].

Advances in Heat TransferVolume 40 ISSN 0065-2717DOI: 10.1016/S0065-2717(07)40001-6

1 Copyright r 2007 Elsevier Inc.All rights reserved

ADVANCES IN HEAT TRANSFER VOL. 40

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Organization of the non-thermal, strongly non-equilibrium plasma atatmospheric pressure is much more challenging. Energy transferred from theplasma electrons to neutral gas tends at high pressures to be transferred toheat through different fast channels of the thermal (ionization-overheating)instability. Increase of temperature significantly accelerates the process, andcooling mechanisms at high pressures are limited. Nevertheless, severalapproaches have been developed to overcome the problems and organize thestrongly non-equilibrium plasma at atmospheric pressure. Between those,we can point out the following major approaches:

� Low discharge power. If the discharge power is sufficiently low, itobviously limits overheating and gas temperature, while electrontemperature should be anyway on the level of 1–3 eV to provideeffective ionization. Such situation takes place, in particular, in thewell-known stationary corona discharges. The approach is not verymuch attractive: there is no overheating, but there is no intensiveplasma as well.

� Short pulse discharges. If the duration of pulses is short enough, over-heating can be avoided even locally. The discharges can generate highconcentration of active plasma species and initiate multiple plasma-chemical processes, while gas temperature remains very low. Goodexample of the approach is a pulsed corona discharge, which becomestoday more and more attractive for many exciting applications.

� Dielectric barrier discharge (DBD). While the pulse duration is con-trolled electronically in the short pulse discharges, the DBD pulses arecontrolled naturally by dielectric barriers even when the conventionalAC voltage is applied. Simplicity of the DBD has made this dis-charges probably the most widely used today. The important problemof the DBDs is their space non-uniformity related to streamer mech-anisms of the generation of the discharges.

� Helium discharges. Uniform discharges can be organized at atmos-pheric pressure in helium without overheating due to its high thermalconductivity and possibility to ionize the gas at relatively low voltagesand powers. In the case of DBD, only small additions of electron-egative gases to helium are permitted without disturbing DBD uni-formity. In the case of RF discharges, admixtures of molecular andelectronegative gases can be significant. Applications of the dis-charges are obviously limited by usage of helium.

� Fast-flow discharges. The non-thermal, strongly non-equilibrium dis-charges can be stabilized at atmospheric pressure in fast gas flows.Intensive convective cooling is able to stabilize even very powerfuldischarges without significant overheating. Flow organization and

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overcoming the gas-dynamic instabilities can be quite challenging insuch systems.

� Micro-discharges. Effective cooling at low pressure and stabilizationof low pressure discharges actually require low values of the ‘‘pd’’parameter that is the product of pressure and characteristic dischargesize. Therefore, the non-thermal, strongly non-equilibrium dischargescan be stabilized at atmospheric pressure if characteristic sizes aresufficiently small, usually in sub-millimeter range.

� Transitional and specifically gliding discharges. Non-equilibrium dis-charges can be organized in transitional regimes of traditionally ther-mal discharges, specifically, by limitation or reduction of the specificpower of the discharges or by effective cooling mechanisms. Thesedischarges characterized by non-thermal mechanisms of ionizationboth in volume and on the electrodes are not ‘‘very cold’’ (usuallytheir temperature essentially exceeds room temperature at least lo-cally), but not as hot as actual thermal discharges. Gliding dischargesare good examples of such transitional or ‘‘warm’’ discharges.

The non-thermal plasma may be produced by a variety of electrical dis-charges or electron beams. The basic feature of these various technologies isthat they produce plasma in which the majority of the electrical energyprimarily goes into the production of energetic electrons – instead of heatingthe entire gas stream. These energetic electrons produce excited species – freeradicals and ions – as well as additional electrons through electron-impactdissociation, excitation and ionization of background gas molecules. Theseexcited species play key role in chemical applications of non-thermal plasma.For example, they oxidize, reduce or decompose the pollutant molecules inpollutions control applications. This is in contrast to the mechanism involvedin thermal plasma chemistry, for example in incineration processes, whichrequire heating the entire gas stream in order to destroy the pollutants. As aresult, the low-temperature plasma technologies are highly selective, haverelatively low maintenance requirements and relatively low energy costs.

Some basic phenomena in non-thermal plasma are well understood andanalytically described. This understanding is a basis for the description andnumerical simulation of more complex phenomena and plasma systems.Therefore, in the beginning of this chapter (Sections II.A–III.G) we provide athorough consideration of the well-established phenomena (mechanisms ofelectrical breakdowns and corona discharges). In other parts of the chapterrelated to the discharges intensively used in various cutting-edge techno-logies, we limit our description by presentation of experimental data withqualitative explanations and numerical simulation results when available.While most of the atmospheric pressure plasma systems are started in

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gas-phase, significant attention is attracted in recent years to dischargesgenerated in liquid phase and specifically in water. These multiphase andessentially non-equilibrium discharges are also considered in the Chapter.

II. Townsend and Spark Breakdown Mechanisms

A. THE TOWNSEND MECHANISM OF ELECTRIC BREAKDOWN OF GASES

The electric breakdown is a complicated process of the formation conduc-tive gas channel, which occurs when electric field exceeds some critical value.As the result of the breakdown different kinds of plasmas are generated.Although breakdown mechanisms can be very sophisticated, all of themusually start with an electron avalanche. The electron avalanche is multi-plication of some primary electrons in cascade ionization.

Let us consider first the simplest breakdown in a plane gap of lengthd between electrodes connected to a DC power supply (with voltage V),which provides the homogeneous electric field E ¼ V/d. We can imaginesome occasional formation of primary electrons near cathode providing thevery low initial current i0. Each primary electron drifts to anode, ionizingthe gas (producing secondary electrons) and thus generates an avalanche.The avalanche develops both in time and space, because the multiplicationof electrons proceeds along with their drifts from cathode to anode (seeFig. 1). It is convenient to describe the ionization in avalanche not by theionization rate coefficient, but by the Townsend ionization coefficienta, which shows electron production or the multiplication of electrons (initial

CATHODE

ANODE

dE

ee

e e

e e

e e

e

e e

e eee

FIG.1. Illustration of the Townsend breakdown gap.

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density ne0) per unit length along the electric field: dne/dx ¼ ane or alter-natively ne(x) ¼ ne0exp(ax). The Townsend ionization coefficient is relatedto the ionization rate coefficient ki(E/n0) and electron drift velocity vd as:

a ¼ nind

¼ 1

ndkiðE=n0Þn0 ¼

1

me

kiðE=n0ÞE=n0

(1)

where ni is the ionization frequency with respect to one electron, me isthe electron mobility. Taking into account that breakdown starts at roomtemperature, and the electron mobility is inversely proportional to pressure,it is convenient to present the Townsend coefficient a as the similarity para-meter a/n0 depending on the reduced electric field E/n0.

According to the definition of the Townsend coefficient a, each one pri-mary electron generated near cathode produces exp(ad)�1 positive ions inthe gap (see Fig. 1). We neglect here the electron losses due to recombinationand attachment to electronegative molecules. The electron-ion recombina-tion is neglected because ionization degree is very low during the break-down; attachment processes important in electronegative gases will bediscussed especially below.

All the exp(ad)�1 positive ions produced in the gap from one electron aremoving back to the cathode, and altogether knock out g � [exp(ad)�1] elec-trons from the cathode in the process of secondary electron emission. Here gis the secondary emission coefficient (called the third Townsend coefficient),defined as the probability of a secondary electron generation on the cathodeby an ion impact. Obviously, the secondary electron emission coefficient gdepends on cathode material, the state of surface, the type of gas and re-duced electric field E/n0 (defining the energy of ions). The typical value of gin electric discharges is 0.01–0.1; the effect of photons and meta-stable at-oms and molecules (produced in avalanche) on the secondary electronemission is usually incorporated in the same ‘‘effective’’ g coefficient.

The current in the gap is non-self-sustained as long as g � [exp(ad)�1] isless than one, because positive ions generated by electron avalanche mustproduce at least one electron to start a new avalanche. As soon as electricfield and, hence, the Townsend a coefficient become high enough, the transi-tion to self-sustained current (the breakdown!) takes place. Thus the sim-plest breakdown condition in the gap can be expressed as:

g½expðadÞ � 1� ¼ 1; ad ¼ ln1

gþ 1

� �(2)

Townsend breakdown mechanism is the mechanism of ignition of a self-sustained discharge in gap, controlled by the secondary electron emissionfrom cathode.


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B. THE CRITICAL ELECTRIC FIELD OF TOWNSEND BREAKDOWN

It is possible to derive relations for breakdown electric field based onEq. (2), by rewriting Eq. (1) for the Townsend coefficient a in the followingconventional semi-empirical way, relating the similarity parameters a/p andE/p, proposed initially by Townsend:

ap¼ A exp � B

E=p

� �(3)

The parameters A and B of Eq. (3) needed for numerical calculations ofa in different gases at E/p ¼ 30–500V/cm �Torr, are given in Table I.

Combination of Eqs. (2) and (3) gives the following convenient formulafor the calculation of breakdown reduced electric field as a function of animportant similarity parameter pd:

E

p¼ B

C þ lnðpdÞ (4)

In this equation, parameter B is the same as the one in Eq. (3) and inTable I. The parameter A, is replaced by another one C ¼ lnA�ln[ln(1/g+1)].

The breakdown voltage dependence on the similarity parameter pd, whichcan be found from Eq. (4), is usually referred to as the Paschen curve. Theexperimental Paschen curves for different gases are presented, in particular,in Raizer [3]. These curves have a minimum voltage point, corresponding tothe easiest breakdown conditions, which can be found from Eq. (4):

Vmin ¼ eB

Aln 1þ 1

g

� �;

E

p

� �min

¼ B; ðpdÞmin ¼ e

Aln 1þ 1

g

� �(5)

where eE2.72 is the base of natural logarithm.

TABLE I

NUMERICAL PARAMETERS A AND B FOR CALCULATION OF THE TOWNSEND COEFFICIENT a

Gas A (1/cmTorr) B (V/cmTorr) Gas A (1/cmTorr) B (V/cmTorr)

Air 15 365 N2 10 310

CO2 20 466 H2O 13 290

H2 5 130 He 3 34

Ne 4 100 Ar 12 180

Kr 17 240 Xe 26 350

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The typical value of minimum voltage necessary for breakdown is about300V, corresponding reduced electric field – about 300V/cm �Torr. Theright-hand branch of the Paschen curve (i.e., for the pressure more than aTorr for a gap about 1 cm) is related to a case, when electron avalanche hasboth enough distance and gas pressure to provide intensive ionization evenat not very high electric fields. In this case the reduced electric field is almostfixed and just slowly–logarithmically reducing with pd-growth. The left-hand branch of the Paschen curve is related to a case, when ionization islimited by both the avalanche size and gas pressure. The ionization ratesufficient for breakdown can be provided in such a situation only by veryhigh electric fields.

The reduced electric field at the Paschen minimum (E/p)min ¼ B corre-sponds to the Stoletov constant, which is the minimum price of ionization(the minimum discharge energy necessary to produce one electron-ion pair).The price of ionization can be expressed in the case under consideration asW ¼ eE/a (e is the charge of an electron here), and its minimum, which is theStoletov constant, is equal to Wmin ¼ 2.72 eB/A. The Stoletov constantexceeds the ionization potentials usually several times, because electronsspent their energies not only on ionization but also on vibrational andelectronic excitations. The typical numerical estimation for the minimumionization price in electric discharges with high electron temperatures isabout 30 eV. It is interesting to note that the reduced electric field at thePaschen minimum Eq. (5) does not depend on g and, hence, on a cathodematerial in contrast to the minimum voltage Vmin and the correspondingsimilarity parameter (pd)min.

C. THE TOWNSEND BREAKDOWN MECHANISM IN LARGE GAPS

The above-discussed Townsend mechanism of breakdown, which is rel-atively homogeneous and includes development of independent avalanches,takes place usually at pdo4000Torr � cm (it means do5 cm at atmosphericpressure). In bigger gaps (more than 6 cm at atmospheric pressure) theavalanches essentially disturb the electric field and are not independentanymore. It leads to the spark mechanism of breakdown, which we aregoing to discuss later on. Here we are going to discuss the case with rela-tively large gaps, but still not big enough for sparks.

The reduced electric field E/p necessary for breakdown is logarithmicallyreducing with pd. It is illustrated by the E(d) dependence in atmospheric air,presented in Fig. 2. The bigger gap and the bigger avalanche we have, theless sensitive is the reduced electric field E/p to the secondary electronemission and cathode material. It explains the E/p reduction with pd.


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This reduction in electronegative gases is limited, however, by electronattachment processes. Influence of the attachment processes can be takeninto account in a similar way with ionization by introducing the secondTownsend coefficient b:

b ¼ nand

¼ 1

ndkaðE=n0Þn0 ¼

1

me

kaðE=n0ÞE=n0

(6)

In this equation: ka(E/n0) and na are the attachment rate coefficient andattachment frequency with respect to an electron, respectively. The Town-send coefficient b shows the electron losses due to attachment per unitlength. Combination of a and b gives:

dne

dx¼ ða� bÞne and neðxÞ ¼ ne0 exp½ða� bÞx� (7)

The Townsend coefficient b is in the same way as a is the exponentialfunction of the reduced electric field. But ionization usually exceeds attach-ment at relatively high values of reduced electric fields, and coefficient b canbe neglected with respect to a in the case of short gaps. That explains theabsence of b coefficients in formulas of the previous section.

When the gaps are relatively big (i.e., centimeter range at atmosphericpressure), the Townsend breakdown electric field in electronegative gasesbecomes actually constant and limited by attachment processes. In this case,

FIG.2. Breakdown electric field in atmospheric air [3].

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obviously, the breakdown of electronegative gases requires much highervalues of the reduced electric fields. The breakdown electric fields at highpressures for both electronegative and non-electronegative gases are pre-sented in Table II.

The Townsend mechanism of breakdown was discussed above in the mostgeneral situations. Discussion of specific breakdown mechanisms such aselectric breakdown in microwave, RF and low frequency fields, opticalbreakdown and breakdown of vacuum gaps is out of the scope of thepresent review but can be found for example in Raizer [3].

D. THE SPARK BREAKDOWN MECHANISM

Another breakdown mechanism, the so-called spark, takes place in largegaps at high pressures (d45 cm at 1 atm). The sparks in contrast to theTownsend mechanism provide breakdown in a local narrow channel, with-out direct relation to electrode phenomena and with very high currents (upto 104–105A) and current densities.

The spark breakdown as well as Townsend breakdown is primarily re-lated to the avalanches, but in large gaps they cannot be considered asindependent and stimulated by electron emission from cathode. The sparkbreakdown at high pd develops much faster than time necessary for ions tocross the gap and provide the secondary emission. Thus breakdown voltagein this case is independent of the cathode material, the phenomenon which isalso an evidence of qualitative difference of the Townsend and mechanismsof spark breakdown.

The mechanism of spark breakdown is based on the concept of astreamer, a thin ionized channel, which is growing fast between electrodes.The concept of streamer was originally developed by Raether [4], Loeb [5]and Meek [6]. Streamers are produced by an intensive primary avalanche ifthe space charge of this avalanche is big enough to create electric field withsuch a strength comparable to the applied electric field. This condition of

TABLE II

ELECTRIC FIELDS SUFFICIENT FOR THE TOWNSEND BREAKDOWN OF CENTIMETER-SIZE GAPS AT

ATMOSPHERIC PRESSURE

Gas E/p (kV/cm) Gas E/p (kV/cm) Gas E/p (kV/cm)

Air 32 O2 30 N2 35

H2 20 Cl2 76 CCl2F2 76

CSF8 150 CCl4 180 SF6 89

He 10 Ne 1.4 Ar 2.7


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streamer formation is also known as Meek condition [6]. The details ofstreamer formation and propagation mechanisms will be covered later in thepresent review.

If the distance between two electrodes is more than a meter or evenkilometer long, the individual streamers are not sufficient to provide thelarge-scale spark breakdown (e.g., in the case of a lightning). In this case theso-called leader is moving from one electrode to another. The leader is athin channel-like streamer but much more conductive. Leader actuallyincludes the streamers as its elements. Because all considered types ofbreakdown include avalanche phase as an initial stage of breakdowndevelopment we give detailed description of the avalanche development inthe next section.

E. ELECTRON AVALANCHES

Adding to Eq. (7) similar equations (Ne) for positive (N+) and negative(N�) ions, we have a system of equations that describes an avalanche mov-ing along the axis x:

dNe

dx¼ ða� bÞNe;

dNþdx

¼ aNe;dN�dx

¼ bNe (8)

where a and b are the ionization and attachment Townsend coefficients,respectively. If the avalanche starts from the one primary electron, thenumbers of charged particles – electrons, positive and negative ions – can befound from Eq. (8) as:

Ne ¼ exp½ða� bÞx�; Nþ ¼ aa� b

ðNe � 1Þ; N� ¼ ba� b

ðNe � 1Þ (9)

The electrons in the avalanche move in the direction of non-disturbedelectric field E0 (axis x) with a drift velocity nd ¼ meE0. In the same time, freeelectron diffusion (with diffusion coefficient De) makes the group of elec-trons to spread around the axis x in radial direction r. Taking into accountboth the drift and the diffusion, the electron density in the avalanche can beintroduced in the following form [7]:

neðx; r; tÞ ¼1

ð4pDetÞ3=2exp � ðx� meE0tÞ2 þ r2

4Detþ ða� bÞmeE0t

� �(10)

The avalanche radius rA (where the electron density is ‘‘e’’ times less thanthe electron density on the axis x) is growing up with both time and thedistance x0 of the avalanche propagation in accordance with the

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conventional diffusion relation, which takes into account the Einsteinrelation between electron mobility and free diffusion coefficient:

rA ¼ffiffiffiffiffiffiffiffiffiffi4Det

p¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4De

x0

meE0

r¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi4Te

eE0x0

s(11)

Based on the expression for electron concentration, Eq. (10), we can cal-culate the space distribution of positive and negative ion densities during theshort interval of avalanche propagation, when the ions remain actually at rest:

nþðx; r; tÞ ¼Z t

0

am0E0neðx; r; t0Þdt0 n�ðx; r; tÞ ¼Z t

0

bm0E0neðx; r; t0Þdt0

(12)

A simplified expression for the positive ion density space distribution nottoo far from the x axis can be derived based on Eqs. (10) and (12) in theabsence of attachment and in the limit t-N [5] as:

nþðx; rÞ ¼a

pr2AðxÞexp ax� r2

r2AðxÞ

� �(13)

where rA(x) is the avalanche radius. The ion concentration in the trail ofthe avalanche is growing up along the axis in accordance with exponentialincrease of number of electrons.

Although the avalanche radius is growing up proportionally to x1/2,the visible avalanche outline is wedge-shaped. It means that the visibleavalanche radius is growing up linearly (i.e., proportionally to x). It happensbecause the visible avalanche radiation is determined by the absolute densityof excited species, which is approximately proportional to the exponentialfactor from the Eq. (13), and obviously, grows with x. The visible avalancheradius r(x) can be then expressed from Eq. (13), taking into account small-ness of r at small x, as:

r2ðxÞr2AðxÞ

¼ ax� lnF; rðxÞ � rAðxÞffiffiffiffiffiffiax

p ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4T ex

eE0ax

s¼ x

ffiffiffiffiffiffiffiffiffiffiffi4TeaeE0

s(14)

which explains the linearity of r(t) and wedge-shape of an avalanche. In thisequation F is the exponential factor from the Eq. (13).

The qualitative change in the avalanche behavior takes place when thecharge amplification exp(ax) is high. In this case the production of a spacecharge with its own significant electric field Ea takes place. This local electric


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field Ea should be added to the external field E0. Because the electrons aremuch faster than ions, the electrons always run at the head of avalancheleaving the ions behind, thus creating a dipole with the characteristic length1/a (i.e., distance, which the electrons move before ionization) and chargeNeEexp(ax).

The dipole formation provokes the appearance of the external electricfield distortion. In front of the avalanche head (and behind the avalanche)the electric field has its maximum value (the sum of E0 and Ea), whichobviously accelerates ionization in these areas. Vice versa inside the ava-lanche. The total electric field is lower than the external one, which slowsdown the ionization. Also the space charge creates the radial electric field.The electric field of the charge NeEexp(ax) on the distance about theavalanche radius reaches the value of the external field E0 at some criticalvalue of ax.

Note that when axX14 the radial growth of an avalanche due to therepulsion drift of electrons exceeds the diffusion effect and thus it should betaken into account. In this case the avalanche radius is growing with x as:

r ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

3e

4p�0aE0

3

sexp

ax3

¼ 3

aEa

E0(15)

This fast growth of the transverse avalanche size restricts the electrondensity in the avalanche by the maximum value:

ne ¼�0aE0

e(16)

When the transverse avalanche size reaches the characteristic ionizationlength 1/aE0.1 cm for atmospheric pressure air, the broadening of the ava-lanche head slows down dramatically. Obviously, the avalanche electric fieldis about the external one in this case, see Eq. (15). The typical values ofthe maximum electron density in an avalanche are in the range of1012–1013 cm�3.

When the avalanche head reaches the anode, the electrons sink into theelectrode, leaving the ions to occupy the discharge gap. At the absence ofelectrons, the total electric field is due to the external field, the ionic trail andalso the ionic charge ‘‘image’’ in the anode. The resulting electric field in theionic trail near the anode is less than the external electric field, but it exceedsE0 farther off the electrode. The total electric field reaches the maximumvalue on the characteristic ionization distance (about 0.1 cm from the anodefor atmospheric pressure air).


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F. THE STREAMERS

A strong primary avalanche amplifies the external electric field leadingto the formation of thin weakly ionized plasma channel, so-calledstreamer. When the streamer channel connects the electrodes, the currentmay be significantly increased to form a spark. The avalanche-to-streamertransformation takes place, when the internal field of the avalanche be-comes comparable to the external one, that is when the amplificationparameter ad is big enough. At a relatively small discharge gap, the trans-formation occurs only when the avalanche reaches the anode. Such astreamer is known as the cathode-directed or positive streamer. If thedischarge gap and overvoltage are big enough, the avalanche-to-streamertransformation can take place quite far from anode. In this case the so-called anode-directed or negative streamer is able to grow toward the bothelectrodes.

The cathode-directed streamer starts near the anode. It looks like andoperates as a thin conductive needle growing from the anode. The electricfield at the tip of the ‘‘anode needle’’ is very high, which stimulates the faststreamer propagation in the direction of the cathode. Usually the streamerpropagation is limited by the neutralization of the ionic trail near the tip ofthe needle. The electric field there is so high that it provides electron driftwith velocity about 108 cm/s.

The anode-directed streamer occurs between electrodes, if the primaryavalanche becomes strong enough even before reaching the anode. Thestreamer propagates in the direction of the cathode in the same way ascathode-directed streamer. Mechanism of the streamer growth in the direc-tion of anode is also similar, but in this case the electrons from the primaryavalanche head neutralize the ionic trail of secondary avalanches. However,the secondary avalanches could be initiated here not only by photons, butalso by some electrons moving in front of the primary avalanche.

G. THE MEEK CRITERION OF STREAMER FORMATION

Formation of a streamer requires the electric field of space charge inavalanche Ea to be of the order of the external field E0

Ea ¼e

4p�0r2Aexp a

E0

p

� �x

� �� E0 (17)

Taking the avalanche head radius as the ionization length, i.e., raE1/a,the criterion of streamer formation in the gap with a distance d between


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electrodes can be presented as the requirement for the avalanche amplifi-cation parameter ad to exceed the critical value:

aE0

p

� �d ¼ ln

4p�0E0

ea2� 20; Ne ¼ expðadÞ � 3� 108 (18)

This fundamental and important criterion of the streamer formation isknown as the Meek’s breakdown condition (adX20).

Electron attachment processes in electronegative gases slow down theelectron multiplication in avalanches and increase the value of the electricfield required for a streamer formation. The situation here is similar to thecase of the Townsend breakdown mechanism. Actually the ionization co-efficient a in the Meek’s breakdown condition should be replaced in elec-tronegative gases by a–b. However, practically, when the discharge gaps arenot too big (i.e., in air d p15 cm) – the electric fields required by the Meekcriterion are relatively high, then acb and the attachment can be neglected.

Increasing d in electronegative gases does not lead to a gradual decrease ofthe electric field necessary for streamer formation, but it is limited by someminimum level. The minimal electric field required for streamer formationcan be found from the ionization-attachment balance a(E0/p) ¼ b(E0/p).

We should note that the electric field non-uniformity has a strong influ-ence on the breakdown conditions and an avalanche transformation into astreamer. Quite obviously, the non-uniformity decreases the breakdownvoltage for a given distance between electrodes.

H. THE STREAMER BREAKDOWN MECHANISM

Dawson [8] and Gallimberti [9] proposed a model of the propagation ofquasi-self-sustained streamers. This model assumes very low conductivity ofa streamer channel, which makes the streamer propagation autonomous andindependent from anode. Photons initiate avalanche at a distance x1 fromthe center of the positive charge zone of radius r0. According to the model,the avalanche then develops in the autonomous electric field of the positivespace charge EðxÞ ¼ eNþ=4p�0x2. The number of electrons is increasing byionization as:

Ne ¼Z x2

x1

aðEÞdx

whereas the avalanche radius grows due to diffusion as:

dr2

dt� 4De; rðx2Þ ¼

Z x2

x1

4De

meEðxÞdx

� �1=2(19)


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To provide continuous and steady propagation of the self-sustainedstreamer, its positive space charge N+ should be compensated by the nega-tive charge of avalanche head Ne ¼ N+ at the meeting point of the ava-lanche and streamer: x2 ¼ r0+r. Also the radii of the avalanche andstreamer should be correlated at this point r ¼ r0. All these equations permitto describe the streamer parameters including the propagation velocity,which can be found as x2 divided by the time of the avalanche displacementfrom x1 to x2. The model of the quasi-self-sustained streamer is helpful indescribing the breakdown of long gaps with high voltage and low averageelectric fields (see Fig. 3).

Klingbeil [10] and Lozansky [7] proposed a qualitatively different modelof streamer propagation. In contrast to the above approach, this modelconsiders the streamer channel as an ideal conductor connected to the an-ode. The ideally conducting streamer channel is considered in the frame-works of this model as an anode elongation in the direction of externalelectric field E0 with the shape of an ellipsoid of revolution.

According to the approach of the ideally conducting streamer, thestreamer propagation at each point of the ellipsoid is normal to its surface.The propagation velocity is equal to the electron drift velocity in the

FIG.3. Breakdown voltage in air at 50Hz: (1) rod-rod gap, (2) rod-plane gap.


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appropriate electric field. For calculation of the streamer growth velocity aconvenient formula for the maximum electric field Em at the tip of thestreamer with length l and radius r was proposed by Bazelyan [11]:

Em

E0¼ 3þ l

r

� �0:92

; 10o l

ro2000 (20)

The model of the ideally conducting streamer is in a reasonably goodagreement with experimental results.

I. THE LEADER BREAKDOWN MECHANISM

As discussed above, three processes lead to the spark (or streamer)breakdown mechanism: avalanche to streamer transition; the streamergrowth from anode to cathode; triggering of a return wave of intense ion-ization, which results in a spark formation. This breakdown mechanismsequence is not valid for very long gaps – particularly in electronegativegases (including air). It happens because the streamer channel conductivityis not high enough to transfer the anode potential close to the cathode andstimulates there the return wave of intense ionization and spark. In theelectronegative gases where the streamer channel conductivity is lower thiseffect is especially strong. Also in non-uniform electric fields, the streamerhead grows from strong to weak field region, which slows down its propa-gation. The streamers just stop in the long air gaps without reaching theopposite electrode.

Breakdown of gaps with multi-meter and kilometer long inter-electrodedistances is related to the formation and propagation of the leaders. Withrespect to streamer the leader is a highly ionized and highly conductiveplasma channel growing from the active electrode along the path preparedby the preceding streamers. High conductivity of the leaders makes themmore effective with respect to the streamers in transferring the anodepotential close to the cathode and stimulating there the return wave ofintense ionization and spark. Lighting is the most common natural pheno-mena connected to the leaders.

Heating effect of relatively short centimeter-long streamers is about 10Kwhile for meter-long channels it reaches 3000K near the active electrode.This heating together with a corresponding high level of non-equilibriumexcitation of atoms and molecules probably explains the transformation ofa streamer channel into the leader. The mentioned temperature 3000K isnot enough for sufficient thermal ionization of air, but this temperaturetogether with the elevated non-equilibrium excitation level is high enough


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for other mechanisms of the increase of electric conductivity in plasmachannel.

Thus Gallimberti [12] assumed the mechanism of streamer-to-leadertransition in air related to the thermal detachment of electrons from thenegative ions of oxygen, which are main products of electron attachment inthe electronegative gas. The effective destruction of these negative ions andas a result the compensation of electron attachment becomes possible iftemperature exceeds 1500K in dry air and 2000K in humid air. Such tem-peratures are available in the plasma channel and can provide the formationof the high-conductivity leader in the electronegative gas. Note that duringthe evolution of a streamer in air, the Joule heat is stored at first in thevibrational excitation of N2-molecules. While temperature of air is increas-ing, the VT-relaxation (VT-vibrational translational) grows up exponenti-ally providing the explosive heating of the plasma channel.

So far we have discussed only the general physical features and kinetics ofcharged species in avalanches, streamers and leaders. In the following sec-tions we will consider the role of the avalanches, streamers and leaders in thespecific discharge systems – in particular in corona, spark and dielectricbarrier discharges.

III. The Corona Discharge

A. OVERVIEW OF THE CORONA DISCHARGE

Corona is a weakly luminous discharge, which usually appears at atmos-pheric pressure near sharp points, edges or thin wires where the electric fieldis sufficiently large. Thus, corona discharges are always non-uniform: strongelectric field, ionization and luminosity are actually located in the vicinity ofone electrode. Charged particles are dragged by the weak electric fields fromone electrode to another to close an electric circuit. However at the initialstages of the breakdown, the circuit in the corona discharge is closed bydisplacement current rather than charged particle transport [13]. A coronacan be observed in air around high voltage transmission lines, aroundlightning rods, and even masts of ships, where they are called ‘‘Saint Elmo’sfire’’.

The corona discharge can be ignited with a relatively high voltage, whichmainly occupies the region around one electrode. If the voltage is increasedfurther, the remaining part of the discharge gap breaks down and the coronatransfers into the spark. Here we present only the main physical and engi-neering principals of the continuous corona discharge; more details on thesubject can be found in the publications of Loeb [14] and Goldman [15].


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B. NEGATIVE AND POSITIVE CORONAS

Mechanism for sustaining the continuous ionization level in a coronadepends on the polarity of electrode where the high electric field is located. Ifthe high electric field zone is located around the cathode, we call it negativecorona. If the high electric field is concentrated in the region of the anode,such a discharge is called the positive corona.

Continuity of electric current from the cathode into the plasma is pro-vided by secondary emission from the cathode (mostly induced by ion im-pact). Ignition of the negative corona actually has the same mechanism asthe Townsend breakdown, taking into account non-uniformity and possibleelectron attachment processes:Z xmax

0

½aðxÞ � bðxÞ�dx ¼ ln 1þ 1

g

� �(21)

In this equation a(x), b(x) and g are the first, second and third Townsendcoefficients, describing respectively ionization, electron attachment and sec-ondary electron emission from the cathode. The upper limit of the integra-tion xmax is the distance from the cathode, where the electric field becomeslow enough and a(xmax) ¼ b(xmax), which means that no additional electronmultiplication takes place. The equality a(xmax) ¼ b(xmax) actually corre-sponds to the breakdown electric field Ebreak in electronegative gases. If thegas is not electronegative (b ¼ 0), the integration of Eq. (21) is formally notlimited; however, due to the exponential decrease of the function a(x), aneffective value of xmax can be chosen to limit the integration in Eq. (21).

Note that the critical distance x ¼ xmax determines not only the ioniza-tion, but also the electronic excitation zone, and hence the zone of plasmaluminosity. This means that the critical distance x ¼ xmax can be consideredas the visible size of the corona.

Ionization in the positive corona cannot be provided by the cathodephenomena due to the low electric field at the cathode region. Here ion-ization processes are related to the formation of the cathode-directedstreamers. Ignition conditions can be described for the positive corona usingthe criteria of cathode-directed streamer formation. In this case, the gene-ralization of the Meek’s breakdown criterion Eq. (18) is a good approxi-mation, taking into account the non-uniformity of the corona and possiblecontributions of electron attachment:Z xmax

0

½aðxÞ � bðxÞ�dx � 18� 20 (22)

In comparison with similar ignition criteria Eqs. (21) and (22), the mini-mal values of the amplification coefficients should be 2–3 times lower to


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provide the ignition of a negative corona because ln(l+l/g)E6–8. However,the critical values of the electric field for the ignition of positive and negativecoronas are very close even though these are related to very differentbreakdown mechanisms. Also it was shown that critical values of the electricfield for negative corona ignition do not depend on electrode composition asthey should according to the Townsend breakdown mechanism [16]. Thiscan be explained by the strong exponential dependence of the amplificationcoefficients on the electric field value. Another possible explanation is rela-ted to the contribution of indirect ionization process such as metastables –metastables collisions to the amplification coefficients [16].

C. IGNITION CRITERION FOR CORONA IN AIR

According to Eqs. (21) and (22), the ignition for both positive and nega-tive coronas is mostly determined by the value of the maximum electric fieldin the vicinity of the electrode, where the discharge is to be initiated. Thecritical value of the igniting electric field for the case of coaxial electrodes inair can be calculated numerically using the empirical Peek formula:

Ecr;kV

cm¼ 31d 1þ 0:308ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

d rðcmÞp

!(23)

where d is the ratio of air density to that one corresponding to standardconditions (atmospheric pressure, room temperature); and r is the radius ofinternal electrode. The formula can be applied for pressures 0.1–10 atm,polished internal electrodes with radius rE0.01–1 cm, with both direct cur-rent and AC with frequencies up to 1 kHz. Roughness of the electrodesdecreases the critical electric field by 10–20%.

Although the Peek formula was obtained for the case of coaxial cylindersit can be used also for other corona configurations with slightly differentvalues of coefficients. As an example, the critical corona-initiating electricfield in the case of two parallel wires can be determined using the followingempirical formula:

Ecr;kV

cm¼ 30d 1þ 0:301ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

d rðcmÞp

!(24)

Both Eqs. (23) and (24) correspond to simplified empirical formula for theTownsend coefficient a in air at reduced electric fields E/po150V/(cm �Torr):

a;1

cm¼ 0:14 � d E; kV=cm

31d

� �2

� 1

" #(25)


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Equations (23) and (24) determine the critical value of the corona electricfield. The critical value of electric field is supposed to be reached in the closevicinity of an active electrode.

D. ACTIVE CORONA VOLUME

Ionization of charged particles takes place in corona discharges only inthe vicinity of an electrode where electric field is sufficiently high. This zoneis usually referred to as the active corona volume (see Fig. 4). From thepoint of view of plasma-chemical applications the active corona volume isthe most important part of the discharge because most excitation and re-action processes take place in this zone. External radius of the active coronavolume is determined by the value of the electric field corresponding to thebreakdown value Ebreak on the boundary of the active volume.

The minimum value of voltage required for corona ignition in air (at nor-mal conditions) between a thin wire electrode of radius r ¼ 0.1 cm and co-axial cylinder external electrode with radius R ¼ 10 cm is about 30kV. At thesame time, the electric field near the external electrode is relatively very lowE(R)E0.6 kV/cm, E(R)/pE0.8V/(cm �Torr), and obviously not sufficient forionization. Effective multiplication of charges requires the electric field, whichcan be estimated as EbreakE25kV/cm. This determines the external radius of

Outer GroundedElectrode

Active Volume

Inner PoweredElectrode

rAC

FIG.4. Illustration of active corona volume.


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the active corona volume case as rAC ¼ rEcr/EbreakE0.25 cm. Hence theactive corona volume occupies the cylindrical layer 0.1 cmoxo0.25 cmaround the thin wire.

In general, the external radius of the active corona volume around thethin wire can be determined as:

rAC ¼ V

Ebreak lnðR=rÞ(26)

where V is the voltage applied to sustain the corona discharge. As is seenfrom Eq. (26), the radius of active corona volume is increasing with theapplied voltage.

Similar to Eq. (26), the external radius of the active corona volume gene-rated around a sharp point can be expressed as:

rAC �ffiffiffiffiffiffiffiffiffiffiffiffirV

Ebreak

r(27)

Based on Eqs. (26) and (27), one can compare the active radii of the coronaaround a thin wire and a sharp point:

rACðwireÞrACðpointÞ

� 1

lnðR=rÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiV

rEbreak

r¼ rACðpointÞ

r lnðR=rÞ (28)

Numerically this ratio is typically about three, which illustrates the advan-tage of corona generated around a thin wire, if one wants to produce alarger volume of non-thermal atmospheric pressure plasma effective fordifferent applications.

E. INFLUENCE OF SPACE CHARGE ON ELECTRIC FIELD IN CORONA

Charged particles are produced only in the active corona volume in thevicinity of an electrode. Thus, the electric current to the external electrodeoutside of the active volume is provided by the drift of charged particles(generated in the active volume) in the relatively low electric field. In thepositive corona, these drifting particles are positive ions, whereas in thenegative corona, these are negative ions (or electrons, if corona is generatedin non-electronegative gas mixtures).

The discharge current is determined by the difference between the appliedvoltage V and the critical one Vcr corresponding to the critical electric fieldEcr, and its value is limited by the space charge outside of the active coronavolume. The current of charged particles is partially reflected back by thespace charge formed by these particles. The phenomenon is somewhat


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similar to the phenomenon of current limitation by space charge in sheathes,or in vacuum diodes. However in the case under consideration, the motionof charged particles is not collisionless, but is determined by the drift inelectric field.

The electric current per unit length of the wire i in the corona generatedbetween coaxial cylinders with radii R and r is constant outside of the activecorona volume (where there is no charge multiplication):

i ¼ 2pxenmE ¼ const (29)

Here x is the distance from the corona axis (i.e., along the radial direc-tion); n is the number density of charged particles providing electric con-ductivity outside of the active volume; m is the mobility of the chargedparticles. Assuming the space charge perturbation of the electric field is notvery strong, the number density distribution n(x) can be found in the firstapproximation based on Eq. (29) and non-perturbed electric field distribu-tion:

nðxÞ ¼ i

2pemEx¼ i lnðR=rÞ

2pemV¼ const (30)

Using Maxwell equation for the case of cylindrical symmetry and Eq. (30)one can find the second approximation of the electric field distribution E(x):

1

x

d½xEðxÞ�dx

¼ 1

�0enðxÞ; 1

x

d½xEðxÞ�dx

¼ i lnðR=rÞ2p�0mV

(31)

Integration of the Maxwell equation yields the electric field distribution,which takes into account current and, hence, the space charge as:

EðxÞ ¼ Vcr lnðR=rÞx

þ i lnðR=rÞ2p�0mV

x2 � r2

2x

� �(32)

Equation (32) is valid only in the case of small electric field perturbationsdue to the space charge outside of the active corona volume. Expressionssimilar to Eq. (32), describing the influence of electric current and spacecharge on the electric field distribution could be derived for other coronaconfigurations (see [17]).

F. CURRENT-VOLTAGE CHARACTERISTICS OF A CORONA DISCHARGE

Integration of Eq. (32) over the radius x taking into account that in mostof the corona discharge gap x2cr2, gives the relation between current (per


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unit length) and voltage of the discharge, which is the current-voltage char-acteristic of corona generated around a thin wire:

i ¼ 4p�0mVðV � VcrÞR2 lnðR=rÞ (33)

From this equation, one can see that corona current depends on the mo-bility of the main charge particles providing conductivity outside of the activecorona volume. Since mobilities of positive and negative ions are nearlyequal, the electric currents in positive and negative corona discharges are alsoclose. Negative corona in gases without electron attachment (e.g., noblegases) provides much larger currents because electrons are able to rapidlyleave the discharge gap without forming a significant space charge. Even asmall admixture of an electro-negative gas decreases the corona current.

It is important to mention that the parabolic current-voltage character-istic Eq. (33) is valid not only for thin wires, but for other corona configu-rations. Thus, the coefficients before the quadratic form V(V�Vcr) aredifferent for different geometries of corona discharges (Note I is the totalcurrent in the corona discharge):

I ¼ CVðV � VcrÞ (34)

The current-voltage characteristics for the corona generated in atmos-pheric air between a sharp point cathode with radius r ¼ 3–50 mm anda perpendicular flat anode located at a distance of d ¼ 4–16mm can beexpressed as:

I ;mA ¼ 52

ðd;mmÞ2 ðV ; kVÞðV � VcrÞ (35)

In this empirical relation I is the total corona current from the sharp pointcathode. The critical corona ignition voltage Vcr in this case can be taken as2.3 kV and does not depend on the distance d [15].

G. POWER RELEASED IN A CONTINUOUS CORONA DISCHARGE

Based on the current-voltage characteristics, Eq. (33), the electric powerreleased in the continuous corona discharge can be determined for the caseof a long thin wire with length L as:

P ¼ 4pL�0mV2ðV � VcrÞR2 lnðR=rÞ (36)


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In general cases the corona discharge power can be determined based onEq. (34) as:

P ¼ CV2ðV � VcrÞ (37)

For example, corona discharges generated in atmospheric pressure airaround the thin wire (r ¼ 0.1 cm, R ¼ 10 cm, Vcr ¼ 30 kV) with voltage40 kV release a power of about 0.2W/cm.

The power of the continuous corona discharges is very low and notacceptable for many applications. A further increase of voltage and currentleads to corona transition into sparks. However, sparks can be prevented byorganizing the corona discharge in a pulse-periodic mode. Such pulsedcorona discharges will be discussed in the next section. Although the coronapower per unit length of a wire is relatively low, the total corona powerbecomes significant when the wire is very long. Such situations takes place inthe case of high voltage overland transmission lines, where coronal lossesare significant. In humid and snow conditions, these can often exceed theresistive losses. The two wires generate corona discharges of oppositepolarity. Electric currents outside of active volumes of the opposite polaritycorona discharges are provided by positive and negative ions moving inopposite directions. These positive and negative ions meet and neutralizeeach other between the wires, a phenomenon which results in a decrease ofthe space charge and an increase of the corona current leading to pheno-menal power losses.

IV. Pulsed Corona Discharge

A. OVERVIEW OF PULSED CORONA DISCHARGES

Corona discharges are very attractive for various modern industrial appli-cations such as surface treatment and cleaning of gas and liquid exhauststreams. These discharges are able to generate a high concentration of activeatoms and radicals at atmospheric pressure without heating gas volume.

As was shown previously, the application of the continuous corona dis-charge is limited by very low currents and, hence, very low power of thedischarge, resulting in a low rate of the treatment of materials and exhauststreams.

It is possible to increase both corona voltage and power without sparkformation by using pulse-periodic voltages. Nowadays, the pulsed corona isone of the most promising atmospheric pressure, non-thermal discharges.The streamer velocity is about 108 cm/s and exceeds by a factor of 10 thetypical electron drift velocity in an avalanche. If the distance between


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electrodes is about 1–3 cm, the total time necessary for development ofavalanches, avalanche-to-streamer transition and streamer propagationbetween electrodes is about 100–300 ns. This means that voltage pulses ofthis duration range are able to sustain streamers and effective power transferinto non-thermal plasma without streamer transformations into sparks.

For the pulsed corona discharges the key point is to make pulse powersupplies, capable of generating sufficiently short voltage pulses with steepfront and very short rise time. Some specific methods of generation andparameters for the pulsed corona discharges will be discussed later in thissection. First let us discuss some important non-steady-state phenomenaoccurring in the continuous corona discharges, which should be taken intoaccount in analyzing pulsed corona discharges.

B. CORONA IGNITION DELAY

Since the ignition of the negative corona has the same mechanism as theTownsend breakdown, the ignition delay of the continuous negative coronastrongly depends on cathode conditions and varies from one experiment toanother. Such facility-specific characteristics are one of the reasons whypulsed coronas are more often organized as positive ones. Typical ignitiondelay in the case of positive corona is about 100 ns and in contrast with thenegative corona is not sensitive to the cathode conditions, because streamerbreakdown mechanism is responsible for the ignition. The ignition delay ismuch longer than streamer propagation time, because it is related to thetime for the formation of initial electrons and the propagation of initialavalanches.

Random electrons in the atmosphere usually exist in the form of negativeions, their effective detachment is due to ion-neutral collisions and effec-tively takes place at electric fields of about 70 kV/cm. If humidity is high andthe negative ions are hydrated, the electric field necessary for detachmentand formation of a free electron is slightly higher.

Thus experimental data related to the ignition delay of the continuouscorona actually indicate the same limits for pulse duration in pulsed coronadischarges. This means that there are some advantages of the positive coro-na and the cathode-directed streamers with respect to the negative corona.

C. FLASHING CORONA

Corona discharges sometimes operate in the form of periodic current pulseseven at constant voltage conditions. Frequency of these pulses can reach104Hz in the case of positive corona and 106Hz for negative corona, res-pectively. This self-organized pulsed corona discharge is obviously unable to


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overcome the current and power limitations of the continuous corona dis-charges because a continuous high voltage still promotes the corona-to-sparktransition. However, it is an important step toward non-steady-state coronaswith higher voltage, higher current and higher power.

The flashing positive corona phenomenon can be explained by the effect ofpositive space charge, which is created when electrons formed in streamers fastat the anode but slow positive ions remain in the discharge gap. The growingpositive space charge decreases the electric field near the anode and preventsthe generation of new streamers. Positive corona current is suppressed untilthe positive space charge goes to the cathode and clears up the discharge gap.After that a new corona ignition takes place and the cycle is repeated again.

The flashing corona phenomenon does not occur at intermediate voltageswhen the electric field outside of the active corona volume is sufficiently highto provide effective steady-state clearance of positive ions from the dis-charge gap but not too high to provide an intensive ionization. It is interest-ing to note that the electric current in the flashing corona regime does notfall to zero between pulses, and some constant component of the coronacurrent is continuously present.

The pulse-periodic regime leads to a fundamental increase of coronapower. However, the power increase in this system is still limited by sparkformation because the applied voltage is continuous.

D. TRICHEL PULSES

Negative corona discharges sustained by a continuous voltage also canoperate in a pulse-periodic regime at a relatively low value of voltage closeto the ignition value. The pulse duration in the negative corona is short,approximately 100 ns. If the mean corona current is 20 mA, the peak value ofthe current in each pulse can reach 10mA. The pulses disappear at highervoltages, and in contrast to the case of the positive corona the steady-statedischarge exists till transition to spark.

The pulse-periodic regime of the negative corona discharge is usually refer-red to as Trichel pulses, which are similar to those of the flashing coronadiscussed above, though with some peculiarities. The growth of avalanchesfrom cathode leads to the formation of two charged layers: (a) an internalone which is positive and consists of positive ions; (b) an external one whichis negative and consists of either negative ions (in air or other electronegativegases) or electrons in the case of electropositive gases.

The Trichel pulses are not generated in electropositive gases. Because ofthe high mobility of electrons, they reach an anode quite fast. As a result,the density of the space charge of electrons in the external layer is very lowand the electric field near the cathode is not suppressed. The positively


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charged internal layer even increases the electric field in the vicinity of thecathode and provides even better conditions for the active corona volume.Thus, only electronegative gases may sustain the Trichel pulses.

The negative ions in electronegative gases form a significant negative spacecharge around the cathode, which cannot be compensated by a narrow layer ofpositive ions. Thus, the space charge of the negative ions suppresses the electricfield near the cathode and, hence, suppresses the corona current. Subsequently,when the ions leave the discharge gap and are neutralized on the electrodes, thenegative corona can be reignited, and the cycle again can be repeated.

E. PULSED CORONA DISCHARGES SUSTAINED BY NANO-SECOND PULSE

POWER SUPPLIES

Pulsed corona discharge sustained by nano-second pulse power suppliesgenerates pulses with a duration in the range of 100–300ns, which is suffi-ciently short to avoid the corona-to-spark transition. The power supply shouldprovide a high voltage rise rate (0.5–3kV/ns), which results in higher coronaignition voltage and higher power. As an illustration of this effect, Fig. 5shows the corona inception voltage as a function of the voltage rise rate [18].

Co

ron

a In

cep

tio

n V

olt

age

[kV

]

Voltage Raise Rate [kV/ ns]0 1 2 3 4 5

0

30

60

90

120

FIG.5. Corona inception voltage as a function of the voltage rise rate.


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The high voltage rise rates also result in better efficiency of several plasma-chemical processes requiring higher electron energies. In these plasma-chemical processes (i.e., plasma cleaning of gas and liquid steams) highvalues of mean electron energy are necessary to decrease the fraction of thedischarge power consumed to the vibrational excitation of molecules, and tostimulate ionization and electronic excitation and dissociation of molecules.

The nano-second pulse power supply technology is used in different ap-plications such as Marx generators, simple and rotating spark gaps, elec-tronic lamps, thyratrones and thyristors with possible further magneticcompression of pulses (see, for example, [19]) and transistors for the highvoltage pulse generation.

In general, the pulsed corona can be relatively powerful, luminous andquite nice looking. More information about the physical aspects and ap-plications of the pulsed corona discharge can be found elsewhere [18,20,21].An example of practical application of the pulsed corona discharge is a pilotplant for treatment of volatile organic compound (VOC) emissions in thepaper industry developed by the Drexel Plasma Institute (see Fig. 6).

F. CONFIGURATIONS OF PULSED CORONA DISCHARGES

Most typical configurations of the pulsed corona as well as continuouscorona discharges are based on using thin wires, which maximize the activedischarge volume. One of these configurations is illustrated in Fig. 7. Lim-itations of the wire configuration of the corona are related to the durabilityof the electrodes and also to the non-optimal interaction of discharge vol-ume with incoming gas flow, a phenomenon which is important for theplasma-chemical applications.

From this point of view, it is useful to use another corona dischargeconfiguration based on multiple stages of pin-to-plate electrodes [22]. Thissystem is obviously more durable and it is able to provide a good interaction

FIG.6. Large-volume, atmospheric pressure pulsed discharge plasma for treating volatile

organic compound (VOC) emissions. Left picture: discharge operation at 4 kW. Right picture:

overview of the discharge system pilot plant.


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of the incoming gas stream with the active corona volume formed betweenthe electrodes with pins and holes.

Combination of pulsed corona discharges with other methods of gastreatment is very practical for many different applications. For example, thepulse corona was successfully combined with catalysis to achieve improvedresults in the plasma treatment of automotive exhausts [17] and for hydro-gen production from heavy hydrocarbons [23].

Another interesting technological hybrid application is related to thepulsed corona coupled with water flow. Such a system can be arrangedeither in a form of shower, which is called the spray corona or in a thinwater film on walls, which is usually referred to as the wet corona (seeFig. 8). Such plasma scrubbers are especially effective in air cleaning proc-esses, where plasma just converts a non-soluble pollutant into a soluble one.

WIRE ELECTRODETHERMOCOUPLE

THERMOCOUPLE

FUR

NA

CEFU

RN

AC

E

FIG.7. Pulsed corona discharge in wire-cylinder configuration with preheating.


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V. Dielectric-Barrier Discharge

A. OVERVIEW OF DIELECTRIC BARRIER DISCHARGES

As was discussed before, a corona-to-spark transition can be prevented inpulsed corona discharges by employing nano-second pulse power supplies.There is also another approach helping to avoid the spark formation in astreamer channel. This approach is based on the use of a dielectric barrier inthe discharge gap that stops electric current and prevents spark formation.Such a discharge system is called a dielectric barrier discharge (DBD). Thepresence of a dielectric barrier precludes a DC operation of the DBD, whichusually operates at frequencies between 0.05 and 500 kHz. Sometimesdielectric barrier discharges are also called silent discharges due to theabsence of sparks, which are accompanied by local overheating, generationof local shock waves and noise.

The DBDs have a large number of industrial applications because theyoperate at strongly non-equilibrium conditions at atmospheric pressure andat reasonably high power levels without using sophisticated pulse powersupplies. This discharge is industrially applied in ozone generation, CO2

lasers, and as a UV-source in excimer lamps. In addition, the DBD in air iscommonly used in the polymer web modification where it is known com-mercially as ‘‘corona discharge treatment.’’ It is used to treat polymer sur-faces in order to promote wettability, printability and adhesion [24]. Thisnon-equilibrium discharge is especially advantageous for the web conversionindustry because it operates at atmospheric pressure and ambient temper-ature. The use of the so-called ‘‘corona treatment’’ as well as other varioussurface modification methods for the manufacture of many different typesof products on moving webs is extensively described in the literature [25].

b)

WATER INJECTION NOZZLES

WATER SPRAY

THERMOCOUPLE

a)

WATER INJECTION NOZZLE

O- RING

WATER FILM

THERMOCOUPLE

FIG.8. Modification of corona discharge shown in Fig. 7: wet (a) and spray (b) corona

discharges.


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DBD application for pollution control is quite promising, but the largestexpected DBD application is related to plasma display panels for large-areaflat television screens. Strong thermodynamic non-equilibrium and simpledesign are the distinctive properties of DBD, which permit the expansion ofits applications to low temperature atmospheric pressure plasma chemistry.DBD has a big potential to be a prospective technology of exhaust cleaningfrom CO, NOx and volatile organic compounds [26]. Successful use of DBDreported in a recent research on plasma-assisted combustion may result innew applications [27].

Important contributions in fundamental understanding and industrialapplications of DBD were made recently by Kogelschatzs, Eliasson andtheir group at ABB [28]. However, this discharge actually has a long history.It was first introduced by Siemens in 1857 to create ozone which determinedthe main direction for investigations and applications of this discharge formany decades to come [29]. Important steps in understanding the physicalnature of the DBD were made by Klemenc in 1937 [30]. Their work showedthat this discharge includes a number of individual tiny breakdown chan-nels, which are now referred to as microdischarges and whose relationshipwith streamers are intensively investigated.

B. PROPERTIES OF DIELECTRIC BARRIER DISCHARGES

The dielectric barrier discharge gap usually includes one or more dielectriclayers, which are located in the current path between metal electrodes. Twospecific DBD configurations, planar and cylindrical, are illustrated in Fig. 9[31]. Typical clearance in the discharge gaps varies from 0.1mm to severalcentimeters.

High VoltageElectrode

DielectricBarrier

GroundElectrode

HighVoltage

ACGenerator

DielectricBarrier

DischargeGap

GroundElectrode

FIG.9. Common dielectric-barrier discharge configurations [31].


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Breakdown voltages of these gaps with dielectric barriers are practicallythe same as those between the metal electrodes. If the dielectric barrierdischarge gap is a few millimeters, the required AC driving voltage with afrequency in a range of 500�500 kHz is typically about 10 kV at atmos-pheric pressure.

The dielectric barrier can be made from glass, quartz, ceramics or othermaterials of low dielectric loss and high breakdown strength. Then a metalelectrode coating can be applied to the dielectric barrier. The barrier–elec-trode combination also can be arranged in the opposite manner, e.g., metalelectrodes can be coated by a dielectric material. As an example, steel tubescoated by an enamel layer can be effectively used in the dielectric barrierdischarge.

In most cases, dielectric barrier discharges are not uniform and consist ofnumerous microdischarges distributed in the discharge gap as can be seenfrom Fig. 10. The physics of microdischarges is based on an understanding

FIG.10. The storage phosphor image of filaments in the dielectric barrier discharge gap in

air obtained from experimental setup using 10 excitation cycles at 20.9 kHz and a discharge gap

of 0.762mm, discharge area is 5 cm� 5 cm.


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of the formation and propagation of streamers, and subsequent plasmachannel degradation. The electrons in the conducting plasma channelestablished by the streamers dissipate from the gap in about 40 ns, while theheavy and slowly drifting ions remain in the discharge gap for several micro-seconds (see Tables III and IV). Deposition of electrons from the conductingchannel onto the anode dielectric barrier results in charge accumulation andprevents new avalanches and streamers nearby until the cathode and anodeare reversed (if applied voltage is not much higher than voltage necessary forbreakdown). The usual operation frequency used in the dielectric barrierdischarges is around 20 kHz, therefore the voltage polarity reversal occurswithin 25 ms. After the voltage polarity reverses, the deposited negativecharge facilitates the formation of new avalanches and streamers in the samespot. As a result, a many-generation family of streamers is formed that ismacroscopically observed as a bright filament that appears to be spatiallylocalized.

It is important to clarify and distinguish terms streamer and micro-discharge. An initial electron starting from some point in the discharge gap(or from the cathode or dielectric that cover the cathode in the case of awell-developed DBD) produces secondary electrons by direct ionization and

TABLE IV

CALCULATED MICRODISCHARGE CHARACTERISTICS FOR DBD (1MM GAP, AIR, 1 ATM.)

Duration time Charge transferred

DBD Microdischarge (0.2mm radius) 40 ns 10�9 C

� Electron avalanche 10 ns 10�11C

� Cathode directed streamer 1 ns 10�10C

� Plasma channel 30 ns 10�9C

DBD microdischarge remnant 1ms Z10�9C

TABLE III

TYPICAL PARAMETERS OF A DBD MICRODISCHARGE

Streamer lifetime 1–20 ns Filament radius 50–100mmPeak current 0.1A Current density 0.1–1 kA/cm2

Electron density 1014–1015 cm�3 Electron energy 1–10 eV

Total transported

charge

0.1–1 nC Reduced electric

field

E/n ¼ (1–2)(E/

n)PaschenTotal dissipated

energy

5 mJ Gas temperature Close to average,

about 300K

Overheating 5K


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develops an electron avalanche. If the avalanche is big enough (the Meekcondition), then the cathode-directed streamer is initiated (usually from theanode region). Streamer bridges the gap in few nanoseconds and forms aconducting channel of weakly ionized plasma. Intensive electron current willflow through this plasma channel until the local electric field is collapsed.The collapse of the local electric field is caused by the charges accumulatedon dielectric surface and the ionic space charge (note that ions are too slowto leave the gap for the duration of this current peak). Group of localprocesses in the discharge gap initiated by avalanche and developed untilelectron current termination usually called a microdischarge.

After electron current termination there is no more electron-ion plasma inthe main part of a microdischarge channel. However, high level of vibra-tional and electronic excitations in channel volume along with charges depo-sited on the surface and ionic charges in the volume allow us to separate thisregion from the rest of the volume and call it microdischarge remnant.Positive ions (or positive and negative ions in the case of electronegative gas)of the remnant slowly move to electrodes resulting in low and very long(� 10 ms for 1mm gap) falling ion current. The microdischarge remnant willfacilitate the formation of a new microdischarge in the same spot as thepolarity of the applied voltage changes. That is why it is possible to seesingle filaments in DBD. If microdischarges would form at a new spot eachtime the polarity changes, the discharge would appear uniform. Thus fila-ment in DBD is a group of microdischarges that forms on the same spoteach time when the polarity is changed. The fact that microdischarge rem-nant is not fully dissipated before the formation of next microdischarge iscalled a memory effect.

Typical characteristics of the DBD microdischarges in a 1-mm gap inatmospheric air are summarized in Table III.

The snapshot of the microdischarges in a 0.762mm DBD air gap pho-tographed with the help of storage phosphor on one electrode is shown inFig. 10. As seen in the figure, the microdischarges are spread over the wholeDBD zone quite uniformly.

Charge accumulation on the surface of the dielectric barrier reduces theelectric field at the location of a microdischarge, resulting in current termi-nation within just several nanoseconds after breakdown (see Table III). Theshort duration of microdischarges leads to very low overheating of thestreamer channel, and the DBD plasma remains strongly non-thermal.

The principal properties of a microdischarge for most of frequencies donot depend on the characteristics of the external circuit, but only on the gascomposition, pressure and the electrode configuration. An increase of powerjust leads to the generation of a larger number of microdischarges per unittime, which simplifies scaling of the dielectric barrier discharges.


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Modeling of the microdischarges is closely related to the analysis of theavalanche-to-streamer transition and streamer propagation. Detailed two-dimensional modeling of the formation and propagation of relevant stream-ers can be found in numerous publications [32–36].

Interesting phenomena can occur due to the mutual influence of micro-discharges in a DBD. These are related to the electrical interaction of mi-crodischarges with residual charges left on the dielectric barrier and with theinfluence of excited species generated in one microdischarge on the forma-tion of another microdischarge [37].

C. PHENOMENA OF MICRODISCHARGE INTERACTION: PATTERN FORMATION

Although DBDs have been intensively studied for the past century, themicrodischarge interaction was discovered only recently [35]. This interac-tion is responsible for the formation of microdischarge patterns reminiscentof two-dimensional crystals (Fig. 10). Depending on the application, mi-crodischarge patterns may have a significant influence on DBD performanceparticularly when spatial uniformity is required.

The formation of microdischarges in DBD was discussed in the previoussection. The charge distribution associated with streamers and the localelectric field in the gap associated with plasma channel and microdischargeremnant are illustrated in Fig. 11. The left side of Fig. 11 shows a streamer

FIG.11. Illustration of electric field distortion caused by microdischarge remnant. Streamer

formation (left side) and plasma channel (and microdischarge remnant) electric field distortion

(right side) is due to space charges. The solid curve is the superposition of the electric field from

the microdischarge and the applied electric field. In presence of a space positive charge, the

electric field is increased at cathode and decreased at the anode.


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propagating from the anode to the cathode while attracting additionalavalanches. The resulting plasma channel and microdischarge remnant thatforms, shown on the right side of the figure, have a net positive chargebecause the electrons leave the gap much faster than ions. The residualpositive charge (together with the deposited negative charge in the case ofdielectric surface) influences the formation of nearby families of avalanchesand streamers and, therefore, the formation of neighboring microdischarges.The mechanism of the influence is the following: positive charge (or dipolefield in the case of deposited negative charge) intensifies the electric field inthe cathode area of the neighboring microdischarge and decreases the elec-tric field in the anode area. Since the avalanche-to-streamer transitiondepends mostly on the near-anode electric field (from which new streamersoriginate), the formation of neighboring microdischarges is actually preven-ted, and microdischarges effectively repel each other. The quasi-repulsionbetween microdischarges leads to the formation of short-range order thatis related to a characteristic repulsion distance between microdischarges.Observation of this cooperative phenomenon depends on several factors,including the number of the microdischarges occurring and the operatingfrequency. For example, when the number of microdischarges is not largeenough (when the average distance between microdischarges is larger than acharacteristic interaction radius), no significant microdischarge interactionis observed. When the AC frequency is too low to keep the microdischargeremnants from dissipation (note that low frequency means that period islonger than the typical life time of microdischarge remnant or ‘‘memoryeffect’’ lifetime) microdischarge repulsion effects are not observed.

In addition, DBD cells operated at very high frequencies in the mega-hertz region will not exhibit microdischarge repulsion because the very highfrequency switching of the voltage interferes with ions still moving to elec-trodes (see [28,29] for detailed explanation of ion trapping effect andestimation of frequency at which it becomes significant). Formation ofmicrodischarge pattern in DBD was investigated both from theoretical andexperimental perspective [38].

The experimental image shown in Fig. 10 suggests that filaments (micro-discharge families) space themselves out. To model the interaction betweenmicrodischarges, it can be assumed that an avalanche-to-streamer transitiondepends only on the local value of the electric field and the discharge gap.Once the microdischarge is formed, the electric field of the microdischargeremnant decreases the external applied electric field in the fashion describedabove. The average effective field in the local region near the anode wherethe avalanche-to-streamer transition occurs decreases and, as a conse-quence, the formation of new streamers at the same location is preventedunless there is an increase in the external applied voltage. We should


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emphasize that the observation of microdischarge filaments in DBD is possi-ble when both electrodes are covered by dielectric materials as well as in thecase when one electrode is not covered, meaning that no surface dischargecan be deposited on this electrode. Thus, the repetition of microdischargesat the same spot depends on the volume charge mostly, and the surfacecharge deposition is not critical. When the externally applied field variesquickly with respect to the microdischarge remnant dissipation lifetime inthe system, the microdischarges will stay separated by a distance corre-sponding to the length scale of the field inhomogeneity. If the applied elec-tric field is high enough, it will cause microdischarges to be developed ineach unoccupied space so that the gap becomes filled from end to end.

In the unipolar or DC case (i.e., before polarity changes), one of theelectrodes remains positive and the other is negative. The streamer alwaysmoves in one direction so that subsequent streamers and thus micro-discharges have a small probability of forming in the same place until themicrodischarge remnant has dispersed. A different situation appears in thecase of alternating voltage. There is no need to wait until the micro-discharges remnant dissipates. Instead, the probability of appearance of astreamer in the location of the microdischarges remnant increases when thevoltage is switched. After the voltage is switched, the electric field of themicrodischarge remnant adds to the strength of the applied electric fieldthereby increasing the local field. The increased electric field increases thelikelihood for a new streamer to occur at the same place. The net result isthat if the original streamer is formed just before voltage switching, there isan increased probability of streamers occurring in the same place or nearestvicinity. The remainder of this section describes the Monte-Carlo approachthat is useful for the simulation of microdischarge interactions.

The general cellular automata (CA) scheme consists of a lattice of cellsthat can have any dimension and size coupled with a set of rules for deter-mining the state of the cells. At any time a cell can be in only one state.From a physical perspective, each cell represents a volume in the gap locatedbetween the electrode surfaces. The upper and lower surfaces of each cell arebounded by the dielectric surfaces of the electrodes themselves, and theheight of each cell is defined by the gap distance. The CA transformationrules define a new state for a cell after a given time step, using data aboutthe states of all the cells in the CA and additional information, such as thedriving voltages imposed upon the system as a whole. It is assumed thatthe probability for the occurrence of the streamer depends only on the localvalue of the electric field. The position of a streamer strike is determinedusing a Monte-Carlo decision for given probability values in each cell. Oncethe position of streamer strike is known a plasma channel is formed at thesame place and the total charge transferred by this microdischarge is


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assigned to the cell to be used later in electric field calculations. Since thetime lag between streamers is random, an additional Monte-Carlo simula-tion can be used to decide whether a streamer will occur or not. If streamerwill not strike the plasma channel will not be formed and there will be nomicrodischarge.

It is not necessary to specify the charge transferred by the microdischarge.Instead, it can be dynamically calculated during simulation based on the localelectric field strength. The charge transferred by an individual microdischargedecreases the electric field inside the microdischarge channel because it cre-ates a local electric field opposing the externally applied electric field (i.e., thecollapse of electric field in microdischarge channel). Thus, the total chargetransferred by the microdischarge is the amount of charge that decreases thelocal electric field to zero. In other words, charge passes through the micro-discharge channel established in a CA cell until the local electric field drops tozero. Although it seems not be the case especially in electronegative gases,where electric field does not collapse to zero, this assumption is good enoughto represent the interaction between microdischarges.

The probability of a streamer striking is calculated from the local electricfield by the following formula:

PðEÞ ¼ 1� 1

1þ exp SE � E0

E0

� � (38)

where E is the electric field in the cell, E0 is the critical electric field necessaryfor the streamer formation given by the Meek condition, and S is a para-meter related to the ability of the discharge to accumulate the memory aboutprevious microdischarges. When S is large, the memory effect has a neg-ligible influence on the operation of DBD, and the probability function willbe a step function that represents the Meek condition for the streamerformation. When S is small, the memory effect significantly affects theprobability of streamer formation. The streamer formation is influenced bya number of factors. The presence of the vibrationally and electronicallyexcited species and negative ions increase ionization coefficient (i.e., the firstTownsend coefficient) and thus lower the electric filed required for ava-lanche-to-streamer transition. Furthermore, the discharge operating fre-quency also influences the streamer formation so that the memory effect isfrequency dependent. The value of S can be determined empirically fromexperimental data.

The typical results of the simulation can be seen in Fig. 12. The grayscale intensity at any particular cell is proportional to the number ofstreamers striking the cell. The simulation shows that the occurrence of


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microdischarges across the simulation lattice is non-uniform: some regionsare well treated by microdischarges whereas some are not treated at all. Thisnon-uniformity is the result of interactions between the microdischarges.Some calculated characteristics of the DBD microdischarges are presentedin Table IV. Simulation results for an image analysis were post-processedfor better comparison with experimental images. The intensity of a micro-discharge feature in a cell is given by the simulation, and the location of themicrodischarge is assumed to be at the center point of the cell. The size ofeach circular microdischarge feature is taken as the theoretically calculateddiameter of the plasma channel. This information was used to construct adigital image with a pixel size equivalent to that in the experimental images.

Experimental results as well as theoretical ones derived from the probabi-listic models are images with features that correspond to microdischarges. Itis natural, then, to consider image analysis methods as a technique to makecomparisons. Although there are many possible methods that could be

FIG.12. Enlarged central portion of simulated microdischarge pattern in DBD. Simulation

conditions are the same as for experimental image in Fig. 10. The size of the microdischarge

footprint is the same as in Fig. 10.


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employed for this purpose, the two-dimensional correlation function and theVoronoi polyhedron approach proved to be the most useful.

Voronoi polyhedra analysis defines polyhedral cells around selected fea-tures in an image, and the distribution of polyhedra types in the analysis canbe used as a comparative tool. Voronoi polyhedra analysis is the excellenttool for measuring the homogeneity of patterns as well as for comparison ofdifferent patterns. Homogeneity can be easily estimated from distributions ofthe Voronoi cell surface areas and used for comparison. Also the topo-logy of the pattern can be compared using distribution of the number of sidesof Voronoi cells. This type of comparison is extremely useful in this case as itis invariant to stretching and rotation of the patterns, and also invariant tothe particular positions of the microdischarge footprints. Although micro-discharge patterns were never analyzed before using Voronoi polyhedra thistype of analysis is a standard for analysis of Coulomb crystals. The Voronoipolyhedra analysis of an experimental image and its simulation are shown inFigs. 13 and 14, respectively. The Voronoi analysis of a random dot patternis shown in Fig. 15 (the case without microdischarge interaction). A com-parison of the Voronoi analysis of the random dot pattern with the simulatedand experimental results show that the random pattern is very different,demonstrating the importance of short-range interaction between the mi-crodischarges in DBD. One way to express numerically the difference be-tween the images is to count the number of different-sided polyhedradetermined in the Voronoi analysis. Unlike the random dot pattern, most ofthe polyhedral cells found in the analysis of the experimental and simulatedimages have six interior sides (six angles). This corresponds to the hexagonallattice and thus implies radial symmetry of the interaction. This type ofinteraction was observed experimentally as well as predicted by modeling.

The correlation function is widely used for a post-processing in crystallo-graphy and can provide some indications of the correlation between featuresin a data set. The correlation function of the experimental image and thesimulation are shown in Fig. 16 with open and solid signs, respectively. Thecorrelation function for random dots is shown in Fig. 16 with line withoutsymbols. As is expected, a random distribution of dots on a plane does notshow any periodic oscillations in the correlation function. The correlationfunction for a completely ordered lattice should show strong oscillations orpeaks indicating that all the features in the image are related by well-definedunit cell vectors. As a spatial correlation between features in the imagedecreases, the peaks in the correlation function level off. For example,the correlation function for a two-dimensional liquid with short-range cor-relation will look similar to experimental and modeling curves in Fig. 16,where the strong oscillation shows up at short distances and then dampensout as a result of disorder. The overall agreement of the correlation function


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plots for the experimental and simulated images demonstrates that the fea-tures observed in the experimental image are not arranged randomly but arestrongly influenced by microdischarge interactions in the DBD. It was foundthat under certain conditions streamers in DBD do not strike randomly andthe microdischarges they form interact and arrange themselves into a regu-lar filament pattern. The obtained discharge images suggest that the short-range interactions between microdischarges are present in the discharge.

The microdischarge interaction model based on the assumption that theavalanche-to-streamer transition and microdischarge formation are influ-enced by the microdischarge remnants allows simulating both microdischargeinteraction and pattern formation. Simulation results show qualitative agree-ment with experimental ones, demonstrating the importance of microdis-charge interaction in barrier discharges. A short-range interaction betweenmicrodischarges and resulted filament pattern can be predicted using themodel of interaction.

FIG.13. Voronoi polyhedra analysis of the experimentally obtained microdischarge loca-

tions from image shown in Fig. 10. The polyhedra cells are color coded according to number of

angles in each polyhedron. The cells in the image, obtained experimentally, are mainly six-sided

cells and have close sizes.


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Using Voronoi polyhedra analysis, simulation results were compared withexperimental ones, yielding convincing evidence of microdischarge interactionin DBD and demonstrating the validity of the present model and assumptions.

D. SURFACE DISCHARGES

Closely related to the DBD are surface discharges generated at dielectricsurfaces imbedded by metal electrodes in a different way. The dielectricsurface essentially decreases the breakdown voltage in such systems becauseof the creation of significant non-uniformities of the electric field and hencea local overvoltage. The surface discharges, as well as the DBD, can besupplied by AC or pulsed voltage.

A very effective decrease of the breakdown voltage can be reached in thesurface discharge configuration, where one electrode just lays on the dielectric

FIG.14. Voronoi polyhedra analysis of the simulated microdischarge locations from image

shown in Fig. 12. The polyhedra cells are color coded according to number of angles in each

polyhedron . The cells on the image obtained in simulation are mainly six-sided cells and have

close sizes.


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plate with another one partially wrapped around [39]. This discharge is calleda sliding discharge. It can be pretty uniform in some regimes on the dielectricplates of a large surface area over 1m� 1m at voltages not exceeding 20kV.

The component of electric field Ey normal to the dielectric surface playsan important role in the generation of the pulse-periodic sliding dischargethat does not depend essentially on the distance between electrodes alongthe dielectric. That is why the breakdown voltages of the sliding dischargedo not follow the Paschen law.

Two qualitatively different modes of the surface discharges can beachieved by changing the applied voltage amplitude: (A) incomplete one(sliding surface corona) and (B) complete one (sliding surface spark). Pic-tures of these discharges are presented in Fig. 17. The sliding surface coronadischarge ignites at voltages below the critical breakdown value and has alow current limited by charging the dielectric capacitance. Active volumeand luminosity of this discharge are localized near the igniting electrode anddo not cover all the dielectric.

FIG.15. Voronoi polyhedra analysis of a random dot pattern for comparison with Figs. 13

and 14. The polyhedra cells are color coded according to number of angles in each polyhedron.

Area of different cells varies significantly.


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FIG.16. Two-dimensional correlation functions of: (open signs) experimental image from

Fig. 13; (solid signs) simulation data from Fig. 14; and (no signs) data form random-point

distribution (shown for comparison).

z

x

A B

FIG.17. (A) Incomplete surface discharges and (B) complete surface discharges (He,

p ¼ 1 atm, eE5, d ¼ 0.5mm, pulse frequency 6� 1013Hz) in parallel plate electrode configu-

ration. Cathode is on the left on both pictures [40].


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The sliding surface spark (or the complete surface discharge) takes placeat voltages exceeding the critical one corresponding to breakdown. Here, theformed plasma channels actually connect electrodes of the surface dischargegap. At low overvoltages, the breakdown delay is of about 1 ms. In this casethe multiple-step breakdown phenomenon starts with the propagation of adirect ionization wave, which is followed by a possible more intense reversewave related to the compensation of charges left on the dielectric surface.After about 0.1 ms, the complete surface discharge covers the entire dis-charge gap. The sliding spark at a low overvoltage usually consists of onlyone or two current channels.

At higher overvoltages, the breakdown delay becomes shorter reaching ananosecond time range. In this case, the complete discharge regime takesplace immediately after the direct ionization wave reaches the oppositeelectrode. The surface discharge consists of many current channels in thisregime. In general, the sliding spark surface discharge is able to generate theluminous current channels of very sophisticated shapes, usually referred toas the Lichtenberg figures.

The number of the channels depends on the capacitance factor e/d (i.e.,the ratio of dielectric permittivity over thickness of dielectric layer), whichdetermines the level of electric field on the sliding spark discharge surface.This effect is illustrated in Fig. 18 and is important in the formation of largearea surface discharges with homogeneous luminosity. Many interestingadditional details related to physical principles and applications of the slid-ing surface discharges can be found in Baselyan and Raizer [39].

E. THE PACKED-BED CORONA DISCHARGE

The packed-bed corona is an interesting combination of a DBD and asliding surface discharge. In this system, a high AC voltage (about 15–30kV)is applied to a packed bed of dielectric pellets and creates a non-equilibriumplasma in the void spaces between the pellets [42,43]. The pellets effectivelyrefract the high-voltage electric field, making the field essentially non-uniformand stronger than the externally applied field by a factor of 10–250 dependingon the shape, porosity and dielectric constant of the pellet material.

A typical scheme for organizing a packed-bed corona is shown inFig. 19(a); a picture of the discharge is presented in Fig. 19(b). The dischargechamber shown on the figure is shaped as coaxial cylinders with an innermetal electrode and an outer tube made of glass. The dielectric pellets areplaced in the annular gap. A metal foil or screen in contact with the outsidesurface of the tube serves as the ground electrode. The inner electrode isconnected to a high-voltage AC power supply operating on a level of15–30 kV at a fixed frequency of 60Hz or at variable frequencies.


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In this discharge system the glass tube serves as a dielectric barrier toinhibit a direct charge transfer between electrodes and as a plasma-chemicalreaction vessel. The packed-bed corona is specifically known for its appli-cation in air purification systems and other environmental control processes.

n, chan/cm

K

3

12

8

01.0 2.0

4

0.8

0.6

0.4

0.2

d-1, mm-1

1

2

4

FIG.18. Linear density of channels n (1, 2) and surface coverage by plasma K (3, 4) as

function of d�1 inverse dielectric thickness: He (1, 3) and Air (2, 4) [41].

OUTLET

ELECTRODE

INLET

DIELECTRICBARRIER

PACKED BED

GROUNDSCREEN

(a) (b)

FIG.19. Packed-bed corona: scheme (a) and picture (b) [42].


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F. ATMOSPHERIC PRESSURE GLOW DBD

DBDs can exhibit two major discharge modes: filamentary mode and ho-mogeneous or glow mode. The filamentary mode (that was discussed pre-viously) has been a topic for active investigations in the past several years.A lot of experimental and theoretical work have been done in this area. Mostindustrial DBD applications utilize the filamentary mode. However, for ahomogeneous treatment of surfaces, or for the deposition of thin films, theglow discharge mode has obvious advantages over the filamentary one.DBDs in a glow mode or atmospheric pressure glow discharges (APG) withthe average power densities comparable to those of filamentary dischargeswill be of enormous interest for applications if a reliable control over it couldbe achieved. Such discharges can be effectively organized in a DBD con-figuration. The APG permits arranging the barrier discharge homogeneouslywithout streamers and other spark-related phenomena. Practically, it is im-portant that the glow mode of DBD can be operated at much lower voltages(down to hundred volts) with respect to those of traditional DBD conditions.

A detailed explanation of the operation of the APG is not known. It isclear, however, that streamers can be avoided by using applied electric fieldbelow the Meek criteria. If the electric field is less than required by the Meekcriteria for streamer formation, a discharge will operate in an avalanchemode because there will be no streamers. Discharge that operates in theavalanche mode and relies on occasional formation of primary electrons isusually called dark discharge. Dark discharge current is limited by the rate offormation of occasional primary electrons, which is usually very low in theabsence of an external ionization source. Being not-self-sustained dark dis-charges are very weak and thus useless for practical applications that requirehigh specific powers. One avalanche produces Np ¼ exp(a � d)�1 positiveions. If these positive ions will be able to cause the emission of at least oneelectron on the average from the dielectric surface, a new avalanche will beformed and the dark discharge will undergo the transition to self-sustainedTownsend discharge. Thus, the criterion for transition from dark to Town-send discharge is ðexpðadÞ � 1Þg41, where g is the coefficient of the second-ary electron emission (also known as the third Townsend coefficient). Thecurrent of Townsend discharge is only limited by the external circuit and bycharge accumulation on the dielectric surface. When the space charge in theTownsend discharge becomes large enough (when the discharge current in-creases above a certain value) to cause a significant disturbance of the ap-plied electric field, then the transition to the glow discharge occurs [1].

Secondary emission from dielectric surfaces relies upon adsorbed elec-trons (with binding energy about 1 eV) that were deposited during previousexcitation (high voltage) cycle. If enough electrons ‘‘survive’’ voltage


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switching time without recombining with positive ions (or attaching to formnegative ions) they can trigger the transition from dark to Townsend modeof the discharge. Electron ‘‘survival’’ time or memory effect is critical for theorganization of APG and depends on properties of dielectric surface as wellas operating gas [44]. It is clear that in electronegative gases memory effect isweaker than in non-electronegative ones because of loss of electrons due toattachment. If the memory effect is strong enough, transition from dark toTownsend mode can be accomplished, and a powerful uniform dischargecan be obtained in the absence of streamers. A streamer discharge canalways be produced while the organization of APG in the same conditions isnot always possible. This can be explained by the fact that streamer dis-charge is not sensitive to the secondary electron emission from the dielectricsurface while it is critical for the operation of APG.

It is an established fact that a glow discharge will undergo a contractionphase with increase of pressure due to thermionic instability. Because ofinstabilities the glow discharge is usually produced at low pressures (about1Torr). In the case of APG, the thermionic instability is reduced by usingalternating voltage, thus the discharge operates only when voltage is highenough to satisfy the Townsend criteria, and for the rest of the time thedischarge is idle. This idle operation phase allow time for dissipations ofheat and active species. If time between excitation cycles is not enough forthe dissipation then instability will develop and the discharge will undergo atransition to the filamentary mode. Transition from APG to filamentarymode with increasing frequency was observed experimentally [45].

It is interesting to note that in case of APG the avalanche-to-streamertransition will depend on the preionization level in the discharge. Meekcondition was derived for isolated avalanche. In case of high preionizationlevel, avalanches will be produced close to each other and will electrostaticallyaffect each other. Such electrostatic interactions between avalanches will de-pend on the distance between them. If two avalanches develop close enoughto each other then transition to streamer can be prevented and the dischargewill remain uniform. In order to derive a modified Meek condition let usassume two avalanches separated by the distance L and start simultaneously(note that R is the radius of the avalanche at the time it reaches the anode).Electric field will be the superposition of electric fields produced by twoavalanches:

E ¼ 1

4p�0

Q

R2� Q

ðL� RÞ2� �

¼ Q

4p�0R2

1� 2ðR=LÞð1� R=LÞ2

!

¼ E0 1� R2

ðL� RÞ2� �

ð39Þ


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In this equation E0 is the electric field produced by one avalanche as it appearsin the original Meek derivation [46]. By repeating original Meek derivationwith a modified electric field one can get the condition for the avalanche-to-streamer transition when avalanches can not be considered as isolated:

1� 2ðR=LÞð1� R=LÞ2 � 1� ðR=LÞ2 (40)

ad � ðR=LÞ2 � const (41)

ad � constþ neR2d (42)

In Eq. (42) the average distance between avalanches is approximated usingpreionization concentration. Constant in Eqs. (41) and (42) depends onoperational gas, for example in air at 1 atm this constant equals to 20. Themodified Meek criterion suggests that the avalanche-to-streamer transitioncan be avoided by increasing avalanche radius and providing sufficientpreionization.

The operational gas plays a very important role in the transition to APGmode. For example, helium has a very high electronic excitation level and noelectron energy loss on vibrational excitation, resulting in high values ofelectron temperatures at lower levels of the reduced electric field. Also, fastheat and mass transfer processes in helium prevent contraction and otherinstability effects in the glow discharge at high pressures. The same proc-esses can be important in preventing the generation of space-localizedstreamers and sparks. More details regarding the APGs can be found else-where [47–49] and in Section VII of this chapter where the APG is consi-dered not only as a type of the DBD, but as a broader group of dischargesorganized in a wide range of frequency.

G. FERROELECTRIC DISCHARGES

Special properties of DBD of practical interests can be obtained by usingferroelectric ceramic materials of a high dielectric permittivity (e41000) asthe dielectric barriers [50]. Today, ceramics based on BaTiO3 are one of themost employed ferroelectric materials for DBDs.

Important physical peculiarities of the ferroelectric discharges are relatedto the physical nature of the ferroelectric materials, which in a given temper-ature interval can be spontaneously polarized. Such a spontaneous polar-ization means that the ferroelectric materials can have a non-zero dipolemoment even in the absence of an external electric field. The electric


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discharge phenomena accompanying the contact of a gas with a ferroelectricsample were first observed in detail by Robertson and Baily [51]. The firstqualitative description of this sophisticated phenomenon was developed byKusz [52].

The long-range correlated orientation of dipole moments can be de-stroyed in ferroelectrics by thermal motion. The temperature at which thespontaneous polarization vanishes is called the temperature of ferroelectricphase transition or the ferroelectric Curie point. When the temperature isbelow the ferroelectric Curie point, the ferroelectric sample is divided intomacroscopic uniformly polarized zones called the ferroelectric domains.

The directions of the polarization vectors of individual domains in theequilibrium state are set up in a way to minimize the internal energy of thecrystal and to make the polarization of the sample as a whole close to zero.Application of an external AC voltage leads to overpolarization of theferroelectric material and reveals strong local electric fields on the surface.As it was shown in Hinazumi et al. [53], these local surface electric fields canexceed 106V/cm, which stimulate the discharge on ferroelectric surfaces.

The active volume of the ferroelectric discharge is located in the vicinity ofthe dielectric barrier, which is essentially the narrow interelectrode gap typi-cal for the discharge. Thus, the scaling of the ferroelectric discharge can beachieved by using some special configurations. One such special dischargeconfiguration is comprised of a series of parallel thin ceramic plates. Highdielectric permittivity of ferroelectric ceramics enables such multi-layersandwich to be supplied by only two edge electrodes. Another interestingconfiguration can be arranged by using a packed bed of the ferroelectricpellets. Non-equilibrium plasma is created in such a system in the samemanner as in the void spaces between the pellets.

VI. Spark Discharges

A. DEVELOPMENT OF A SPARK CHANNEL, A BACK WAVE OF STRONG ELECTRIC

FIELD AND IONIZATION

When streamers provide an electric connection between electrodes andneither a pulse power supply nor a dielectric barrier prevents the furthergrowth of current, it opens an opportunity for development of a spark.However, the initial streamer channel does not have a very high conductivityand usually provides only a very low current of about 10mA. Thus, somefast ionization phenomena take place after the formation of an initialstreamer channel to increase the degree of ionization and the current, and toinitiate an intensive spark.


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The potential of the head of the cathode-directed streamer is close to theanode potential. This is the region of a strong electric field around thestreamer’s head. While the streamer approaches the cathode, this electricfield is obviously growing. It stimulates an intensive formation of electronson the cathode surface and its vicinity and subsequently their fast multi-plication in this elevated electric field. New ionization waves much moreintense than the original streamer now start propagating along the streamerchannel but in the opposite direction from the cathode to anode. This isusually referred to as the back ionization wave and propagates back to theanode with an extremely high velocity of about 109 cm/s.

The high velocity of the back ionization wave is not directly the velocityof an electron motion, but rather the phase velocity of the ionization wave.The back wave is accompanied by a front of intensive ionization and theformation of a plasma channel with a sufficiently high conductivity to forma channel of the intensive spark.

The radius of the spark channel grows to about 1 cm, which corresponds toa spark current increase of 104–105 A at current densities of about 104A/cm2.The plasma conductivity grows relatively high and a cathode spot can beformed on the electrode surface. Interelectrode voltage decreases lower thanthe initial one, and the electric field becomes about 100V/cm. If voltage issupplied by a capacitor, the spark current obviously starts decreasing afterreaching the mentioned maximum values.

The detailed theory of the electric sparks was developed by Drabkina [54]and Braginsky [41]. Extensive modern experimental and simulation materialon the subject can be found in a book of Baselyan and Raizer [39].

B. LASER DIRECTED SPARK DISCHARGES

A modification of sparks can be done by the synergetic application ofhigh voltages with laser pulses [55,56]. It is interesting that laser beams candirect spark discharges not only along straight lines but also along morecomplicated trajectories. Laser radiation is able to stabilize and direct thespark discharge channel in space because of three major effects: local pre-heating of the channel, local photoionization and optical breakdown of gas.

The preheating of the discharge channel creates a low gas density zone,leading to higher levels of reduced electric field, which is favorable for sparkpropagation. This effect works best if special additives provide the requiredabsorption of the laser radiation. For example, if CO2-laser is used forpreheating, a strong effect on the corona discharge can be achieved whenabout 15% ammonia (which effectively absorbs radiation on a wavelengthof 10.6 mm) is added to air. At a laser radiation density of about 30 J/cm2,the breakdown voltage in the presence of ammonia decreases by an order of


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magnitude. The maximum length of the laser-supported spark in theseexperiments was up to 1.5m. Effective stabilization and direction of thespark discharges by CO2-laser in air were also achieved by admixtures ofC2H2, CH3OH and CH2CHCN.

The photoionization by a laser radiation is able to stabilize corona dis-charge without significantly changing the gas density by means of localpreionization of the discharge channel. UV-laser radiation (e.g., Nd-laser orKrF-laser) should be applied in this case. Ionization usually is related to thetwo-step photoionization process of special organic additives with a rela-tively low ionization potential. The UV KrF-laser with pulse energies ofapproximately 10mJ and pulse duration of approximately 20 ns is able tostimulate the directed spark discharge to 60 cm length. Note that the laserphotoionization effect to stabilize and direct sparks is limited in air by fastelectron attachment to oxygen molecules. In this case photo-detachment ofelectrons from negative ions can be provided by using a second laser ra-diating in the infrared or visible range.

The most intensive laser effect on the spark generation can be provided bythe optical breakdown of the gases. The length of such a laser spark canexceed 10m. The laser spark in pure air requires a power density of Nd-laser(l ¼ 1.06 mm) exceeding 1011W/cm2.

VII. Atmospheric Pressure Glows

APG is not a separate type of electric discharges. As it was mentionedearlier, the creation of uniform low temperature discharges at atmosphericpressure is a significant scientific and technological challenge. Therefore, manyscientists are trying to make their discharges as uniform as possible. Whenthey reach any success they usually call their discharges as APG (this term wasfirst introduced by Okazaki and his colleagues [57] for the glow mode of DBD(see more in Section V.F), or by more sophisticated names, for example, oneatmosphere uniform glow discharge plasma (OAUGDP) [58]. Unfortunately, inmany cases, the conditions resulted in the formation of uniform discharges arenot clear enough to be reproduced. Therefore, the physics of such dischargesis not well-developed. Nevertheless, because of the importance of these dis-charges, we are coming to this topic again after Section V.F and will presenthere available data regarding such discharges and some hypotheses.

It is of note that the ‘‘uniformity’’ of different APGs is usually limited:They can be non-uniform in time, or they can be non-uniform in space inany particular time moment, but uniform in average. Otherwise they can benon-uniform at the beginning of the operation and become uniform aftersome time, or vice versa.


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A. RESISTIVE BARRIER DISCHARGE

The resistive barrier discharge (RBD) was proposed by Alexeff in 1999[59,60]. This discharge can be operated with DC or AC (60Hz) powersupplies and is based on the DBD configuration. However, instead of adielectric barrier, a highly resistive sheet (i.e., few MO/cm; this ratherstrange unit was used by Laroussi et al. [61]) is used to cover one or both ofthe electrodes [61]. In a later publication, Thiyagarajan et al. [62] mentionedthat ‘‘The reactor usually consists of top wetted high resistance ceramicelectrode and a bottom electrode. The unglazed ceramic resistive barrier hasa resistance of 1 MO with a dimension of 20 cm� 20 cm� 1 cm’’. This highlyresistive sheet plays the role of distributed resistive ballast, which preventsthe discharge current from reaching a high value and, therefore, preventsarcing. It was found that if helium was used as the ambient gas between theelectrodes and if the gap distance was not too large (i.e., 5 cm and below), aspatially diffuse discharge could be maintained for time durations of severaltens of minutes. They [62] provided some data regarding the discharge pa-rameters and plasma properties: ‘‘It functions with a direct current (dc)power supply of 30 kV and 10mA, or with a low-frequency line powersupply of 120V, 60Hz, fed through a neon-sign step-up transformer, whichproduces an output voltage of 15 kV across its two secondary terminals.’’‘‘Based on the microwave attenuation experiments, with a transmitter fre-quency of 2.5GHz, the electron density is measured as 1011 cm�3’’. How-ever, if 1% of air was mixed with helium, the discharge formed filaments.According to Laroussi et al. [61], the filaments appeared randomly withinthe discharge volume.

Regarding randomness of the distribution of filaments in barrier dis-charges, Kogelschatz [63], who is one of the most well-known specialists inthis area, admitted that it was his incorrect statement that was broadlyaccepted and cited by a number of authors. Recently, the existence of theorder in the filament distribution was shown and explained (see Section V.Cand Chirokov [38] for more details).

It is interesting to note that even when driven by a DC voltage, the currentsignal of RBD exhibited a pulsed form with pulses of few microseconds at arepetition rate of few tens of kHz. Laroussi et al. [61] stated that ‘‘when thedischarge current reached a certain value, the voltage drop across the resis-tive layer became large to the point where the voltage across the gas becameinsufficient to ignite the discharge. Therefore, as the discharge extinguished,the current dropped rapidly and the voltage across the gas increased to avalue capable of initiating the discharge again.’’ Temporal non-uniformityof DC-driven RBD was also confirmed by the output signal of a photo-multiplier, which was mounted to observe the light emission from the


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discharge. The photomultiplier signal showed light pulses occurring at thesame time and same duration as the current pulses. In addition, it was notedthat consecutive current pulses were not necessarily similar, especially inmagnitude. As the physics of RBD was not carefully studied yet, it is notclear if the reported temporal non-uniformity is an inherent property of thisdischarge or if it can be suppressed by an appropriate system of an electricalcircuit adjustment.

Wang et al. [64] reproduced the pulsed regime that was reported by Alexeff[59] after the analysis of the role and necessary parameters of dielectric. Theyconsidered that the resistive layer should be equivalent to distributed resis-tors and capacitors in parallel, as shown in Fig. 20. They reported that whenthe electric field applied to the gas, Egas, reaches to the value of the gasbreakdown field, Eon, the gas discharges and the charged particles rapidlycharge the distributed capacitors, forcing Egas to rapid decrease to Eoff, anddischarge extinction. Then, the charged capacitors discharge through thedistributed resistors and Egas recovers to Eon, leading to gas being brokendown again. Based on the above analysis, the development of RBD wasnumerically simulated with different values of resistivity r and permittivity eof the resistive layer, and with known values of Eon and Eoff for helium gas,which were obtained from experiments with uniform helium DBD:Eon ¼ 300V/mm and Eoff ¼ 125V/mm. With the known Eon and Eoff, theproduct rer of the resistive layer required for obtaining a kHz repetition rateof RBD current pulses using 50Hz AC voltage was calculated to be in arange of rer ¼ (109�1011)O cm. After testing a number of materials, a sili-cate powder was chosen, from which a resistive layer of 1mm thickness was

FIG.20. The equivalent circuit for RBD according to [64].


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fabricated. The resistivity and relative permittivity of the layer were8.3� 108O cm and 17.9, respectively, which gave rer ¼ 1.5� 1010O cm, fall-ing into the desirable range. With this layer, RBD could be obtained in a5.5-mm helium gap using a 50Hz line power. Fig. 21 presents the appliedvoltage and the repetitive current pulses.

It is of note that the uniform mode of DBD was also obtained initially fordischarges in helium [57]. If the current pulsation is an inherent property ofRBD, the similarity between DBD and RBD becomes very clear. The maintechnical difference between these discharges is that in RBD the resistivebarrier should absorb a significant portion of the available power to act asresistive ballast. This significant power dissipation can limit possible appli-cations of the discharge.

B. ONE ATMOSPHERE UNIFORM GLOW DISCHARGE PLASMA

One atmosphere uniform glow discharge plasma (OAUGDP) is a regis-tered trademark of the discharge system developed initially at the Universityof Tennessee by Roth and his colleagues [58]. This discharge is very similarto a traditional DBD, but it is uniform. Situation with this discharge is veryunusual: people heard about this discharge from 1994 [65] but they couldnot reproduce it. Explanation of Roth presented in his book [58] about anion-trapping mechanism did not help because many research and industrialDBD systems operated with the same external parameters as OAUGDP,but they did not produce uniform plasmas. Simulation work which was used

FIG.21. The applied voltage with a frequency of 50Hz and the repetitive current pulses in

RBD according to [64].


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to support this theory [66] was done in one-dimensional approach. Thus, itcould not in principle reveal the formation of streamers (see Section II.F),which was one of the primary reasons of the non-uniformity in DBDs. Alsothe conclusion made on the basis of this theory [58] contradicted to theexperimental data. The theory of Roth says that at high AC frequencieswhen plasma components, electrons and ions become ‘‘trapped’’, the dis-charge should be more non-uniform. Experiments showed that it is rela-tively easy to support a uniform RF CCP (APPJ technology, Section VII.C)at alpha mode (see also Eastman Kodak patents [67]). The key question thatexists and has not been answered about OAUGDP is the following: whatmechanism prevents the formation of two-dimensional structures in a rel-atively powerful discharge (0.5–1.0W/cm2, the values that are typical forDBD), that results in the transition from avalanches to streamers and theformation of filaments in other discharges (see Section V). Rahel (from theUniversity of Tennessee) and Sherman (from Atmospheric Glow Techno-logies, Inc., the company that is commercializing the OAUGDP technology)[68] stated that ‘‘an independent effort to duplicate the Knoxville group’sreported creation of diffuse discharge in air or other electronegative gas wasunsuccessful’’ with reference to Miralaı et al. [69]. This is evident that theproperties of discharge and/or experimental system are not clearly andcomprehensively described. Rahel presented two movies at the IWM-2006meeting [70]: the first movie made in Knoxville, TN, demonstrated thetransition from a filamentary mode of DBD to a diffuse mode in air atatmospheric pressure (some pictures obtained using the system presented inFig. 22, are presented by Rahel and Sherman [68]); the second movie, madeafter his return to Czech Republic using a specially reproduced OAUGDPsystem, also demonstrated the transition of the filamentary mode, but not tothe diffuse mode. A new mode was also filamentary, but filaments weremore numerous and less intense.

Therefore it is clear that the initial state of OAUGDP is filamentary, butafter that something happens that suppresses the stability of the filaments. Itis important to remember that the stability of the filaments is based on the‘‘memory effect’’ (see Section V): electrons deposited on the dielectric sur-face promote the formation of new streamers at the same place again andagain by adding their own electric fields to the external electric field.According to Rahel, the only difference between the systems was that di-electrics of the same material (Pyrexs sheets) were ordered from two differ-ent vendors. This experimental data together with the presentation of Roth[71] show that the key feature of OAUGDP systems may be hidden in theproperties of particular dielectrics that are not stable in plasma and prob-ably become more conductive during a plasma treatment. In order to findthe role of different materials, let us compare properties of Pyrexs


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borosilicate glass (similar to the one used in Rahel and Sherman [68]) withthose of quartz (fused silica) often used in DBD applications. It is possibleto see [72] that the electrical conductivity of the former is almost four ordersof magnitude higher than that of the latter. Thus, it is very probable thatplasma can further increase the conductivity of borosilicate glass, for ex-ample, by UV radiation. In that case this system transforms into the resistivebarrier discharge (RBD, described earlier, see Section VII.A) working at ahigh frequency in a range of 1–15 kHz.

It is important to understand that not only the volumetric, but also thesurface conductivity of dielectric can promote the DBD uniformity, if it is inan appropriate range. To suppress the ‘‘memory effect’’ it is necessary toremove the negative charge spot formed by electrons of a streamer duringthe half period of voltage oscillation (i.e., before polarity changes), and thesurface conductivity can help with this. On the other hand, when the surfaceconductivity is very high, the charge cannot accumulate on the surface dur-ing DBD current pulse of several nano-seconds and cannot stop the filamentcurrent. Fig. 23 presents the equivalent circuit for one DBD electrode withsurface conductivity. So, DBD parameters of such a circuit for 10 kHzshould be the following: 0.1mscRCc1 ns, where resistances and capa-citances should be defined for the characteristic radius of streamer inter-action [73], that depends on many parameters (gas composition, the distancebetween electrodes, discharge power, etc.) but is on the order of 1mm.

FIG.22. Experimental set-up for OAUGDP structure study [68]: A–water electrodes;

HV–high voltage probes; PMT–photomultiplier probe; CT–current transformer; BIAS–para-

sitic current elimination tool; Cv–variable capacitor; OSC–oscilloscope; PC–computer; SIG-

NAL–harmonic signal generator; RF AMP–radio frequency power amplifier; CCD–digital

camera.


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Regarding the formation of the discharge uniformity of OAUGDP, theimportance of the procedure of the discharge ignition is not clearly under-stood yet. As it became clear from the movies shown by Rahel at the IWM-2006 [70], the voltage of the discharge should be kept at a low level from thebeginning. In that case, the luminosity appears after 10–60 s of existence ofthe dark discharge and the accumulation of surface charge on dielectrics,and then the area of the uniform discharge (or non-uniform, if you are notlucky) appears and grows. From our own experiments we learned that fol-lowing this procedure was not a warranty of success. Though this procedurecan be important, it is not always necessary. Aldea et al. [74] presented theresults on the creation of a uniform plasma in argon DBD during the firstcycles of voltage oscillations when DBD electrodes were covered by PEN(Polyethylene naphthalene) or PET (Polyethylene teraphtalate) foils of0.1–0.2mm thickness. They indicated that these types of dielectric surfaceswere critical for a uniform discharge development. When other dielectricswere used, a filamentary discharge with a large density of filaments thatcovered a large area of the electrode surface was observed from the firstpulses. These data do not clarify the situation very much, but at least showthat dielectrics can play a crucial role for the DBD uniformity.

In summary, though the existence of the uniform DBD or OAUGDP indifferent gases is not questionable anymore, and a large number of publi-cations have been published on this matter, including experimental andtheoretical papers [75], the properties of this discharge and conditions for itscreation are still not very clear.

C. ELECTRONICALLY STABILIZED APG

Electronically stabilized APG is a very promising approach of the crea-tion of the uniform mode of DBD that does not have its own name yet. Itwas developed by a research group from the Eindhoven University ofTechnology and Fuji Photo Film B.V., the Netherlands [74,76]. As dem-onstrated by Aldea et al. [77], the simplicity of the approach is veryimpressive.

Aldea et al. [74] showed the interesting experimental results about thecreation of a uniform plasma in argon DBD during the first cycle of voltage

FIG.23. The equivalent circuit for one DBD electrode with surface conductivity.


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oscillations with a relatively low amplitude (i.e., ad of about 3, where a is thefirst Townsend ionization coefficient, and d is the interelectrode gap dis-tance) although they did not explain the mechanism clearly. The existence ofthe Townsend discharge at such a low voltage requires an unusually highsecondary electron emission coefficient which should be greater than 0.1.They stated that ‘‘the existence of the atmospheric glow is due to a yetunknown physical mechanism that allows the plasma generation at lowfields’’.

Probably, it is possible to explain such a high secondary electron emissioncoefficient and the breakdown during the first oscillations of a low voltage ifone remembers that most polymers have very low surface conductivities. Theexistence of surface charges as a result of cosmic rays, for example, that couldbe easily detached by the applied electric field, can be one of the reasons whyit is not necessary to have the long induction time of the dark discharge thatis required for OAUGDP with glass electrodes (see Section VII.B).

Aldea et al. [74] explained the reason of the instability of APGs. Theyargued that the key issue that must be overcome for a stable plasma gene-ration is the glow-to-arc transition. At the glow mode of DBD, the length ofcurrent pulse when the heat power release exists, is very short (about 5 ms),and the power density is relatively low, while the time between the pulses(about 50 ms) is long enough for a temperature non-uniformity rela-xation. The reason of channel instability may be a ‘‘memory effect’’ (seeSection V.C) – a local charge deposition promotes the formation of newelectron avalanche or streamer at the same place.

In spite of the lack of a good theoretical explanation on the obtainedresults and discharge instability, Aldea et al. put forward a very interestingapproach how to stabilize the glow mode [74]. They proposed that the glowDBD filamentation could be prevented using an electronic feedback to fastcurrent variations [76]. Fig. 24 shows one of the patent pictures, whichshows the total current and voltage waveforms for DBD in argon with anactive displacement current control.

Aldea et al. [77] explained the essence of this approach as follows: ‘‘if theplasma is in series with a dielectric, a RC circuit will be formed. The fila-ments or the large current density plasma varieties will have a smaller RCconstant. The difference in RC constant can be used to ‘‘filter’’ them becausethey will react differently to a drop of the displacement current (displace-ment current pulse) of different frequency and amplitude. A simple LCcircuit, in which during the pulse generation the inductance is saturated, wasused to generate displacement current pulses.’’ Aldea et al. [77] claimed thatthe method of the uniformity stabilization was successfully used in the caseof large power densities in the range of 100W/cm3 in a large variety of gasessuch as Ar, N2, O2, and air.


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If this method demonstrates both the high stability and reproducibility, itmay be a major breakthrough for DBD that can open new application areas.However, it is necessary to emphasize that the uniformity may not be sogood for many cases. Streamers generate very high local electric fields thatresult in the appearance of high-energy electrons, promoting some specificchemistry. Therefore, the chemistry in the APG will be different from thefilamentary DBD chemistry, and if one wants to choose a system for aparticular application, one should carefully take this difference into account.

D. ATMOSPHERIC PRESSURE PLASMA JET

The RF atmospheric glow discharge or atmospheric pressure plasma jet(APPJ) [78] is one of the most developed and carefully studied systemsamong APGs. Hicks et al. [78] from UCLA and Los Alamos National Lab-oratory [79,80] made a significant progress in the APPJ study. They devel-oped both planar and co-axial systems, where the discharge gap was in theorder of 1mm (1.6mm), and frequency was in the MHz range (13.56MHz).They used the APPJ for the plasma-enhanced chemical vapor deposition(PECVD) of silicon dioxide and silicon nitride thin films. Later an Austriangroup studied a and g modes in contaminated helium [81] and argon [82]. AKorean group made significant changes in the system design [83]. Theoreticalmodeling of the APPJ was conducted by groups from the University ofTexas at Austin [84], Drexel University [85] and Loughborough University,Leicestershire, U.K. [86].

The APPJ is a RF CCP discharge that can operate uniformly only innoble gases, mostly in helium. The discharge in pure helium has a very

It

Va

-100

-50

50

0

100

0 20 40 60 80

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

t, µs

I t, m

AV

a ,103 V

FIG.24. Total current and voltage waveforms for DBD in argon with active displacement

current control [76].


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limited number of applications since helium is not reactive. For potentialindustrial applications the various reactive species such as oxygen, nitrogen,nitrogen trifluoride, etc. could be added to the discharge.

Apparently in order to achieve both higher efficiency and higher reactionrate, the concentration of the reactive species in the discharge has to beincreased. It was found experimentally that if the concentration of reactivespecies exceeds a certain level (which is different for different species, but inall cases is on the order of several percents), the discharge becomes unstable(i.e., the discharge undergoes a transition to arc).

The stability of APPJ discharge depends on the various discharge para-meters (such as an operating frequency) and the electric properties of thereactive species added to the discharge. The loss of the stability can lead tothe extinction of the discharge or transition to a thermal ‘‘arc’’ [87]. Thestability of the discharge is one of the most challenging problems in APPJ[85,88]. These studies [85,88] examined the mechanism of the instability andhow it is affected by the presence of reactive species in the discharge. It wasshown that the major mechanism responsible for APPJ discharge ‘‘arcing’’ isa– g transition [85]. Some details that led to this conclusion as well as rele-vant information regarding this transition are presented below.

Before discussing the physics and stability of the APPJ, it is necessary tomake a short overview of RF discharges. RF discharges were introduced inthe 19th century when RF power generators with a sufficient power becameavailable. However, these discharges did not have any practical applicationsfor a long time because inexpensive RF power supplies and RF diagnosticequipment were not readily available. It was much easier and less expensiveto produce DC discharges than RF discharges. Nevertheless, the RF dis-charges posses several important advantages over the DC discharges. Theseadvantages in principle can outweigh the complexity and price of the RFdischarges. Some of these advantages are discussed below.

It is possible to use a reactive ballast resistance with RF discharges so thatthe efficiency of the plasma generation can increase because a reactive bal-last does not dissipate power. In the microelectronic industry the use of RFdischarges eliminates the problems with a spattering of cathode and thecontamination of plasma. In RF discharges, electrodes can be placed out-side the main discharge chamber, and thus a plasma contact with the elec-trodes can be avoided. This is impossible to achieve with the DC dischargessince they cannot operate in open electric circuits. The RF discharges aremore flexible and scalable than the DC discharges because they can operatein open electric circuits. The RF discharges can be produced in a variety ofdifferent geometries and sizes. Due to these apparent advantages, the RFdischarges became a hot research area in 1960s when gas lasers were in-vented. Note that almost 25% of all CO2 lasers are currently based on the


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RF discharges [89]. The RF discharges are also used commonly for etching,sputtering and film deposition in the microelectronic industry [90].

There are two major configurations of the RF discharges: capacitivelycoupled plasma (CCP) and inductively coupled plasma (ICP) discharges.The CCP discharges are produced between two electrodes, while the ICPdischarges are produced inside an inductive coil. Although the detail dis-cussion of the ICP discharge is out of the scope of this review, severalimportant differences should be pointed out. The electric field in the CCP ismuch higher than that in the ICP, and the CCP discharge can stay in a non-equilibrium regime even at moderate pressures. The ICP discharges at at-mospheric pressure operate only in a quasi-equilibrium (thermal) regime.The APPJ discharge is a capacitively coupled non-equilibrium discharge.Typical configurations of CCP RF discharges are shown in Fig. 25. Elec-trodes can be placed either inside or outside a discharge chamber (so-calledelectrodeless discharge). In most APPJ configurations, electrodes are insidethe chamber.

The key features of all RF discharges are as follows: the ion density doesnot follow changes in the electric field but only responds to a time-averagedelectric field. In addition, the wavelength of an electromagnetic wave islarger than the system size.

In the APPJ discharge configuration the distance between electrodes isabout 1mm, which is much smaller than the size of the electrodes (about10 cm� 10 cm). Thus, in this case the discharge can be considered onedimensional, and the effects of the boundaries on the discharge can beneglected. The electric current in the discharge is the sum of the current dueto the drifts of electrons and ions, as well as the displacement current due tothe capacitance of the discharge system. Since the mobility of the ions isusually 100 times smaller than the electron mobility, the current in thedischarge is mostly due to electrons. Considering that the typical ionic driftvelocity in APPJ discharge conditions is about 3� 104 cm/s, the time neededfor ions to cross the gap is about 3 ms which corresponds to a frequency of0.3MHz. The frequency of the electric field is much higher, and thus ions inthe discharge do not have enough time to move, while electrons move fromone electrode to another as the polarity of the applied voltage changes. The

FIG.25. Typical configurations of RF CCP discharges. Configurations with electrodes in-

side and outside discharge chamber are shown.


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typical space-time structure of the discharge is shown in Fig. 26. The thinlayers close to the electrodes are called sheathes. The plasma between twosheathes is called the positive column since it have a positive potential [89].Note that the positive potential of the plasma is formed due to drift-diffu-sion losses of the electrons.

The overall discharge voltage consists of the voltage on the positive col-umn Vp (called plasma voltage) and the voltage on the sheath Vs. Thevoltage on the positive column Vp slightly decreases with an increase of thedischarge current density [91]. It happens because a reduced electric fieldE/N in plasma, which defines the balance of charged species, is almostconstant [92] and equals to E/pE2V/(cm �Torr) for helium discharge [89]. Ifthe density of neutral species is constant, the plasma voltage will be constantas well. But the density of neutrals slightly decreases with the electric currentdensity since high currents cause a gas temperature to rise. At higher gastemperatures, a lower voltage is needed to support the discharge and sub-sequently the plasma voltage decreases.

Sheath thickness can be approximated from the amplitude of electrondrift oscillations [89] resulting in ds ¼ 2mE/oE0.3mm, where m is an elec-tron mobility, o ¼ 2pf is the frequency of the applied voltage and E is anelectric field in plasma. The upper limit of an ion density was estimated fromthe Townsend breakdown condition (see Section II.A) applied to the sheath[85]. Assuming the secondary emission coefficient of g ¼ 0.01, the critical iondensity np(crit) in helium RF before the a– g transition was calculated to be3� 1011 cm�3.

Dynamics of the sheath voltage is very important for the dischargestability and overall understanding of the APPJ discharge operation. Thethickness of both sheathes can be found from the following formula:

ds1ðtÞ ¼ 0:5 dsð1� cosðotÞÞ; ds2ðtÞ ¼ 0:5dsð1þ cosðotÞÞ (43)

FIG.26. Space-time structure of RF CCP discharge.


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The voltage drop across the sheath can be found by integrating the Poissonequation with the density np equal to the density of the ions (since there areno electrons in the sheath). From the integration of Eq. (43) the followingexpressions for the sheath voltage can be obtained:

V s1ðtÞ ¼ 0:25Vs0ð1� cosðotÞÞ2; V s2ðtÞ ¼ �0:25V s0ð1þ cosðotÞÞ2(44)

where Vs0 is given by Eq. (45), where e is the elementary charge (i.e., thecharge of electron) and e0 is the electrical permittivity of vacuum.

V s0 ¼ 0:5eZpd2s=�0 (45)

Using the critical ion density np(crit) ¼ 3� 1011 cm�3 calculated above, thecritical sheath voltage can be calculated to be Vs0E300V. This estimation isin a good agreement with other published data [86].

Despite the fact that the sheath voltage has a non-harmonic temporalbehavior, Eq. (44), the sum of the voltages on both sheathes is a harmonicfunction and given by the following equation:

V sðtÞ ¼ V s1ðtÞ þ V s2ðtÞ ¼ V s0 cosðotÞ (46)

Since the total voltage drop on the sheath is harmonic, it is possible tobuild an equivalent electric circuit of the discharge as shown in Fig. 27.

FIG.27. Equivalent electric circuit of RF CCP discharge.


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The total specific capacitance of both sheathes, i.e., the combination oftwo time-dependent capacitances of both sheathes, is constant and is givenby the following equation in terms of capacitance per unit area:

Cs ¼ �0=ds (47)

Although the plasma (positive column) on the equivalent circuit is repre-sented using a capacitance and a resistance connected in parallel, the capaci-tance of the positive column is usually much smaller than that of the sheathand can be neglected for the sake of simplicity in simple analytical estima-tions [91].

The equivalent circuit is a powerful tool to understand the dynamics ofthe discharge. For example, the discharge power can be easily derived as afunction of the applied voltage using this approach. The power density perunit of area of the discharge W is equal to the product of the plasma voltageVp and the conductivity current density j (note that the displacement currentdoes not contribute to the power dissipation) as shown:

W ¼ jVp (48)

The current that passes through the plasma is equal to the current in thesheath, which can be determined using the capacitance of the sheath Cs andthe frequency o of the applied voltage.

j ¼ V sCso (49)

The voltage in the sheath Vs can be expressed in terms of the total voltage Vand the plasma voltage Vp neglecting the capacitance of the plasma as

V2 ¼ V2s þ V2

p (50)

After substituting Eqs. (48) and (49) into Eq. (50), the following expressioncan be obtained for the power dissipated in the discharge:

W ¼ jVp ¼ VpV sCso ¼ VpV so�0=ds ¼ Vpo V2 � V2p

� �1=2�0=ds

(51)

A typical power density for the APPJ helium discharge is on the level of10W/cm2 which is approximately 10 times higher than that in the DBD dis-charges (see Section V), including the uniform modification (see Section VII.B).

The power density that can be achieved in the uniform RF discharge islimited by several possible instability processes, which can lead to physicalchanges in plasma and compromise the plasma uniformity. Two most


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commonly encountered instabilities are thermal instability and a– g transi-tion instability. The a– g instability is the transition to a discharge formknown as a g discharge. The two forms of the RF discharge known as a andg discharges were reported by Levitsky in 1957 [93]. The transition to theg discharge occurs when the secondary electron emission from the electrodesbecomes important and causes the formation of the cathode layers similar tothe cathode layers in the DC glow discharges. The discussion of the differentdischarge modes is well beyond the scope of this review and can be foundelsewhere [89].

Although the g discharges can have a diffusive plasma column and bequite uniform, the very high power dissipation near electrodes along with alow electron temperature makes this discharge much less interesting for thepractical applications. The high power dissipation near the electrodes inthe g discharge can lead to a permanent damage of the electrode surface(so-called ‘‘arcing’’ of the APPJ), and thus this discharge mode should beavoided. Fig. 28 [81] demonstrates the a– g transition.

While both types of the instability lead to undesirable physical changes inthe discharge, it was important to identify the type of instability that affectsthe APPJ. Knowing the type of the instability responsible for the ‘‘arc’’formation in the APPJ can help to suppress this instability and stabilize theAPPJ discharge in a wider range of plasma power.

FIG.28. Photographs of the gap for various RF input powers of the large area APPJ

operated with helium at a gap spacing of 2.5mm (on the left side are pictures shown taken

directly with a digital camera, on the right side those taken in combination with an optical

microscope): (a) 140W, (b) 360W and (c) 440W [81].


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The most common type of the instability in high-pressure discharges is thethermal instability. Thermal instabilities of plasma were the subject of consi-derable research efforts in the past [91,94]. The thermal stability of RFdischarges is very well understood. The development of thermal instabilityin plasma is as follows:

dne "! dðjEÞ "! dT "! dN #! dðE=NÞ "! dTe "! dne " (52)

Subsequently, the chain of the events leads to the thermal instability. Eachstep in the chain is explained below

� The positive fluctuation of the electron density dnem leads to an in-crease of the electric current density djm, since the electric current inthe discharge is mostly due to an electron drift;

� An increase in the electric current density causes an increase in thepower dissipation in plasma d(jE)m. This happens only if the electricfield E remains unchanged;

� An increase in the power dissipation obviously results in an increasein the gas temperature dTm;

� If the gas temperature increases, the gas density will decrease dNk(Here the gas pressure is assumed to be constant);

� A decrease in the gas density causes an increase in the reduced electricfield d(E/N)m;

� An increase in the reduced electric field leads to a high ionization rateand an increased production of electrons dTem.

It is not necessary to start with an increase in the electron density. Anyevent in the chain can be considered as a starting point without changing theentire logic. It is important to note that the electric field should be constantfor this type of the instability to develop. If the electric field is somehowreduced in response to an increased current density, the thermal instabilitywill not develop, which is exactly the case applicable for the APPJ discharge.An analysis of the thermal instability of APPJ system [85] showed that thecritical power density for a thermal instability development should be on thelevel of 3W/cm2, which is much less than an experimentally observed value(about 10W/cm2), suggesting that there may be another reason of the APPJdischarge instability.

It was shown experimentally that a stable discharge can be produced witha power density that exceeds the threshold for the thermal instability. Themechanism that suppresses the development of the thermal instability wasproposed by Vitruk [91], who provided detailed discussions on this mecha-nism. As it was pointed out earlier, the derivation of the thermal instabilitycondition is based on fact that the electric field in plasma is constant, which


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would be true if there were no sheathes. The total applied voltage is the sumof the voltage drops in the sheath and plasma column (see Eq. (50)). Whilethe amplitude of the total voltage is constant, that of the plasma voltage isnot because the capacitance of the sheath acts like a ballast element that isplaced in series with the plasma (see Fig. 27). The sheath plays a very impor-tant role in stabilizing plasma and protecting it from the thermal instability.Thus, the condition for the thermal instability has to include the effect of thesheath, and this approach was first proposed by Vitruk [91]. Chirokov [85]derived the thermal instability conditions for the APPJ discharge taking intoaccount the sheath effect. He reported that the discharge in the a mode wasself-stabilized with respect to the thermal instability by means of a sheathcapacitance. The stabilization effect of the sheath can be quantitativelydescribed by the R parameter, which is the square of the ratio of the plasmavoltage to the sheath voltage. The smaller R, the more stable the discharge iswith respect to the thermal instability (see Fig. 29). For example, if R ¼ 0.1,the critical discharge power density becomes W E190W/cm2, which is muchhigher than that observed experimentally.

As it was pointed out earlier, the electric field in the non-equilibriumsteady plasma is almost constant and does not depend on the size of thesystem. For a helium discharge the electric field in plasma is equal toE/p ¼ 2V/(cm �Torr) [89]. Thus the voltage drop across plasma depends onthe length of the plasma column, which is linearly proportional to the gapdistance. When the gap distance increases, the plasma voltage increases aswell, while the voltage drop across the sheath stays constant, meaning thatthe discharge with a small gap distance will be more stable than that with alarge gap distance.

FIG.29. Effect of sheath on thermal instability of plasma. Critical power density as func-

tion of ratio R is shown. Area above the curve indicates unstable discharge.


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In order to estimate a typical value of the R parameter for the heliumAPPJ discharge the following values were considered: ds ¼ 0.3mm,Vs ¼ 300V and d ¼ 1.524mm. Thus, R becomes R ¼ (Vp/Vs)

2 ¼ 0.36.The value of R is in an excellent agreement with the results obtained from

a numerical simulation [85]. The critical discharge power density corre-sponding to R ¼ 0.36 is 97W/cm2. If the stabilizing effect of the sheath wasnot taken into account, the thermal instability condition predicted a muchlower critical power density than that measured experimentally, indicatingthe importance of the sheath stabilization. However, when the effect of thesheath is considered, the predicted power densities are much higher thanthose observed experimentally, meaning that the APPJ discharge remainsthermally stable in a wide range of power densities as long as the sheathremains intact. As shown by Chirokov [85] the effect that defines thedynamics of the sheath is the a– g transition.

In the a discharge the volumetric ionization is a dominating mechanismfor sustaining the plasma, while in the g discharge the main mechanism is thesecondary electron emission from the electrodes [89]. The a–g transitionhappens because of the electrical breakdown of the sheath. The breakdownof the sheath occurs when the electric field in the sheath exceeds the criticalvalue that can be obtained from the Townsend condition (Eq. (2), seeSection II.A),

gðexpðadsÞ � 1Þ ¼ 1 (53)

where g is the secondary electron emission coefficient, a the ionizationcoefficient and ds the thickness of the sheath in the a discharge (i.e., beforethe a–g transition). This transition condition is in an excellent agreementwith experimental data [89]. Equation (53) was derived in Section II.A forDC discharge (i.e., constant electric field), while in RF discharge the electricfield is a function of time. The sheath breakdown condition, specifically forRF discharge, was derived by Chirokov [85], who determined the critical iondensity of np(crit) ¼ 3� 1011 cm�3 and a sheath voltage of Vs ¼ 300V, thesame values obtained earlier using Eq. (53).

The plasma model of APPJ used by Chirokov [85] was based on a sim-plified set of fluid equations (i.e., the first moment of the Boltzmann equa-tion for each charge species). Plasma properties are modeled using a localfield approximation. The validity of the local field approximation for theconsidered plasma is very well justified. In addition to plasma equationsChirokov [85] also used a heat transfer solver to dynamically calculate thegas temperature based on the power dissipated in plasma. He took intoconsideration the most important processes for the operation of the RFdischarge: both drift and diffusion of electrons and ions, electric field


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distortion by space charge; ionization, attachment and recombinationkinetics; secondary electron emission from electrodes and increase of the gastemperature due to the power dissipation in plasma. The processes respon-sible for the thermal instability as well as for a–g transition were thereforeincluded in the model. Thus, this model should be capable of simulatingthe RF discharge and two most important types of instabilities takingplace in this discharge. The governing equations were discretized using theScharfetter–Gummel approximation of fluxes which was commonly used forplasma modeling and simulation. A time integration of the governing equa-tions was accomplished using ‘‘VODE’’ ODE solver [91].

From the preliminary CFD simulation, it was found that the gas flow in aflat APPJ could be considered laminar and fully developed since the cor-responding Reynolds number was small and the entrance length was muchsmaller than the length of a flat jet. In all considered cases the gas tem-perature in the flat jet was affected mostly by the conduction due to the highthermal conductivity of helium and a small discharge gap. Convection, onthe other hand, played a minor role in the thermal balance. The temperaturegradients in electrodes were much smaller than that in plasma since thethermal conductivity of aluminum (note that the electrodes of the simulatedsystem were water cooled and made from aluminum) was much higher thanthat of helium. Thus, the heat transfer from plasma was limited by heatconduction in the gap more than in electrodes. Therefore, a constant tem-perature boundary condition could be used on the electrodes to determinethe gas temperature distribution in plasma. In the plasma model, the tem-perature of the electrodes was assumed to be constant and set to be 300K inall simulations, resulting in an excellent agreement with the results of CFDanalysis.

Simulated results [85] revealed the behavior of the APPJ discharge at thefollowing conditions: in pure helium and in helium with additions of ni-trogen and oxygen at different applied voltages and frequencies, withdifferent coefficients of the secondary electron emission. In the simulationsconducted by Chirokov, the discharge stability was limited by the sheathbreakdown caused by the secondary electron emission. Thermal stability ofthe discharge was assured by the ballast resistance of the sheath. However,the secondary electron emission destroyed the sheath when the appliedvoltage was high enough and thus left the discharge unprotected with re-spect to the thermal instability. Simulations strongly indicated that the mainmechanism of the discharge instability was the sheath breakdown thateventually led to the thermal instability. Thus, a more effective dischargecooling would not solve the stability problem because it did not protectdischarge from the sheath breakdown. Nevertheless, it should be noted that


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the discharge cooling is important since the sheath breakdown depended onthe reduced electric field that increased with temperature. Despite the factthat the thermal stability of helium discharge was better compared to thedischarge with oxygen addition, a higher critical power could be achievedwith oxygen addition. The higher critical power density of the dischargewith oxygen addition was explained by a higher electric field needed for thesheath breakdown. Simulated results [85] are in good agreements with theexperimental observations [79,80].

As mentioned earlier, Moon et al. [83] significantly modified the APPJsystem (see Fig. 30) and produced an atmospheric pressure uniform conti-nuous glow plasma in ambient air assisted by argon feeding gas using a13.56MHz RF source. Based on the measured current–voltage curve andoptical emission spectrum intensity, they concluded that the plasma was free

FIG.30. (a) Schematic diagram of the experimental setup and (b) a photograph of the

generated plasma [83].


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from streamers and arc. Within the operation range of argon flow rate andRF power, the measured rotational and vibrational temperatures were in arange of 490–630K and 2000–3300K, respectively. From the spatial meas-urement of the total optical emission intensity, and rotational and vibra-tional temperatures, they obtained the plasma showing a very highuniformity of over 93% in the lengthwise direction. The plasma size was200mm� 350mm� 35mm. In another case, a plasma was produced in ascaled-up version of 600mm in length, presumably aiming for large-areaplasma applications.

Thus, APPJ is a very well characterized system that still has a potentialfor further modification and improvement. Present understanding andavailable numerical models should allow to make such modifications andimprovements fruitful in the future.

E. ROLE OF NOBLE GASES IN ATMOSPHERIC GLOWS

According to the currently available information it is much easier togenerate atmospheric glows in helium and argon than in other gases,especially electronegative ones. The assumption that a high thermal con-ductivity can play a key role for a uniformity support does not explain theresults from experiments with Ar-based APPJ discharge systems. Probably itis more important for uniformity that noble-gas-based discharges have asignificantly lower voltage, and consequently a lower power density helps toavoid the thermal instability development. From this standpoint it is clearthat a clean nitrogen should provide better conditions for the uniformityprotection than air or even a small addition of oxygen to nitrogen. Thepresence of oxygen results in the appearance of an electron attachmentprocess, which causes demands of a high voltage for the discharge support.As a result, the power density increases and it is more difficult to prevent thethermal instability.

There is another hypothesis that can explain the positive influence ofnoble gases on the discharge uniformity, a known phenomenon which iscalled the resonance absorption of UV radiation in atomic (noble) gases.This resonance radiation absorption causes a fast ionization transfer thatwas used for the explanation of a supersonic speed of MW discharge propa-gation in waveguides [95]. The same mechanism can cause the expansion ofdischarge channels. Note that the arc channel diameter is much larger forargon than for air or nitrogen. Larger diameters of discharge channels canpromote an overlapping of these channels or avalanches in DBD, for exam-ple, and help to protect the discharge uniformity. It is of note that thesehypotheses should be considered as hypotheses only until a more compre-hensive theory of the uniform DBD is developed.


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VIII. Microplasmas

Microplasmas or microdischarges recently became very popular, andalready the Third International Workshop on Microplasmas was organizedin 2006 [70]. One may ask what kinds of discharges can be considered asmicroplasmas. In general, we can call it a microdischarge if at least onedimension of the discharge has a size of 1mm or less. Thus, barrier dis-charges with a large surface area (see Section V) can be considered asmicroplasmas because of two reasons: (1) the discharge gaps in DBDs oftenhave a size less than 1mm; (2) the filaments in DBDs have a typical dia-meter of 0.1mm. A number of papers at the International Workshop onMicroplasmas were devoted to DBD phenomena. However, the DBD sys-tems in the industry have relatively large sizes: for example, ‘‘corona’’treaters for polymer film modifications and ozonizers have a size of severalmeters. Therefore, there is no reason to consider a discharge systemas microplasma unless the scaling down brings some new properties andphysics.

In general, scaling down with a similarity parameter pd should not changethe properties of discharges significantly (see Section II.B), although one canoften see confusions in the literature [96], which states that ‘‘pd scaling isquestionable when d decreases to be commensurate with l and a fully de-veloped cathode fall cannot be accommodated within the MD structure’’.This statement is at least confusing because the mean free path l for elec-trons should also be scaled down with growth of pressure p (or more cor-rectly density n).

The new properties that may be obtained from scaling down plasma sizeare listed below.

� The size reduction of non-equilibrium plasmas can increase the powerdensity to a level typical for thermal discharges. However, the stronginfluence of diffusive losses typical for low-pressure discharges canprevent plasma from reaching an equilibrium state. Note that an in-tense conductive cooling can be considered also as a diffusive loss.

� At a high pressure, a volumetric recombination may exceed the rate ofthe loss by diffusion, which can result in a significant plasma com-position change with pressure. For example, as a result of the for-mation of a large number of molecular ions in noble gases, theirconcentration may exceed that of monomer ions [96].

� Sheathes which have a typical size of tens of microns at atmosphericpressure occupy a significant portion of the plasma volume.

� It is possible to move plasma system parameters to the ‘‘left’’ side ofthe Paschen curve. For some gases, the Paschen curve minimum can


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be at about pd ¼ 3 cm �Torr (see Section II.B), meaning that a 30 mmdischarge gap at atmospheric pressure will be already at the left sideof the curve even at the room temperature.

From the practical standpoint these properties could result in a formationof the positive differential resistance of a discharge, a phenomenon which isvery important because it allows to support many discharges in parallelfrom a single power supply without using multiple ballast resistors. Anotherimportant consequence can be a high average electron energy in the micro-plasmas. Furthermore, it is difficult to imagine a thermal plasma system in amicroscale. These kinds of external characteristics as well as some uniquetechnological opportunities that come from a small scale itself producedsignificant interests in these discharges.

Most microplasma systems have been based on three well-known dis-charges: glow, DBD and hollow cathode discharge. Therefore, we will in-itially consider examples of these microdischarges in this review, and thenexamine their variations as well as high-frequency microplasma systems.

A. MICRO GLOW DISCHARGE

Let us start with recent comments made by Foest et al. [97], who statedthat ‘‘Spatially confining atmospheric pressure, non-equilibrium plasmas todimensions of 1mm or less is a promising approach to the generation andmaintenance of stable glow discharges at atmospheric pressure’’. We canstart our discussion from a ‘‘non-confined’’ glow discharge at atmosphericpressure as it allows to study the discharge physics without the complica-tions from different confinements.

Several research groups are now actively working with ‘‘non-confined’’glow discharges at atmospheric pressure. For example, a group from theTroitsk Institute of Innovation and Fusion Research, Russia [98]; a groupfrom the Institute of Molecular and Atomic Physics in Minsk, Belarus[99,100]; and a group from Drexel University, Philadelphia [101,102]. Thefirst two groups attempted to create atmospheric pressure cold glow dis-charge of a significant volume with some success: they developed glow dis-charges with a gap size of about 15mm, which utilized convective cooling(see Section IX) and were significantly larger than the typical size of mi-crodischarges. Drexel University group studied a similar system but with asmaller size [101]. Atmospheric pressure DC glow discharges were generatedbetween a thin cylindrical anode and a flat cathode. The discharge wasstudied using an inter-electrode gap spacing in the range of 20 mm–1.5 cm sothat one could see the influence of the discharge scale on plasma properties.


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A low-pressure normal glow discharge is one of the most studied non-equilibrium plasma discharges and descriptions of this discharge can befound in introductory plasma textbooks [1,3]. In a voltage vs. current dia-gram, the normal glow discharge corresponds to a region between theTownsend discharge and the arc discharge, where the discharge voltageremains essentially constant for varying plasma currents. Glow dischargesat high pressures are hardly attainable due to instabilities which lead to aglow-to-arc transition [103]. As the pressure increases the current densityincreases until it reaches the threshold for the development of instabilitiesleading to a transition to the arc phase. The glow-to-arc transition is thusthe transition from a non-thermal to thermal discharge. There are gen-erally two steps resulting in such a transition: (1) contraction and thermal-ization of the discharge resulting from the heating of the neutrals (i.e.,thermal or ionization-overheating instability and (2) heating of the cathoderesulting in the transition from the secondary electron emission to thethermionic emission of electrons at the cathode. Generally, the thermalinstability is suppressed in low-pressure discharges due to plasma cooling bythe walls.

Methods to create DC glow discharges at atmospheric and lower pres-sures have been reported. Fan [104] used a water cooling of the electrodes toproduce stable discharges in hydrogen and nitrogen at currents below 2A.In air, although appeared as a stable glow, high frequency transitions be-tween glow and arc were observed even at the lowest current tested(� 100mA). Gambling and Edels [105] created glow discharges in air forcurrents between 10mA and 0.5 A, reporting that a stable arc could beobtained above 0.5A. In a similar discharge in hydrogen [106] a transitionfrom glow to arc was reported to occur at around 1.5A.

Staack et al. [101] reported a successful operation of glow discharges inatmospheric pressure air at currents lower than those reported by Gamblingand Edels [105]. Voltage–current characteristics, the visualization of thedischarge (Fig. 31) and estimations of the current density indicated that thedischarge was operating in the normal glow regime. Emission spectroscopyand gas temperature measurements using the second positive band of N2

indicated that the discharge formed a non-equilibrium plasma. For 0.4 and10mA discharges, rotational temperatures were 700 and 1550K, whilevibrational temperatures were 5000 and 4500K, respectively. It was possibleto distinguish a negative glow, Faraday dark space and positive columnregions of the discharge (see Fig. 31). The radius of the primary column wasabout 50 mm, which was relatively constant with changes in the electrodespacing and discharge current. Estimations showed that this radial size wasimportant in balancing the heat generation and diffusion and in preventingthermal instabilities and the transition to an arc.


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Generally, there is no significant change in the current–voltage charac-teristics or discharge for different electrode materials or polarity [101]. Thereare several notable exceptions to this for certain configurations as given :(a) For a thin upper electrode wire (o100 mm) and high discharge currents,the upper electrode melts. This occurs when the wire is the cathode, indi-cating that the heating is due to energetic ions from the cathode sheath andnot resistive heating. (b) For a medium sized wire (� 200 mm) as the cath-ode, the width of the negative glow increases as the current increases until itcovers the entire lower surface of the wire. If the current is further increasedthe negative glow ‘‘spills over’’ the edge of the wire and begins to cover theside of the wire. This effect is analogous to the transition from a normal

FIG.31. Images of glow discharge in atmospheric pressure air at (a) 0.1mm, (b) 0.5mm, (c)

1mm and (d) 3mm electrode spacings [101].


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glow to an abnormal glow in low-pressure glow discharges. However, thereis no increase in the current density since the cathode area is not limited. Forsufficiently large electrode wires this effect will not occur. (c) In air dis-charges with oxidizable materials as the cathode, the negative glow movesaround the cathode electrode leaving a trail of oxide coating behind untilthere is no clean surface within the reach of the discharge and the dischargeextinguishes.

Figure 32 shows the characteristics of the discharges corresponding topowers between 50mW and 5W [101]. For a small spacing of electrodes thecurrent–voltage characteristics are relatively ‘‘flat’’, what is consistent withthe idea of this being a normal glow discharge. For a normal glow dischargein air the potential drop at a normal cathode sheath is around 270V [1]. Thedischarge voltage drop above that occurs mostly in the positive column. Fora larger electrode spacing the current–voltage characteristics has a negativedV/dI (i.e., negative differential resistance). This is due to the dischargetemperature increase with gap length that results in a conductivity growth.A short discharge loses heat energy through the thermal conductivity ofelectrodes. A long discharge cooling is not efficient because the thermalconductivity of gas is much lower than that of metal electrodes; therefore,the temperature of the long discharge is higher. Such a behavior demon-strates an appearance of a new property as a result of the size reduction tomicroscale. Diffusive heat losses can balance the increased power densityonly at elevated temperature of a microdischarge and the traditionally coldglow discharge becomes ‘‘warm’’.

FIG.32. Voltage–current characteristics for atmospheric pressure glow microdischarge in

air at several electrode spacings [101].


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An operation of the APG microdischarges in different gases is generallysimilar to the glow discharge in air. Some notable exceptions are as follows[101]: (a) Each gas has distinct discharge colors and spectral lines corre-sponding to the species. (b) In helium the scale of the discharge in everydimension is larger than that for a similar current discharge in air. (c) Inhelium the maximum electrode spacing achieved is 75mm. (d) In hydrogenthe primary column has standing striations for some conditions, probably ofthe same variety as seen in low-pressure discharges. Figure 33 shows animage of the standing striations in the hydrogen discharge at atmosphericpressure. (e) In both hydrogen and helium, higher discharge currents can beachieved without the transition to an arc or overheating of the electrodes.(f) The argon discharge is narrower and is prone to transition to an arc atlower currents than an air discharge.

FIG.33. Image of the glow discharge in atmospheric pressure hydrogen. Positive column

and negative glow are visible. In addition standing striations are visible in the positive column

[101].


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Various measurements confirmed that the discharge might be consideredas a normal glow discharge. Significant analytical and heuristic formulationsare available to describe the parameters of a low-pressure normal glowdischarge [1,3]. Some of those formulations that assume a room temperaturegas were compared with experimental results [101]. The scaling with densityinstead of pressure and the variation with gas temperature were checked andtaken into account when modifying well-known formulations for atmos-pheric pressure glow microdischarge [101]. The replacement of p in therelations by an effective pressure, peff ¼ pTn/T, was a sufficient correction inmost cases, where p is the pressure in Torr, Tn is the normal gas temperature(293K) and T is the actual gas temperature.

Using the experimentally measured parameters (i.e., current density, tem-perature and electric field) discharge parameters such as the electron density,the reduced electric field, the electron temperature and ionization degreewere calculated [101]. Table V summarizes these parameters for the dis-charges corresponding to two conditions at which temperature measure-ments were made, i.e., 0.4 and 10mA. Based on the results given in Table V,one can conclude that the atmospheric pressure DC microdischarge is anormal glow discharge thermally stabilized by its size and can maintain ahigh degree of vibrational-translational non-equilibrium.

TABLE V

DISCHARGE PARAMETERS IN A DC ATMOSPHERIC PRESSURE GLOW MICRODISCHARGE IN AIR AT

DISCHARGE CURRENTS OF 0.4 AND 10MA

Discharge current (mA)

0.4 10

Electrode spacing (mm) 0.05 0.5

Discharge voltage (V) 340 380

Discharge power (W) 0.136 3.8

Negative glow diameter (mm) 39 470

Positive column diameter (mm) – 110

Electric field in positive column (kV/cm) 5.0 1.4

Translational temperature (K) 700 1550

Vibrational temperature (K) 5000 4500

Negative glow current density (A/cm2) 33.48 5.8

Positive column current density (A/cm2) – 105

E/n (V cm2) 4.8� 10–16 3� 10–16

Te (eV) 1.4 1.2

ne in negative glow (cm–3) 3� 1013 7.2� 1012

ne in positive column (cm–3) – 1.3� 1014

Ionization degree in negative glow 3� 10–6 15� 10–7

Ionization degree in positive column – 3� 10–5


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Farouk et al. [102] used a hybrid model to simulate an atmospheric pres-sure glow microdischarge in argon. The simulations were carried out for thedischarge with an inter-electrode gap spacing of 200 mm. Parameters of anexternal circuit that included power supply with a fixed voltage, a variableserial resistor and a capacitor (that represents a stray capacitance) wereincluded into the simulation. The predicted voltage–current characteristicsand current density profiles identified the discharge to be a normal glowdischarge. The prediction of the neutral gas temperature indicated that thedischarge formed a non-thermal, non-equilibrium plasma. Predictions fromthe numerical modeling were compared favorably with the experimentalmeasurements.

It is of note that the above-mentioned simulation using a personal com-puter was possible because of a small size of the simulation domain. This isan important feature of microdischarges, i.e., a possibility of the simula-tion using sophisticated models, which were originally developed for a low-pressure plasma.

B. MICRO DBDS FOR PLASMA TV

Although, the glow discharge is one of the most extensively studiedplasma systems, the best known plasma system may be a plasma TV. Eachplasma TV screen (plasma display panel – PDP) is essentially a matrix ofsub-millimeter fluorescent lamps, which are controlled in a complex way byelectronic drivers. Each pixel of a PDP is composed of three elementary UVemitting discharge cells. The UV light is converted into visible light byphosphors in three primary colors. The plasma in each cell of PDP is gener-ated by DBDs operating in a rare gas mixture at a typical pressure of500Torr. Although this pressure is below 1 atm, we consider these dis-charges in this review because the difference in pressure is not so large to becrucial for discharge physics. The AC voltage is in a form of square wavewith a frequency of the order of 100 kHz, and a rise time of about200–300 ns. In the ON state, a current pulse of less than 100 ns flowsthrough the cell at each half cycle. Although plasma TV systems are welldeveloped already, the key challenge currently includes a relatively highpower consumption (in comparison with liquid crystal displays – LCD) anda relatively high cost of manufacturing. More complete information can befound in a recent review [107].

It is interesting to note that the plasma display panel was originally inven-ted by Bitzer and Slottow at the University of Illinois in 1964 for a PLATOcomputer system [108]. The original monochrome (usually orange or green)panels enjoyed popularity in the early 1970s because the displays were rug-ged and needed neither a memory nor refresh circuitry. However, in the late


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1970s semiconductor memory chips were used to make CRT displays in-credibly cheap, and PDP lost its niche in the market. In 1975, Weber fromthe University of Illinois sought to create a color plasma display, finallyachieving that goal in 1995. Today, the superior brightness and viewingangle of color plasma panels have caused these displays to have a resurgenceof popularity.

The initial PDPs were monochrome displays where Penning Ne–Ar mix-tures (typically 0.1% Ar in Ne) were used, and the light emitted by thedischarges was due to the characteristic red–orange emission of neon. In thecolor plasma displays, the gas mixture (Xe–Ne or Xe–Ne–He) emits UVphotons which excite phosphors in three fundamental colors. Each pixel istherefore associated with three microdischarge cells. Various designs of theplasma display have been proposed since the last 30 years. Here, we intro-duce three dominant concepts: an alternative current matrix (ACM) sus-tained structure, an alternative current coplanar (ACC) sustained structure,and the direct current with a pulse-memory drive PDP. In the ACM struc-ture, the microdischarges take place at the intersection of line and columnelectrodes covered by a dielectric layer, as in the original design of Bitzerand Slottow [108]. In the ACC structure (also known as TSD for three-electrode surface discharge) the sustained discharges occur between sets ofparallel electrodes on the same plate, and the addressing is provided byelectrodes on the opposite plate, which are positioned orthogonal to thecoplanar electrodes. Note that ‘‘addressing’’ means the ability to ignite adesirable microdischarge only, not all of them. The ACC structure has beenrecently adopted by most companies producing plasma TVs. The perform-ances (i.e., lifetime and efficacy) of DC PDPs are less than those of ACPDPs. Figure 34 presents simplified schemes of coplanar (ACC) and matrix(ACM) electrode configurations of AC PDPs.

FIG.34. Coplanar (ACC) and matrix (ACM) electrode configurations of AC PDPs [107].


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In traditional industrial applications the DBDs generally operate at a highpressure, for a gap length of the order of 1mm to a few centimeters. Underthese large pd (pressure� gap length) conditions, the discharges operateusually in a streamer regime (see Section V). In DBDs for PDPs, the elec-trode gap length is very short, of the order of 100 mm, and the pressure p isabout 500Torr such that the pd product is of the order of a few Torr � cm.For small pd values, the discharges do not operate in a streamer regime butin a glow discharge regime. It is essential to operate in this regime becausethe ability to control each discharge separately and the reproducibility of thedischarges are of paramount importance in a PDP.

Since addressing a cell in the ACC structure is a little more complex thanin the case of ACM, we present only a relatively simple ACM addressing.A sustaining AC voltage, Vs, is constantly applied between the line andcolumn electrodes. The amplitude of the sustaining voltage must be smallerthan the breakdown voltage of the discharge cells. In order to turn a cell tothe ON state, a voltage pulse (i.e., a writing pulse) is applied between the lineand column defining the selected cell. The amplitude of this voltage pulse islarger than the breakdown voltage of the cells. A glow discharge forms andis quickly quenched by the charging of the dielectric layers that creates avoltage across the gas gap opposing the voltage across the electrodes. At theend of this ‘‘writing’’ pulse, the charges on the dielectric surfaces above eachelectrode are –Q and +Q, accordingly. At the beginning of the next halfcycle of the sustaining voltage, the voltage due to the charge on the dielectricsurfaces above the dielectrics now adds to the applied voltage and the gasgap voltage (or ‘‘cell voltage’’) is again above the breakdown voltage. Thus,a new discharge pulse is initiated. In Fig. 35, the charges on the dielectricsurfaces are (–Q, +Q) after the writing pulse, (+Q, –Q) after the firstsustaining pulse, and so on. Erasing is accomplished by applying a voltagepulse smaller than the sustaining voltage such that the charge transferredduring the pulse is Q instead of 2Q. After the erasing pulse the charges onthe surface at the beginning of the next half cycle are zero. The writing,sustaining and erasing pulse voltages can easily be chosen if one knows the‘voltage transfer curve’ of the cell. These curves and the stability conditionsof the sustaining regime have been analyzed by Slottow for the ACMstructure [109]. Thus, a relatively simple idea of using micro DBD for thelight emission combined with a relatively complex electronic control resultedin commercially successful plasma TVs.

C. MICRO HOLLOW CATHODE DISCHARGE

Roth made the following comment on the traditional low-pressure hollowcathode discharge (HCD) in his book [58]: ‘‘Applications of this source have


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proliferated without an adequate analytical theory of the physical processesby which they operate’’. Other books on low-temperature plasma also do notprovide any significant information regarding the physics of HCD. Thus, bothRaizer [3] and Fridman [1] recommend a relatively old book in Russian [110].Several configurations of low pressure HCD systems can be found in the bookof Roth [58]. Fridman [1] describes the HCD phenomenon as follows: ‘‘Ima-gine a glow discharge with a cathode arranged in two parallel plates with theanode on the side. If the distance between the cathodes gradually decreases, atsome points the current grows 100 to 1000 times without a change of voltage.The effect takes place when two negative glow regions overlap, accumulatingenergetic electrons from both cathodes’’. It is not easy to imagine the exper-iment described above, especially because in glow discharges the current isstabilized usually by serial resistors. White [111] described the HCD and itsI–V characteristics, in detail, including experiments with a real micro HCDwith a spherical cavity of the cathode having a diameter of 0.75mm. Ac-cording to White, the major features of the HCD that distinguish it from thenormal (‘‘flat’’ cathode) glow discharge (see Fig. 36) are as follows: (1) HCDextends and flattens the volt–ampere characteristics for the same cathode areaand (2) the cathode current density at HCD can be quite high (see Fig. 37).Kushner [96,112] considered that the discharge can be called as HCD only if‘‘beam’’ electrons emitted from the cathode due to the secondary electronemission have a ‘‘pendulum’’ motion and they can reach the cathode sheath ofthe opposite side of the hollow cathode.

FIG.35. Example of a sequence of writing, sustaining and erasing pulses in an ACM PDP.

The voltage pulses, current pulses and charges on the dielectric surfaces after each pulse are

shown [109].


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A high-density plasma of HCD is one of the reasons why such a systembecame so popular, and why many scientists are still trying to produce HCDat atmospheric pressure. Bell Telephone Laboratories investigated such asystem in 1950s [111] in the framework of the development of current stabi-lizing lamps. It would be nice if the scientists who are doing numericalsimulations of micro HCD [96,112,113] could verify their models using thewell documented and comprehensive experiments [111].

FIG.36. Cavity cathode cross-section from [111]. Typical operating parameters are: cavity

diameter 0.75mm; aperture diameter 0.185mm; discharge current 10mA; neon pressure

100Torr.

0 4 8 12 16 20

80

120

160

Discharge Current, mA

Vol

tage

, V

A

FIG.37. Current–Voltage characteristic of 0.75mm diameter cavity cathode (see Fig. 36)

(solid curve) and plane cathode (dashed curve) having 20 times the area [111]. The voltage

discontinuity at 2mA marks the point at which the discharge transfers from the face of the

cathode to the cavity (gas – neon, 100Torr).


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Significant information regarding the micro hollow cathode discharges(MHCD) can be found elsewhere [114], where the description on the topic ismore phenomenological than fundamental. According to the available datathe sustainable operation of the HCD is limited by so-called ‘White-Allis’similarity that relates the discharge sustaining voltage V to (pD) and (I/D),where I is the discharge current and D is the effective hole diameter. If (pD) isin the range of 0.1–10Torr � cm, the discharge develops in stages (see Fig. 37).At low currents, a ‘‘pre-discharge’’ is observed, which is a glow dischargewith the cathode fall outside the hollow cathode structure. As the currentincreases and the glow discharge starts its transformation to the abnormalglow discharge with a positive differential resistance, a positive space chargeregion moves closer to the hollow cathode structure and can enter the cavity.After that, the positive space charge in the cavity acts as a virtual anode,resulting in the redistribution of the electric field inside the cavity. At thecenter of the cavity, a potential ‘‘trough’’ for electrons appears, forming acathode sheath along the cavity walls. At this transition from the axial pre-discharge to a radial discharge, the sustaining voltage drops (e.g., see 2mApoint in Fig. 37). Sometimes this transition is not so sharp, and in that case anegative slope in the voltage–current characteristic curve (i.e., a negativedifferential resistance) appears, which is traditionally referred as the ‘‘hollowcathode mode’’. From this standpoint, some microdischarges that have beendeveloped recently can be considered as MHCD. For example, the systemsthat were developed at Old Dominion University [115,116] (Fig. 38) and inUppsala University, Sweden [117] (Fig. 39).

Coming back to the classical paper of White [111] one can see that thevoltage drop near the hollow cathode is less than voltage drop at a cathodesheath of normal glow discharge. However, Raizer [3] showed that the glowdischarge has a unique property of a self-organization that results in thecathode sheath formation with a voltage drop almost equal to the minimum

dcba

Dielectric

Metal

FIG.38. Hollow cathode discharge geometries studied in [116]. System (d) demonstrates

hollow cathode mode when operates in argon with pressure at least up to 250Torr.


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of the Paschen curve. On the other hand, it should be clear from Section II.Bthat the reduced electric field at the Paschen minimum (E/p)min ¼ Bcorresponds to the Stoletov constant, which is the minimum price of anionization (i.e., the minimum discharge energy necessary to produce oneelectron-ion pair). The Stoletov constant exceeds the ionization potentialusually several times because electrons spend their energy not only on theionization but also on vibrational and electronic excitations. It means thatthe HCD has another way of a self-organization that reduces the price of theionization below the Stoletov constant. In general, it is possible because ofthe existence of the ‘‘beam’’ electrons [3] that can have the energy close tothe cathode fall value, and the high-energy electrons are more efficient in theionization than the usual thermal electrons. ‘‘Beam’’ electrons are a smallfraction of the total number of the electrons emitted from the cathode

FIG.39. Schematic diagram and V–I characteristics of the atmospheric pressure cylindrical

RF hollow cathode discharge with cathode diameter 0.4mm. Neon flow 1000 sccm [117].


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surface due to the secondary electron emission. The ‘‘beam’’ electrons donot collide with molecules during their passages through a sheath. Becauseof the long free paths (as a result of the statistical distribution of free paths)that are on the order of magnitude larger than the mean free path, ‘‘beam’’electrons obtain a high energy in the strong electric field of the cathodesheath. Beam electrons exist in the normal glow discharge [3] as well as inthe HCD. However, a lower sheath voltage at the HCD means that thefraction of ‘‘beam’’ electrons in the HCD should be larger than that in thenormal glow discharge. Another possible reason for the reduced cathodefall value is an increase in the secondary electron emission coefficient g.Although the dependence of the sheath voltage on g is weak (logarithmic,see Eq. 5 in Section II.B), a significant increase of g can result in a decreaseof the cathode sheath voltage.

We provide some possible explanations on the HCD effect next.

(a) The most popular explanation is the ‘‘pendulum’’ motion of the‘‘beam’’ electrons between cathodes, resulting in the formation of adense plasma inside the hollow cathode. As it was mentioned before,some researchers [96,112] considered the pendulum motion as amajor characteristic of the hollow cathode. Kushner numericallysimulated the microdischarge with the pyramidal cathode (Fig. 8.13)[96] and the discharge system that was developed at Old DominionUniversity (d, Fig. 11) [112]. In the former case [96] Kushner foundthe ‘‘pendulum’’ motion of the ‘‘beam’’ electrons and classified thepyramidal cathode structure as a hollow cathode system, though thismicrodischarge did not demonstrate the negative differential resist-ance in experiments [118]. In the latter case [112] Kushner did notfind the ‘‘pendulum’’ motion of the ‘‘beam’’ electrons at a pressureof 250Torr, and did not classified this system as a hollow cathodedischarge, though this microdischarge did demonstrate the negativedifferential resistance in experiments [116] at this pressure. It ap-pears that a classical system of White [111] (Fig. 36) did not satisfythe criterion of ‘‘pendulum’’ motion of the ‘‘beam’’ electrons also.Estimated sheath thickness was much less than the cavity diameter[111]. Therefore, according to our opinion, the ‘‘pendulum’’ motionof the ‘‘beam’’ electrons should not be the major description of thehollow cathode effect although it can contribute to the plasma den-sity increase. The plasma density increase can be explained relativelysimply based on an analogy to a highway traffic. If we consider aglow discharge as a highway for electrons, the positive end of thecathode dark space where the electron concentration reaches itsmaximum (because of the ionization by ‘‘beam’’ electrons) and the


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corresponding electric field is close to zero [1,3], can be considered asa starting place for an electron rally: a large density and a low speedof electrons. Then, electrons begin to accelerate toward the anode,getting a drift velocity in a uniform electric field, which is similar to ahighway traffic. It is necessary to remember that along this line newelectrons appear, and the same number of electrons finishes theirtrips at the wall. Now, if we put several starting positions (e.g., twocathodes in front of each other) at the beginning of the highway andremove the possibility for electrons to escape to the wall (note that inthis case walls are negatively charged cathodes that repel electrons),we will get not only a high density of electrons (like cars on the rallystart), but really a traffic jam. New electrons appear because of theionization and the secondary electron emission (i.e., new cars com-ing to the starting point from all sides), but can escape only alongthe same narrow ‘‘highway’’. Although, the high electron density is acharacteristic feature of hollow cathode systems, it is not clear if itcan be the major reason of the ‘‘hollow cathode mode’’ (i.e., neg-ative differential resistance).

(b) The secondary electron emission coefficient g increases becauseplasma photons are more effectively captured in a quasi-closed ge-ometry. It is important to note that in simulation works related toHCD [96,112,113], g is supposed to be rather large (0.15 in Kushner[96,112], 0.2 in Kim et al. [113]) so this photon influence may havealready been implicitly included in the analysis. On the other hand,Kushner [112] attempted to find the influence of photons, but with-out a firm conclusion regarding the importance of this influence.

(c) Enhanced ion collection. Really, in a glow discharge, a large numberof ions formed in the vicinity of a cathode are lost for the secondaryelectron emission because of their ambipolar drifts to the side walls.On the other hand, if one considers a breakdown between two par-allel plates for a Paschen curve derivation, there should be no ionlosses. Therefore, this mechanism alone can not explain the reduc-tion of the cathode voltage drop below the Paschen curve minimum.

(d) The influence of the opposite cathode can reduce the cathode sheaththickness (e.g., because of the formation of denser plasma – seeexplanation (a)), and less number of electrons experiences collisionsinside the sheath, and a fraction of ‘‘beam’’ electrons becomeslarger. Increase in the fraction which gives a very efficient ionizationcan significantly change the sheath voltage. Note that simulationsmade by Kushner and Kim et al. [96,112,113] confirmed theimportance of these ‘‘beam’’ electrons in the ionization balance ofthe HCD.


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(e) Influence of metal ions on the ionization inside the hollow cathode.White [111] demonstrated a significant transfer of electrode materialinside the hollow cathode. If anyone makes simple estimations basedon his results [111], it is possible to show that the number of metalatoms in gas phase could be comparable with the total number ofions. In that case the ionization should be much easier (i.e., theionization potential of metal atoms is significantly less, and thePenning ionization mechanism should work extremely well). Alsothe bombardment of a cathode by the metal atoms of the samematerial can be more efficient from the standpoint of the secondaryelectron emission.

Probably it is possible to make other hypotheses regarding the HCDmechanism. As this type of discharges becomes popular again, new simu-lation techniques will probably allow us to better understand what mayhappen inside the hollow cathode.

D. OTHER MICRODISCHARGES AND MICRODISCHARGE ARRAYS

The power of one microdischarge is so small that individual microdis-charges have limited applications. Thus, most industrial applications requiremicrodischarge arrays or microplasma integrated structures. Plasma TV isan example of such a complex structure. However, for most imaginableapplications of microdischarges (such as light sources, chemical reactors,surface treaters, etc.) complex structures probably may not be economicallyattractive. The simplest structure may be the one that consists of multipleidentical microdischarges electrically connected in parallel. For a stable op-eration of such structures, each discharge should have a positive differentialresistance (i.e., the current–voltage characteristics should have a positiveslope (see Fig. 39). Most microdischarges have this property as a result of asignificant increase in the power losses with a current increase (i.e., thepower and voltage should grow to compensate the power losses that takeplace, for example, because of thermal conductivity to the confinement), anda number of arrays of the discharges having this property have beendeveloped and tested.

One of the examples is the array consisted of microdischarges with in-verted, square pyramidal cathodes (Fig. 40). An optical micrograph of a3� 3 array of microdischarges of 50mm� 50mm each, separated (center-to-center) by 75mm, was presented by Park et al. [118]. All of the micro-discharges had common anode and cathode, i.e., the devices were connectedin parallel. The array operated in 700Torr of Ne. At ignition, the voltage andcurrent for this array were 218V and 0.35 mA, respectively, and the array was


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able to operate at a high power loading (433V and 21.4mA). It wasdemonstrated that the emission from each discharge was spatially uniform.

Another example of a microdischarge array is a so-called ‘fused’ hollowcathode (FHC) source [117] based on the simultaneous RF generation ofhollow cathode discharges (Fig. 38) in an integrated open structure withflowing gas. The resulting FHC discharge was very stable, homogeneous,luminous and volume filling without streamers. The power consumption wason the order of one Watt per cm2 of the electrode structure area which istypical for the traditional DBD. Experiments for the system with the totaldischarge area of 20 cm2 were performed. The concept of the source is ex-tremely suitable for scaling-up for different gas throughputs. The FHCsource represents a non-equilibrium atmospheric plasma source suitable forthe treatment of the gas. Moreover, its design offers catalytic reactions bothin the bulk of plasma and at solid surfaces composing an open structure [117].

In some cases it is beneficial to connect microdischarges in series, forexample, to increase a radiant excimer emittance. Example of such a systemconsists of two hollow cathode discharges with negative differential resist-ance [112]. Such a system can be used for the creation of an excimer laser.Laser devices require a long gain length to achieve the threshold. One of thestrategies to produce the long gain length is to alternately stack cathode andanode structures in a single bore. Kushner [112] investigated the dynamics ofmultistage microdischarge devices with 100–200 mm diameter with a currentof a few milliampere, and a pressure of many hundreds of Torr, taking intoaccount the gas thermal rarefaction and transport.

Very interesting phenomena of a self-organization were observed in themicrodischarge of the geometry similar to that presented in Fig. 38d, butwith a larger opening and opposite polarity (i.e., the hole was in the anode)[119]. The cathode consisted of a molybdenum foil that was 250 mm thick.A 250-mm thick layer of alumina with a circular opening was placed on thetop of this cathode. The anode, a 100 mm molybdenum foil, was placed onthe top of the dielectric with the same size circular opening. The diameter ofthe dielectric and anode opening was varied from 0.75 to 3.5mm. Xenonwas used as a fill gas at pressure varying from 75 to 760Torr. The discharge

PS

-

+MetalDielectricSemiconductor

FIG.40. Geometry of a single discharge from the arrays described in [118] and numerically

simulated in [96].


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was operated in a DC mode, and both DC voltage and current were re-corded. The glow discharge structure in this electrode configuration wasreduced to only the cathode fall and negative glow, with the negative glowplasma conducting the current radially to the circular anode. Therefore, thistype of plasma is a called cathode boundary-layer microdischarge [114,119].

The discharge plasma could be observed in the visible range using a CCDcamera with a microscope lens. In some cases, a vaccum UV imaging systemwas used to observe the plasma emission at the xenon excimer emissionwavelength of 172 nm. Photographs indicated the transition from a homo-geneous plasma to a structured plasma when the current was reduced belowa critical value that was dependent on pressure. The plasma pattern con-sisted of filamentary structures arranged in concentric circles. The structureswere most pronounced at pressures below 200Torr and became less regularwhen the pressure was increased. Fig. 41 [119] demonstrates some patternsthat appear as a result of the microdischarge self-organization.

Self-organization in the plasma is a rather common phenomenon. A pat-tern formation in the DBD as a result of the interaction of microdischargeswas discussed already in Section V.C [38,73]. Significant attentions werepaid to the self-organization in plasma during the Third InternationalWorkshop on Microplasmas [70,120,121].

FIG.41. Development of plasma patterns with reduced current in a xenon discharge at a

pressure of 75Torr. The diameter of the anode opening in this case is 1.5mm [119].


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Non-equilibrium microdischarges at atmospheric pressure can also existat a relatively high power and even in the regimes typical for an equilibriumplasma. For example, Drezin [122] reported the use of a microarc discharge,which was created in a gap of 0.01–0.1mm with a discharge voltage ofU ¼ 1.5–4.5 V, and a current of I ¼ 40–120A. This arc is similar to someextent to the cathode boundary-layer microdischarge discussed earlier be-cause it exists without an ‘‘arc column’’. The main difference between thetwo discharges is that in the microarc, up to 95% of the electrical energy istransferred to the anode (similar to e-beam), which is qualitatively differentfrom the case of the cathode boundary-layer discharge. The microarc wasused for the generation of metal droplets and nano-powders (when operatedin a pulsed mode) as well as for a local hardening of metal surfaces [122]. Itis of note that the major physical difference between the glow discharge andthe arc is the mechanism of the electron emission from the cathode: thesecondary electron emission in the case of the glow discharge, while thethermionic emission in the case of arc discharge [1].

Considering microplasma systems from the operational frequency, we canstate that microdischarges could be produced in all possible frequencyranges. DC microdischarges were already discussed. Low- and medium-frequency AC discharges can be based on the DBD principle (see SectionVIII.B about Plasma TVs). A relatively simple large-area plasma sourcesystem based on the DBD approach was presented by Sakai et al. [123]. Sucha system can be used for material treatments. An integrated structure namedcoaxial-hollow micro dielectric barrier discharges (CM-DBDs) was con-structed by stacking two metal meshes covered with a dielectric layer made ofalumina with a thickness of about 150mm. The test panel had an effectivearea with 50mm in diameter in which hundreds of hollow structures wereassembled with each hollow area of 0.2mm� 1.7mm. He or N2 was used asthe discharge gas in the pressure range from 20 to 100kPa, and the firingvoltage was less than 2 kV even at the maximum pressure. Bipolar square-wave voltage pulses were applied to one of the mesh electrodes. The pulsewidth of both positive and negative voltages was varied from 3 to 14ms andthe intermittent time was set at 1ms. The repetition frequency of this pulsetrain was adjusted typically to 10 kHz. In each coaxial hole, the dischargeoccurs along the inner surface. The intensity of each microdischarge wasobserved to be uniform over the whole area throughout the pressure range.The fundamental plasma parameters were measured using a single probe inthe downstream region of microdischarges using an auxiliary flat electrodeset apart from the mesh electrode plane. The occurrence of an extended glowwith a length of some millimeters was observed in He but not in N2. Theelectron density derived by the probe data in He at 100kPa was about3� 1011 cm–3, suggesting a value of more than 1012 cm–3 in the active


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microdischarge region. Sakai et al. [123] emphasized that the CM-DBDsconfiguration had a rather low operating voltage (typically 1–2kV) since thescaling parameter pd was of the order of several tens of Pa �m, lying ataround the Paschen minimum. Note that the plasma in this system was stableover a wide range of external parameters without filamentation or arcing.

Another system that demonstrates an interesting behavior at a kilohartzrange, is so-called capillary plasma electrode (CPE) discharge [97,114]. Theoperating principle of this discharge is not well understood. The CPE dis-charge uses an electrode design, which employs dielectric capillaries thatcover one or both electrodes of a discharge device. Although the CPE dis-charge looks similar to a conventional DBD, the CPE discharge exhibits amode of operation that is not observed in DBDs, the so-called ‘‘capillary jetmode’’. The capillaries, with diameter in the range from 0.01 to 1mm and alength-to-diameter (L/D) ratio from 10:1 to 1:1, serve as plasma sources andproduce jets of high-intensity plasma at a high pressure. The jets emergefrom the end of the capillary and form a ‘‘plasma electrode’’. The CPEdischarge displays two distinct modes of operation when excited by a pulsedDC or AC. When the frequency of the applied voltage pulse is increasedabove a few kilohartz, one observes first a diffuse mode similar to the diffuseDBD as described by Okazaki [124]. When the frequency reaches a criticalvalue (which depends strongly on the L/D value and the feed gas), thecapillaries become ‘‘turned on’’, and bright intense plasma jets emerge fromthe capillaries. When many capillaries are placed in close proximity to eachother, the emerging plasma jets overlap and the discharge appears uniform.This ‘‘capillary’’ mode is the preferred mode of operation of the CPE dis-charge [97]. At this capillary mode, the CPE is similar to the ‘‘fused’’ hollowcathode (FHC) source [117]. At a high frequency even dielectric capillariescan work as hollow cathodes because for a capacitively coupled RF plasmain the gamma mode a dielectric surface is also a source of secondary emittedelectrons similar to metal cathodes in glow or HCDs.

In the RF frequency range (13.56MHz), a so-called plasma needle isunder intense investigations for potential medical applications [125](Fig. 42). This discharge has a single-electrode configuration and is opera-ting in helium. This type of plasma operates near the room temperature,allows the treatment of irregular surfaces, and has a small penetrationdepth. These characteristics give the plasma needle a great potential for usein the biomedical field. Experiments have shown that the plasma needle iscapable of bacterial decontaminations and localized cell removals withoutcausing a necrosis to the treated or neighboring cells. Areas of detached cellscould be made with a resolution of 0.1mm, indicating that the precision ofthe treatment can be very high. Plasma particles, such as radicals and ions aswell as emitted UV light interact with the cell membranes and cell adhesion


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molecules, therefore causing detachment of the cells. The penetration of theplasma radicals in liquid was also tested, where densities in a mM range wereobserved. In Kieft [125] the plasma needle was confined in a plastic tube,through which helium flow was supplied (Fig. 42). The discharge was foundto be entirely resistive; the measured voltage was in the range of140–270Vrms, resulting in an excellent agreement with results producedfrom modeling. From the resistance data, the electron density was estimatedto be 1017m–3. Optical measurements showed also a substantial UV emis-sion in the range of 300–400 nm. Active oxygen radicals (O and OH) weredetected. At low-flow speeds of helium, the density of molecular species inthe plasma was found to increase.

Typical RF discharges, both ICP and CCP, were also produced at mi-croscales at atmospheric pressure. These plasmas were non-equilibriummainly because of the small size of the systems. Reduction in size requires acorresponding reduction in wavelength, or an increase in frequency. Thus, aminiaturized atmospheric pressure ICP jet source was developed for a port-able liquid analysis system [126a]. The plasma device was a planar-type ICPsource (Fig. 43) that consisted of a ceramic chip with an engraved dischargetube and a planar metallic antenna in a serpentine structure. The chip con-sisted of two dielectric plates with an area of 15mm� 30mm. A dischargetube with a dimension 1mm� 1mm� 30mm (h/w/l) was mechanically en-graved on one side of the dielectric plate and a planar antenna was fabri-cated on the other side of the plate. An atmospheric pressure plasma jet witha density of approximately 1015 cm–3 was successfully produced using acompact very high frequency (VHF) transmitter at 144MHz and a power of50W. The electronic excitation temperature of Ar was found to be4000–4500K.

Ichiki et al. [126b] also developed a miniaturized VHF driven ICP jetsource for the production of high-temperature and high-density plasmas in a

FIG.42. Schematic drawing of the plasma needle (Left). Plasma generated by the plasma

needle (Right) [125].


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small space, and its application to localized and ultrahigh-rate etchings ofsilicon wafers. The plasma source consisted of a discharge tube of 1mm indiameter with a fine nozzle of 0.1mm in diameter at one end and a three-turn solenoidal antenna wound around it. The electron density of atmos-pheric pressure argon plasma jets blowing out from the nozzle was estimatedby means of an optical emission spectroscopy to be 1014–1015 cm�3. By theaddition of halogen gases into the downstream region of argon plasma jets,a high-speed etching of fine holes of several hundred micrometers in dia-meter was investigated. The highest etching rates of 4000 and 14mm/minwere obtained for silicon wafers and fused silica glass wafers, respectively.

Iza et al. [127] developed a low-power microwave plasma source based ona microstrip split-ring resonator (Fig. 44) that was capable of operating atpressures from 0.05Torr (6.7 Pa) to 1 atm. The microstrip resonator in theplasma source was operated at 900MHz. Argon and air discharges could beself-started with less than 3W in a relatively wide pressure range. An iondensity of 1.3� 1011 cm�3 in argon at 400mTorr (53.3 Pa) could be pro-duced using only 0.5W power. Atmospheric discharges could be sustainedwith 0.5W in argon. This low power allowed a portable air-cooled oper-ation. Continuous operation at atmospheric pressure for 24 h in argon at1W showed no measurable damage to the source. This kind of microplasmasources can be integrated into portable devices for applications such as bio-MEMS sterilization, small-scale materials processing and microchemicalanalysis systems.

The electrical discharges in the highest frequency range obtained in labo-ratory conditions is optical. Thus, optical discharges or so-called lasersparks are always microdischarges, as they are formed in the focus of a lensthat concentrates the laser light [3]. This kind of discharges was intensely

FIG.43. Photo of the miniaturized ICP jet source [126a].


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studied in 1970s when powerful pulsed lasers were developed, and very longlaser sparks of several meter length were produced. Then continuous opticaldischarges were produced using CO2 lasers. Researches tried to clarify thebreakdown conditions at an optical frequency. The breakdown voltage wasfound to decrease with increasing wavelength (in a good agreement with thetheories of bremsstrahlung absorption and photoionization (see [1]) anddecreased significantly if gas was contaminated with dust particles.

To conclude this section, we want to emphasize again that microplasmasin most cases are very similar to conventional low-pressure plasmas butscaled-down according to the pd similarity law. In addition to this similarity,microplasmas have their peculiarities related to an increased power andelectron density that can be balanced by diffusive losses only partially. Thisresults in a temperature increase in scaled-down systems. Competition be-tween three- and two-body processes as well as the competition with diffu-sion losses can result in a significant change in plasma compositions in thescaled-down systems. The comparison of microplasmas with similar macro-scale atmospheric pressure plasmas shows that the former should have alower gas temperature; sheathes in microplasmas can occupy a significantportion of the volume; and breakdown conditions are close to the Paschencurve minimum, or even are on the left side of it. Very often microdischargeshave a positive differential resistance that is very important from the prac-tical standpoint. In addition, almost always microplasmas are far from thethermodynamic equilibrium.

IX. Gliding Discharges (GD) and Fast Flow Discharges

Both conventional thermal and non-thermal discharges cannot simulta-neously provide a high level of non-equilibrium, high electron temperature

FIG.44. Ar plasma at 1W. (a) View of the device operating at 9Torr (1.2 kPa); (b) Close-

up view of the diffuse plasma at 20Torr (2.67 kPa); (c) Close-up view of the confined plasma at

760Torr (101.3 kPa) [127].


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and a high electron density. However, most prospective plasma-chemicalapplications require both: a high power for an efficient reactor productivityand a high degree of non-equilibrium to support selectively chemical proc-esses. Thus, one of the challenges of the modern plasma chemistry is tocombine the advantages of thermal and non-thermal plasma systems.Powerful and high-pressure discharges that can generate non-equilibriumplasma can be applied to various industrial problems, such as large scaleexhaust gas cleaning, pollution control, fuel conversion, hydrogen produc-tion and surface treatment.

One of the possible ways to create such a hybrid plasma is to use a non-stationary transient type of discharges that evolve during a cycle from aquasi-equilibrium to a strongly non-equilibrium discharge with a still rel-atively high level of electron density. Traditionally, this kind of discharge iscalled a gliding arc (GA) [128–130], although it is not an arc at all. There-fore, we will use a more general name gliding discharge (GD). Because of thehigh electron density during the non-equilibrium stage of the GD evolution,the GDs are very effective for the above-mentioned plasma-chemicalapplications.

Conventional GD, traditionally called GA, is an auto-oscillating periodicphenomenon developing between at least two diverging electrodes sub-merged in a laminar or turbulent gas flow. Self-initiated at the upstreamnarrowest gap, the discharge forms the plasma column connecting the elec-trodes of opposite polarity. This column is further dragged by the gas flowtoward the diverging downstream section. The discharge length grows withincreasing distance between electrodes until it reaches a maximal possiblevalue, usually determined by a power supply unit [128]. After this point thedischarge extinguishes but momentarily reignites itself at the minimum dis-tance between the electrodes and a new cycle starts. A photograph of a GAdischarge taken by a regular camera can be seen in Fig. 45. With the help ofa high speed camera one can see the evolution of the discharge at it is shownin Fig. 46.

The conventional ‘‘flat’’ GA (Fig. 45) starts as an electrical breakdown ina narrow gap between two diverging electrodes in a gas flow when theelectric field in this gap reaches approximately 3 kV/mm in air [3]. Thecurrent of the arc increases very fast and the voltage on the arc drops. If thegas flow is strong enough, it forces the arc to move along the divergingelectrodes and to elongate. The growing arc demands more power to sustainitself. At the moment when its resistance becomes equal to the total externalresistance, the discharge consumes one half of the power delivered by thepower supply. This is the maximum power that can be transferred to the arcfrom a constant voltage power supply with serial resistor. Taking into ac-count that thermal arcs consume energy proportionally to their length


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independently on wide-range current variations, one can conclude that GAshould not sustain the elongation beyond this ‘‘critical point’’. Experimentaland theoretical studies [130] showed that in case of a relatively low current,when properties of the GD were far from the properties of thermal arc, GDcould elongate further (so-called an ‘‘overshooting effect’’), because non-equilibrium GD consumed less energy with a current reduction. Also, incontrast to thermal arcs which are cooled predominantly by a conductiveheat transfer [1], the non-equilibrium discharge is ‘‘ventilated’’ by draggingflow (i.e., convective cooling) and becomes wider and less bright (Fig. 46).

FIG.45. Gliding discharge in air [129].


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This ‘‘ventilated’’ relatively cold (‘warm’) discharge is the source of non-equilibrium plasma that can be used in a variety of applications. The non-thermal plasma channel keeps growing until an extinction closes a cycle. Thenext cycle starts immediately after the voltage reaches the breakdown value,usually just after the fading of the previous cycle. A typical repetition rate ofthe discharge is in the range of 10–100Hz, which changes with the gas flowrate: the higher the flow rate, the higher the frequency. During to the highrepetition rate of the GD it is visually observed as a quasi-uniform plasmalayer (Fig. 45).

FIG.46. Gliding discharge evolution shown with 5ms separation between snap shots [128].


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The GA discharge has recently been of great interest due to the co-existence of both equilibrium and non-equilibrium regimes and also its highpower. Many researchers studied the physical phenomena involved and triedto characterize the discharge itself [128,131,132,206]. Czernichowski et al.[132] carried out detailed spectroscopic and electrical measurements for aGA discharge in air, including vibrational and rotational molecular gastemperatures as well as electron temperatures. They reported that the dis-charge began as a quasi-equilibrium discharge with the vibrational temper-atures ranging from 2300–4000K and the electron temperature of about6000K. In the non-equilibrium regime, they found these values to be800–2100K for the translational and rotational temperatures, 2000–3000Kfor the vibrational temperature and 10,000 for the electron temperature.Mutaf-Yardimci et al. [128] studied GAs over a wide range of gas flow ratesand powers to investigate the thermal and non-thermal regimes. The non-equilibrium plasma was observed for low currents and high gas velocities,while the quasi-equilibrium plasma was observed for high currents and lowgas velocities. In addition, the transitional discharge was observed for mode-rate current and high gas velocities. Their gas temperature measurement forthe transitional GA was in the same range of that of Czernichowski.

Based on the experimental data, the evolution of the GA discharge in adiverging channel can be divided into three stages [128,133]: the initialbreakdown-stage, the equilibrium-stage and the non-equilibrium stage. TheGA was first used in chemical applications in the 19th century for the pro-duction of nitrogen-based fertilizers. It became popular again in the early1990s [134,135]. Recent applications involve gas conversion processes, suchas a methane partial oxidation [136] and carbon dioxide reforming [137] orsteam reforming [136,138,139] of methane to produce synthesis gas(CO+H2); an oxidation of low-concentration H2S into SO2 for pollutioncontrol [140,141]; and volatile organic compounds treatments for environ-mental protection [142].

To optimize the benefits of GDs, Karla et al. [143,144] proposed a novelreactor design, where the discharge was created and contained within avortical counter-current flow field (i.e., reverse vortex, ‘‘Tornado’’) (seeFig. 47). This system combined a high local gas velocity (necessary forconvective cooling of the GD) with a relatively high gas residence time in thesystem, providing extremely efficient gas mixing thus ensuring a uniformplasma treatment of the bulk gas flow. The ‘‘Tornado’’ plasma was pro-duced with different electrode configurations: with a spiral electrode(Fig. 48a and 48b); with a circular electrode and subsequent mechanicalelongation of the discharge length (Fig. 48c); and recently with a cup-shapedelectrode (Fig. 49). The system provides an excellent insulation of theplasma region from cold cylindrical walls of the reactor (Fig. 48c). The


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system with a mechanically elongated reactor length (Fig. 48c) was success-fully used for the process of hydrogen generation using a plasma-catalyticprocess of methane partial oxidation [129,145]. The plasma-catalytic processmeans that plasma is used as a volume catalyst, and the power spent for the

Gas in

Gas out

(b) Counter-current flow:axial-radial

velocity field

Gas in

(a) Vortex flow:circumferential

velocitycomponent

Nozzle forvortex flowformation

Gas out

FIG.47. Cylindrical reactor with vortical counter-current flow field (a) vortical velocity

field and (b) axial-radial velocity field.

Electrode 2

Connection wireto power supply

Plasmareactor

Circular ringelectrode

Gas out

Spiral shapeelectrode

Free endof spiral

electrode

a b c

FIG.48. Gliding discharge in a cylindrical reactor with vortical counter-current flow field.

(a) scheme with a spiral electrode; (b) photo image of GA in the system with a spiral electrode;

and (c) photo image of the system with movable circular electrode and with mechanical elon-

gation of GA [143].


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plasma generation is insignificant in comparison with the chemical power ofthe process. Available data show that the gliding discharge in such a systemis non-equilibrium, and the cathode current is supported by the secondaryelectron emission like in the case of APG [101].

Figure 49 demonstrates a promising and novel scheme of designing a GDreactor with a vortical counter-current flow that was recently produced atthe Drexel Plasma Institute. This reactor does not have any obstacles forthe vortical flow and has relatively massive electrodes that are outside thereaction zone, thus preventing them from being overheated. This reactordesign consists of two major metal parts: a cylindrical cup, which is the firstelectrode; and a flat round diaphragm that covers the cup, which acts as thesecond electrode. Gas flow entering tangentially between these electrodeselongates the GA that originates in the shortest gap between the two elec-trodes, to the maximal possible length, where the arc becomes strongly non-equilibrium. After that, the length of the non-equilibrium GD can stabilize,in that case electrode spot trajectories will be circular. Otherwise, GD elon-gation by a vortical flow will result in a GD extinction in a cycle and animmediate initiation of the next cycle. Converted gas products flow out ofthe reactor through the diaphragm of the second electrode.

1

2

3

4

5

6

(A)

(B)

FIG.49. Left: Gas and gliding discharge motion in the counter-current vortex reactor with

cup-shaped and diaphragm electrodes. (1) metal cup electrode; (2) diaphragm electrode; (3)

gliding arc initiation; (4) fully elongated gliding arc; (5) trajectories of the electrode spots; and

(6) external and internal spirals of gas motion. Right: Picture of the gliding discharge in this

reactor made through transparent lid of the cap electrode. It is possible to see the trajectories of

electrode spots motion on diaphragm and cap electrodes.


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The GD shown in Figs. 48 and 49 can be called a gliding discharge intornado (GDT). GDT system has two major advantages important in manyplasma-chemical applications that other plasma systems do not have

1. Non-equilibrium ‘‘warm’’ plasma that provides easily controllablelocal temperatures that can be in the optimal range for a particularchemical process (e.g., methane partial oxidation [129]) and a highradical concentration without system overheating.

2. Effective internal recuperation of heat and chemical energy with anexcellent reagent mixing in a counter-current flow [146,147].

These advantages made the GDT attractive for several plasma-chemicalprocesses in the hydrogen production. Several processes based on GDTsystems have already been developed, and some are still under development:methane partial oxidation [129], ignition and combustion support [148], H2Sdissociation, solid biofuel conversion to syn-gas, on-board hydrogen-richgas production, on-board decarbonization of liquid fuel, etc. In short, non-equilibrium GDs, especially in an appropriate geometry, are very promisingfor various plasma chemical applications.

The lower the discharge power, the easier the discharge can be cooled (i.e.,stabilized in the non-thermal state) by a convective flow. Akishev at al. [98]reported that a non-contracted (diffuse) regime of APG in a pin-to-planegeometry (DC polarity is opposite to that used by Staack et al. [101], seesection VIII.A) with the gap size of 12–15mm were supported by airflowwith a velocity of 55m/s. By varying the discharge current they could showthat it was possible to make a smooth transition from a negative corona to asteady-state diffusive glow discharge. This discharge precedes the spark. Insome cases, a transient spark can be followed again by a glow discharge, butin this case the glow discharge is not diffusive – it has a constricted orfilamentary form [98] (similar to that demonstrated in Fig. 31). We also havetested this discharge geometry in helium atmosphere (see Section VIII.A)and found that it is possible to avoid the spark formation at all and to makea smooth transition from the diffuse mode of the glow discharge to theconstricted one.

In a powerful fast flow discharge, the flow speed reaches several hundredmeters per second, often larger than the speed of sound. These dischargescan also provide a high power with a high non-equilibrium, similar to glid-ing discharges. Fast flow discharges have not been studied very extensivelybecause of technical difficulties, but experimental studies on moderate pres-sure microwave discharges for various plasma-chemical applications[149–151], glow discharges for laser active media creation [152], and DCdischarges for flame ignition and stabilization [153,154] have been con-ducted.


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X. Plasma Discharges in Water

A. NEEDS FOR PLASMA WATER TREATMENT

The rising concern associated with the availability of potable water is anissue that has paralleled the continual increase in global population andinternational development. From a global perspective, an estimated 1.1 bil-lion people are unable to acquire safe drinking water [155]. The need forimproved methods of water treatment exists on both a political andhumanitarian dimension, and is evident within the populations of develop-ing countries and industrialized nations. Contaminated water can beattributed to a number of factors, including chemical fouling, inadequatetreatment and deficient or failing water treatment and distribution systems.An additional cause of contamination is the presence of untreated bacteriaand viruses (collectively termed microorganisms) within the water. Specificcauses and cases of illness and death have been attributed to the inadvertenthuman ingestion of these microorganisms.

As estimated by the Environmental Protection Agency (EPA), nearly35% of all deaths in developing countries are related directly to contami-nated water [156]. In addition, densely populated areas within these coun-tries have rendered public treatment and distribution systems inadequate bydissipating the associated water pressure to a level that is unable to supportdaily consumption. For this reason, growing populations have implementedindividual water collection, water storage and water distribution units tosupport their needs, including rooftop tanks and surface water collectionsystems. The non-circulatory nature of these units is conducive to stagnationand increased bacterial growth, and contributes to unsafe water consump-tion. Well water systems are a more viable means of accessing safe drinkingwater, though the water tables that support these systems are not imper-vious to contamination. The increased presence of Escherichia coli (E. coli),along with various other bacteria within some areas of the United States,has been a cause for national concern [157]. In an effort to inactivate thesebacteria, successful experiments and commercial applications of chemicaltreatments, ultraviolet radiation and ozone injection units have been devel-oped and implemented into potable water delivery systems.

The experimental success and commercialization of these water treatmentmethods are not, however, without deficiencies. With regard to humanconsumption, chemical treatments such as chlorination can render potablewater toxic [158]. Ultraviolet radiation and ozone injection have also beenproven to be two practical methods of bacterial inactivation in water, butthe effectiveness of such methods largely depends upon adherence to regi-mented maintenance schedules. It is because of these deficiencies that the


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importance of research and development of new and improved potable wa-ter treatment systems continues to grow. Therefore improvements in watertreatment methods, especially point-of-use water treatment systems, arebecoming progressively more important both nationally and internationally.

The objective of the present section was to present technical issues in-volved in the development of a point-of-use water treatment system capableof inactivating waterborne microorganisms commonly found in drinkingwater through the implementation of plasma technology. The scope of thesolution should be capable of accommodating the demands associated withdaily household water consumption, have the ability to be integrated intomost domestic and foreign household water delivery systems, and be ableto operate in accordance with drinking water standards developed andemployed by the EPA [159].

B. CONVENTIONAL METHODS FOR DRINKING WATER TREATMENT

Currently, there are many available methods of water treatment and de-contamination, including chlorination, ozonation, UV lamps, in-line filtersand pulsed electric fields. Many of these systems are utilized in large in-dustrial applications; however, other methods such as chlorination, in-linefiltering and UV lamps are applied in point-of-use applications, includingtreatment of well water. These methods have distinct advantages and dis-advantages and were carefully analyzed and considered below.

With regard to water disinfection, chlorine remains both an accepted andwidely employed method of treatment. Chlorine is used to treat drinkingwater supplies due to its ease of use and associated efficiency regarding theinactivation of microorganisms. Regardless of system size, it is one of theleast expensive disinfection methods; however, its toxicity requires strictadherence to accepted concentration levels. An excess of chlorine in adrinking water supply could render the water toxic with regard to humaningestion. Unwanted byproducts resulting from the interaction of chlorinewith other chemicals present in the water can prove corrosive and deteri-orative to the system [160]. In addition, because a chlorination based systemmust be continually replenished, the storage and transportation of thischemical becomes a significant hazard.

In-line filters are commonly used to remove undesirable substances fromwater. Many different types are commercially available, including carbon fil-ters, microfilters and reverse osmosis filters. The key advantage to these filtersis that they require no power to operate, but there are two significant draw-backs to this method. Though these filters are capable of preventing micro-organisms from passing through the system, they are incapable of inactivatingthem leading to bacterial growth in the filters. The small pores needed to trap


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microorganisms also inhibit the flow, resulting in pressure loss across the filter.Significant pressure losses in the system require larger pump selection.

The final method considered for inactivating microorganisms is pulsedelectric field technology. Since the electric field associated with this tech-nology is not strong enough to initiate electrical breakdown in water, thereis no resulting discharge. The mechanism of electroporation caused by theelectric fields effectively deactivates microorganisms. In electroporation, theelectric field creates holes in the membrane of the cell, causing an influx ofwater and cell explosion. At nominal conditions, the energy expense for atwo-log reduction is approximately 30,000 J/L [161]. Researchers at theTechnical University of Hamburg, Germany reported pulsed electric fieldeffects on suspensions of bacteria in water [162]. They reported that theexternal electric pulse produced a membrane potential of more than 1.0Vfor the effective killing of bacteria (see Fig. 50). The mechanism of thepulsed electric field is reported as an electroporation, creating small pores oncell membrane, thus killing bacteria.

Ozonation and UV lamps can be considered as plasma methods of watertreatment and are discussed in the following sections.

C. WATER TREATMENT USING PLASMA DISCHARGE

When an electric field between two electrodes exceeds the breakdownvalue of the medium, the medium is ionized creating a plasma channel. Theplasma discharge not only generates UV radiation, but converts surround-ing water (H2O) molecules into active radical species due to high energylevels. The microorganisms are effectively inactivated when oxidizedthrough contact with active radicals. The chemical kinetics of this inacti-vation remains an area of significant research [163]. Various active speciescan be considered the byproducts of plasma discharge in water. The pro-duction of these species by plasma discharge is affected by several param-eters such as the applied pulse peak voltage, polarity, rise time and width,electrode tip curvature radius, and water properties such as the composition,pH and electrical conductivity [164].

Among these active species, hydroxyl radical, atomic oxygen, ozone andhydrogen peroxide are the most important for sterilization and the removalof unwanted organic compounds in water. In terms of oxidation potential,the hydroxyl radical (2.8 V) is the most powerful, followed by atomic oxygen(2.42V), ozone (2.07V) and hydrogen peroxide (1.78V) [164]. Note thatfluorine has the highest oxidation potential of 3.03V, whereas chlorine hasan oxidation potential of only 1.36V.

In addition to the aforementioned active species, the electrical breakdownin water produces ultraviolet radiation (both VUV and UV) which is useful


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for water treatment. Below, a brief review will be given on UV radiation andozone (i.e., the most well-known active species).

1. Ultraviolet (UV) Radiation Treatment of Water

UV radiation has proven to be effective in decontamination processes and isgaining popularity particularly in European countries because chlorinationleaves undesirable byproducts in water. Measurement of this radiation is con-sidered in terms of dosage, and is the product of intensity [W/cm2] and contacttime (s). Most bacteria and viruses require relatively low UV dosages forinactivation, which is usually in a range of 2000–6000mWs/cm2 for 90% kill.For example, E. coli requires a dosage of 3000mWs/cm2 for a 90% reduction[165]. Cryptosporidium, which shows an extreme resistance to chlorine requiresan UV dosage greater than 82,000mWs/cm2. The criteria for the acceptabilityof UV disinfecting units include a minimum dosage of 16,000mWs/cm2 and amaximum water penetration depth of approximately 7.5 cm [166].

UV radiation in the wavelength range from 240 to 280 nm causes irrep-arable damage to the nucleic acid of microorganisms. The most potentwavelength for DNA damage is approximately 260 nm. Currently, there are

FIG.50. Induction of a transmembrane potential in a cell exposed to an external electric

field [162].


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two types of commercial UV lamps: low-pressure and medium-pressuremercury lamps. The former produces a narrow band of UV light with a peaknear the 254-nm wavelength, whereas the latter produces a broader band ofUV and has a much greater treatment capacity, approximately 25 times[165]. The life of a UV lamp is relatively short, approximately 8000–10,000 hand requires periodic replacement. Effectiveness of this treatment method iscompromised by several additional factors, including biological shieldingand chemical or biological film buildup on the lamp. An advantage of thissystem is that the temperature and pH of the treated water are not signifi-cantly affected and no undesirable products are created [167].

The UV photons can have two possible effects on a microorganism. Oneeffect is through direct collision with the contaminant causing mutation ofthe bacterial DNA. This prevents proper cellular reproduction and effec-tively inactivates the microorganism. Alternatively, the photons can providethe necessary energy to ionize or dissociate water molecules, thus generatingactive chemical species. Both mechanisms increase deactivation of viablemicroorganisms [168]. Recently, it is suggested that the UV system producescharged particles in water such that charge accumulation occurs on theouter surface of the bacterial cell membrane. Subsequently, the electrostaticforce overcomes the tensile strength of the cell membrane, causing its rup-ture at a point of small local curvature as the electrostatic force is inverselyproportional to the local radius square. Note that since the membrane ofgram-negative bacteria such as E. coli often possesses irregular surfaces, UVdisinfection becomes more effective to the gram-negative bacteria than togram-positive ones [169–171].

Researchers at Macquarie University, Australia studied new ultravioletlight sources for the disinfection of drinking water and recycled wastewater[172]. They reported that UV lamps were much more effective than chlorinein dealing with the hundreds of potentially dangerous types of microbes inwater, including the well-known Giardia and Cryptosporidium. The UV ra-diation did not blow the microbe apart as such. Instead, it entered throughthe outer membrane of the bug into the nucleus and actually cut the bondsof the DNA so that the bug could not repair itself and could not reproduce.

2. Ozonation of Water

Ozone is one of the most well-known active chemical species. Ozonation isa growing method of water treatment; ozone gas is bubbled into a contami-nated solution and dissolves in it. The ozone is chemically active and iscapable of efficiently inactivating microorganisms at a level comparable tochlorine. The existence time of the ozone molecules in the solution dependson temperature. At high temperatures ozone decomposition to molecular


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oxygen is taking place faster. Solutions maintained at lower temperaturestend to have faster deactivation times when compared to solutions main-tained at higher temperatures. Achieving a four-log reduction at 20oC withan ozone concentration of 0.16mg/L requires an exposure time of 0.1min[173]. At higher temperatures and pH levels, ozone tends to rapidly decayand requires more exposure time. During to the corrosive and toxic natureof ozone, ozonation systems require a high level of maintenance.

Plasma discharge has been used for the production of ozone in the pastseveral decades to kill microorganisms in water. Ozone has a lifetime ofapproximately 10–60min, which varies depending on pressure, temperatureand humidity of surrounding conditions. Because of the relatively long life-time of ozone, ozone gas is produced in air or oxygen, stored in a tank andinjected to water. Of note is that hydrogen peroxide is also produced whenozone is produced in a plasma discharge in humid air. However, the half lifeof the hydrogen peroxide is much shorter so that it could not be used forconventional water treatment systems.

The feasibility of using ozonation also was tested for the ballast watertreatment for large ships. Drasund et al. [174] reported Ct values for variousorganisms. Note that the Ct value is defined as the product of ozone con-centration C [mg/L] and the required time t [min] to disinfect a microorgani-sm in water. For example, for Ditylum brightwelli – important ballast waterspecies, the Ct value was 50mgmin/L. In other words, if the ozone concen-tration is 2mg/L, it takes 25min of contact time to disinfect this organism inballast water. They reported that ozone reacted with seawater and produceda number of corrosive compounds (mostly compounds of chlorine). The longcontact time between ozone and organisms is beneficial for the disinfection oforganisms but harmful in the corrosion of ballast tank. However, the half lifeof ozone is relatively short such that the corrosion threat may not last verylong. One of the reasons why the ozone has not been used widely in the watertreatment system in the U.S. is a relatively high cost of producing ozone,which requires dry air or concentrated oxygen supply, compressor, ozone gasinjection system and electricity. Furthermore, if ozone gas is accumulated in aclosed space by accident, it can be highly toxic to human.

D. PRODUCTION OF ELECTRICAL DISCHARGES IN WATER

In order to generate electrical discharges in water, one needs to have apulsed high voltage power supply. Electric discharges in water usually startfrom sharp electrodes. If the discharge does not reach the second electrode itis called pulsed corona discharge using analogy with discharges in gases (seeSection IV), and branches of such a discharge are called streamers, thoughthe nature of the discharges in liquids is much less understood than that for


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gaseous discharges. If a streamer reaches the opposite electrode a spark isforming. If the current through the spark is very high (above 1 kA), thisspark is usually called a pulsed arc.

Various electrode geometries have been used for the generation of theplasma discharge in water for the purpose of water treatment. Two of thesimplest geometries are shown in Fig. 51, which are a point-to-plane ge-ometry and a point-to-point geometry. The former is often used for pulsedcorona discharges, whereas the latter is often used for pulsed arc systems.

One of the concerns in the use of the point-to-plane geometry is the adverseeffect of the tip erosion. In a needle-to-plane geometry a large electric fieldcan be achieved due to the sharp edge of the needle with a minimum appliedvoltage V. For a sharp parabolic tip of the needle electrode, the theoreticalmaximum electric field at the needle electrode tip can be given as [3]

Emax ffi2V

r lnð2d=rÞ (54)

where r is the radius of curvature of the needle tip and d a distance betweenthe needle and the plane electrode when the needle is positioned perpendi-cular to the plane. The above equation indicates that the electric field near theelectrode tip will decrease with increasing radius of curvature of the tip.Sunka et al. [175] pointed out that the very sharp tip anode would be quicklyeroded by the discharge and one had to find some compromise between theoptimum sharp anode construction and its lifetime for extended operations.Sunka et al. [175] proposed a coaxial reactor, which consisted of a 6-mmdiameter stainless steel wire anode and a long stainless steel tubule cathode of30-mm inside diameter. In particular, the anode wire was spray-coated by athin (0.2–0.3mm) layer of porous ceramics whose electric conductivity was

HV HV

(A) (B)

FIG.51. Sketches of two simple geometries for plasma discharge in water.


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about 1–3mS/cm. They reported that the ceramic layer increased the electricfield strength on the anode wire surface due to the redistribution of the fieldinside the interelectrode space during the pre-breakdown stage, thus genera-ting a large number of discharge channels, i.e., hundreds of streamers duringeach voltage pulse. Note that the parts of metal electrode will be vaporized inthe case of arc discharges in water, and these metal ions are believed tocontribute to the formation of thermal plasma in water [163].

Another concern in the use of pulsed corona discharges is the limitationposed by the electrical conductivity of water on the production of suchdischarges [175]. In the case of a low electric conductivity of water below10 mS/cm, the range of the applied voltage that can produce a corona dis-charge without sparking is very narrow. On the other hand, in the case of ahigh electric conductivity of water above 400 mS/cm, streamers become shortand the efficiency of radical production decreases, and a denser and coolerplasma is generated. In general, the production of hydroxyl radical andatomic oxygen is more efficient at water conductivity below 100 mS/cm.Al-Arainy et al. [176] pointed out that for the case of tap water, the bulkheating was one of the problems in the use of corona discharges. Theyreported that at a frequency of 213Hz (i.e., a relatively high frequency), thetemperature of the treated water rose from 201C to 551C in 20min, indi-cating a significant power loss and extra loading to the pulse generator.

E. PREVIOUS STUDIES ON THE PLASMA WATER TREATMENT

Locke et al. [163] have recently published a comprehensive review on theapplication of strong electric fields in water and organic liquids with 410references. They explained in detail the types of discharges used for watertreatment, physics of the discharge and chemical reactions involved in thedischarge in water. Below, we introduce several research groups around theworld, who contributed in the study of plasma discharge for water treatment.

Schoenbach and his colleagues at Old Dominion University have studieda feasibility of the application of electrical pulses in the microsecond range tobiological cells for more than two decades [161,177–181]. They used a point-to-plane geometry to generate pulsed corona discharges for bacterial (i.e., E.coli or Bacillus subtilis) decontamination of water with a 600-ns, 120-kVsquare wave pulse. The wire electrode was made of a tungsten wire with75 mm diameter, 2 cm apart from a plane electrode. They reported that theconcentration of E. coli could be reduced by three orders of magnitude afterapplying 8 corona pulses to the contaminated water with the correspondingenergy expenditure of 10 J/cm3 (10 kJ/L). For B. subtilis, it took almost 30corona pulses with an energy expenditure of 40 J/cm3. There was no effect onB. subtilis spores.


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They explained the mechanism of the disinfection of microorganism asfollows: Plasma pulses cause the accumulation of electrical charges at thecell membrane, shielding the interior of the cell from the external electricalfields. Since typical charging times for the mammalian cell membrane are onthe order of 1 ms, these microsecond pulses do not penetrate into cells.Hence, shorter pulses in the nanosecond range can penetrate the entire cell,nucleus and organelles, and affect cell functions, thus disinfecting them.They used high voltage pulse generators to apply nanosecond pulses as highas 40 kV to small test chambers called cuvettes. Biological cells held in liquidsuspension in these cuvettes were placed between two electrodes for pulsing.The power density in these cuvettes was up to 109W/cm3, but the energydensity was rather low. Even under the most extreme conditions, it was lessthan 10 J/cm3, a value that could slightly increase the temperature of thesuspension by approximately 2oC.

Researchers at the Eindhoven University of Technology (The Netherlands)applied pulsed electric fields and pulsed corona discharges to inactivatemicroorganisms in water [182]. They used four different types of plasmatreatment configurations, which are a perpendicular water flow over two wireelectrodes, a parallel water flow along two electrodes, air-bubbling through ahollow needle electrode toward a ring electrode and wire cylinder. They used100 kV pulses (producing a maximum of 70kV/cm electric field) with a 10-nsrising time with 150 ns pulse duration at a maximum rate of 1000 pulse/s. Thepulse energy varied between 0.5 and 3 J/pulse and an average pulse power was1.5 kW with a 80% efficiency. Inactivation of microorganism was found tobe 85kJ/L per one-log reduction for Pseudomonas flurescens and 500 kJ/Lperone-log reduction for spores of Bacillis sereus. They found that coronadirectly applied to water was more efficient than pulsed electric fields. Withdirect corona, they achieved 25kJ/L per one-log reduction for both gram-positive and gram-negative bacteria.

Researchers at the General Physics Institute (GPI), Russian Academy ofSciences, Moscow, Russia used plasma systems to eradicate microorganismsin water-distribution systems, a task which is important in the control ofbiological fouling and the spread of diseases. They used a pulsed electricdischarge system to kill bacteria in potable and wastewaters and at con-taminated surfaces. Microbes including E. coli and coliphages have beentreated by pulsed electric discharges generated by the novel multielectrodeslipping surface discharge (SSD) system. NATO funded a program of workat GPI to develop a novel portable decontamination system for water usingplasma UV technologies [173]. Anpilov et al. [173,183] reported multisparkelectric discharges in water excited along multielectrode metal-dielectricsystems with gas supply into interelectrode gaps. They concluded that theactive species of UV, ozone and hydrogen peroxide effectively sterilized


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bacteria in water. The energy cost of production of one H2O2 molecule intheir system was approximately 150 eV.

Sato and his colleagues at Gunma University (Japan) reported that theycould use plasma discharges in water for the sterilization and removal oforganic compounds such as dyes [181,184–187]. Fig. 52 shows the genera-tion of pulsed plasma discharge in water and the measurement technique.The streamer discharge was produced from a point-to-plane electrode,where a platinum wire in a range of 0.2–1mm in diameter was used for thepoint electrode, which was positioned 1–5 cm from the ground plane elec-trode. Note that they used two types of spark gaps: a triggered spark gap(EG&G Inc. Type GP-22B) with a trigger module (Model TM-11A) and arotating spark gap producing a 50Hz pulse repetition frequency. Theystudied the formation of chemical species from pulsed plasma discharges inwater and their effects on microorganisms. They reported that the hydroxylradicals had extremely short lifetime of 70 ns and diffused only 20 nm beforethey were absorbed in water. They reported that hydrogen peroxide wasproduced through a recombination of hydroxyl radicals, not by electrolyticreaction. They measured the hydrogen peroxide concentration using Glu-cose C II Test Wako method with selective H2O2 scavenger and hydroxylradicals by emission spectroscopic analysis of the discharge light.

They reported an emission spectrum between 200 and 750 nm using anUnisoku USP-500 multichannel analyzer (MA) for the pulsed dischargein distilled water as shown in Fig. 53 [184]. The largest peaks were in the

FIG.52. Pulsed plasma discharge in water and measurement of hydrogen peroxide con-

centration using emission spectroscopic analysis of the discharge light, Sato et al. [184].


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short-wavelength (UV) section of the spectrum, which were believed to bemolecular emissions from hydroxyl radical. Since they used a platinummetal wire for the needle electrode, and if an erosion of the needle took placeduring the discharge, it would have been at an atomic emission line of306.5 nm. Hence, they conducted a study by adding 500mM of 2-propanolto the water and found that the peak at 310 nm disappeared, thus confirmingthat the peak shown in the spectra was indeed from the hydroxyl radical.

Akiyama and his colleagues at Kumamoto University (Japan) studied apossibility of using streamer discharges in water using a wire-to-plane elec-trode configuration, producing high energy electrons, ozone, other chem-ically active species, ultraviolet radiations and shock waves [188–190].A thin wire electrode was placed in parallel with a plane electrode to pro-duce a large volume of streamer discharges. In particular, they produced alarge-volume streamer discharge system for industrial water treatment usinga Marx bank to supply pulsed high voltage of 120–480 kV between twoelectrodes. They studied the mechanism of streamer discharges in water andthe effect of polarity, water conductivity, electrode geometry and hydro-static pressure on the streamers in water. Streamers from a negative pointelectrode (i.e., cathode mode) was more bushy than that from a positivepoint electrode (i.e., anode mode), and streamers from a positive pointelectrode were more filamentary. In both cases, an arc discharge occurredafter the streamer discharges arrived at the plane electrode. The influence ofthe electric conductivity of water on streamer discharges was found to be

FIG.53. Emission spectra from pulsed streamer discharge in distilled water with applied

voltage of 14 kV [184].


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small, and therefore they speculated that bulk heating via ionic currentcontributed little to the initiation of the breakdown process. The uniformityof the streamer discharge depended on the water conductivity, electrodeseparation distance and applied voltage.

Researchers at the University of Wisconsin-Madison (Center for Plasma-Aided Manufacturing) studied the feasibility of using dense medium plasmareactor for the disinfection of various waters [191,192]. The plasma reactorconsisted of a rotating upper electrode at a range of 500–5000 rpm and ahollow conical cross-sectional end piece. The upper electrode had a disc withceramic pin array, and the distance between the pin array and the lowerelectrode could be varied by a screw system. The reactor could be operatedin a batch mode or in a continuous mode. The advantage of the rotating theelectrode was that the rotating action spatially homogenized the multiplemicroarcs, activating a larger effective volume of water. In addition, spin-ning the upper electrode also simultaneously pumped fresh water andvapors into the discharge zone. They showed that the ultraviolet radiationemitted from the electrohydraulic discharge was the lethal agent that inac-tivated E. coli colonies rather than the thermal/pressure shocks or the activechemical species [191–194].

Researchers at the California Institute of Technology developed an elect-rohydraulic discharge reactor. A typical operational condition included adischarge of a 135mF capacitor bank stored energy at 5–10 kV through a 4-mm electrode gap within 40 ms with a peak current of 90 kA [193–195]. Theystudied the survival of E. coli in aqueous media exposed to the above elect-rohydraulic discharges. They reported the disinfection of 3L of a4� 107 cfu/mL E. coli suspension in 0.01M PBS at pH 7.4 by 50 consec-utive electrohydraulic discharges.

Researchers at Pennsylvania State University produced UV radiation us-ing a point-to-plane configuration, where 0.025-mm tungsten wire and cop-per blocks were used for two electrodes [196,198]. A 14-mF capacitor rated at20 kV was used as the energy storage device. They reported that for a storedcapacitor energy of 1500 J, 420 J (� 28%) was converted to the UV radiationwith a peak radiant power of 200MW. They found the maximum efficiencyof radiation at a length of the discharge channel of approximately 3.8 cm.

Researchers at Ebara Research studied the roles of shock waves, ultra-violet emissions and radicals that were created from a pulsed plasma dis-charge when a pulsed high voltage was applied to electrodes submerged inwater (see Fig. 54). The characteristics of the pulsed discharge included highefficiency, no change in temperature and safety for the environment due toits being chemical-free. This technique has many applications such as thedisinfection of microorganisms and the decomposition of toxic chemicals inwater, and the modification of sludge [199].


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Commercial systems to apply plasma discharges directly to water are avail-able fromDynawave [197] and Actix, which are typically known as high energypulsed plasma (HEPP) systems. Compared to the non-thermal plasma dis-charges, these systems for the water treatment have the following drawbacks:

1. Thermal plasma (high-temperature plasma) – a risk of high erosion ofelectrodes, not very effective in the generation of radicals.

2. Very high pressure – it requires high pressure protection, safety con-cern for the application to ordinary piping system.

3. Use of chemicals – these systems use small amounts of coagulant andpolymer. Continuous supply of such chemicals may be a problem ifthe plasma water treatment is for a point-of-use application.

4. Large residence time in a clarifier – this requires a large treatmenttank, which is not practical to many applications.

F. MECHANISM OF PLASMA DISCHARGES IN WATER

When one considers the mechanism of plasma discharge in water, therecan be two different approaches as shown in Table VI. The first approach isto divide electrical breakdown in water to a bubble process and an electronicprocess [188]. The second approach is to classify into partial electrical dis-charge and a full discharge such as arc or spark.

FIG.54. Pulsed-discharge phenomena in water obtained using two electrodes submerged

water at Ebara Research [199].


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In the first approach, the bubble process starts from a microbubble whichis formed by the vaporization of liquid by a local heating in the strongelectric field region at the tips of electrodes. The bubble will grow and anelectrical breakdown takes place within the bubble. In this case, the cavi-tation mechanism is suggested for the slow bush-like streamers [200,201].The appearance of bright spots is delayed from the onset of the voltage, andthe delay time tends to be greater for smaller voltages. The time lag to waterbreakdown was found to increase with increasing pressure, supporting thebubble mechanism in a sub-microsecond discharge formation in water[202,203]. The time to form the bubbles was 3–13 ns, depending on theelectric field and pressure [188]. The influence of the water electrical con-ductivity on discharges in water was found to be small [188]. Hence, bulkheating via ionic current does not contribute to the initiation of the break-down process. The power necessary to evaporate the water during thestreamer propagation can be estimated using the streamer velocity, the sizeof the streamer and the heat of vaporization [190]. Using a streamer radiusof 31.6 mm, a power of 2170 kW was obtained, which must be released into asingle streamer to ensure its propagation in the form of vapor channels. Incase of multiple streamers, the required power can be estimated by multi-plying the number of visible streamers to the power calculated for a singlestreamer.

In the electronic process, electron injection and drift in liquid take place atthe cathode, while hole injection through a resonance tunneling mechanismoccurs at the anode [189]. In the electronic process, breakdown occurs whenan electron makes a suitable number of ionizing collisions in its transitacross the breakdown gap.

In the second approach, electrical discharges in water are divided intopartial electrical discharges and arc and spark discharge [163,184–196, 198]as summarized in Table VII. In the partial discharge the current is trans-ferred by slow ions, producing corona-like discharges, i.e., non-thermalplasma. For a case of high electrical conductivity water, a large dischargecurrent flows, resulting in a shortening of the streamer length due to thefaster compensation of the space charge electric fields on the head of thestreamer. Subsequently, a higher power density, i.e., a higher plasma

TABLE VI

TWO APPROACHES IN THE MECHANISM OF PLASMA DISCHARGE IN WATER

First approach Second approach

Bubble process Partial discharge (corona-like)

Electronic process Arc or spark


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TABLE VII

SUMMARY OF THE CHARACTERISTICS OF PULSED CORONA, PULSED ARC, AND PULSED SPARK [163,

184–196, 198]

1. Pulsed corona� Streamer channels are produced in water� Streamer channels do not propagate across the entire electrode

gap, i.e., partial electrical discharge� Streamer length� order of centimeters; channel width

� 10–20 mm� The current is transferred by ions� Non-thermal plasma� Weak to moderate UV generation� Relatively weak shock waves are produced� Treatment area is limited at a narrow region near the corona

discharge� A few joules per pulse, often less than 1 J per pulse� Operating frequency is in a range of 100–1000Hz� Relatively low current, i.e., peak current is less than 100A.� Electric field intensity at the tip of electrode is 100–10,000 kV/

cm.� A fast-rising voltage on the order of 1 ns, but less than 100 ns.

2. Pulsed arc� The current is transferred by electrons� Almost thermal plasma� An arc channel generates strong shock waves within cavitation

zone� High current filamentous channel bridges the electrode gap� Channel propagates across the entire electrode gap� The gas inside channel (bubble) is ionized� Strong UV emission and high radical density are observed, but

short lived� A smaller gap between two electrodes of � 5mm is needed

than that in pulsed corona� Light pulse from spark discharge includes � 200 nm wave-

length, UV range� Time delay between voltage pulse increase and spark forma-

tion depends on both capacitance size and electric conductivityof water

� Large energy discharges greater than 1 kJ per pulse, desired forwastewater treatment


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density, in the channel is obtained, resulting in a higher plasma temperature,a higher UV radiation, and the generation of acoustic waves. In the arc orspark discharges, the current is transferred by electrons. The high currentheats a small volume of plasma in the gap between the two electrodes,generating an almost thermal plasma, where the temperatures of electronsand heavy particles are almost equal.

When a high voltage–high current discharge takes place between twosubmerged electrodes, a large part of the energy is consumed on the for-mation of a thermal plasma channel. This channel emits UV radiation andits expansion against the surrounding water generates an intense shock wave[175]. These pressure waves can have one of two effects. First, they candirectly interact with the microorganism causing it to explode. Alternatively,the pressure waves can dissociate microorganism colonies within the liquid,thus increasing their exposure to aforementioned inactivation mechanisms.

For the corona discharge in water, the shock waves are often weak ormoderate, whereas for the pulsed arc or spark the shock waves are strong.Locke et al. [163] explained that the reason why the arc and spark producesuch strong shock waves is that the energy input is much higher than that inthe corona. Similarly, between the arc and spark, the arc produces muchgreater shock waves than the spark due to its higher energy input. The watersurrounding the electrodes becomes rapidly heated, producing bubbles,which help the formation of a plasma channel between the two electrodes.The plasma channel may reach a very high temperature of 14,000–50,000Kwith a VUV radiation with a wavelength of 75–185 nm. The plasma channelconsists of a highly ionized, high-pressure and high-temperature gas. Thus,

TABLE VII. (Continued )

� Large current on the order of 100A, with a peak currentgreater than 1000A

� Electric field intensity at the tip of electrode is 0.1–10 kV/cm� Voltage rise time is in a range of 1–10 ms� Pulse duration � 20ms� Temperature of the arc is greater than 10,000K

3. Pulsed spark� Similar to pulsed arc except for short pulse durations and low

plasma temperature� Pulsed spark is faster than pulsed arc, i.e., strong shock waves

are produced� Plasma temperatures in spark and arc channels are a few

thousand and � 20,0001C, respectively


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once formed, the plasma channel tends to expand. The energy stored in theplasma channel is slowly dissipated via radiation and conduction to sur-rounding cool liquid water as well as mechanical work. At the phaseboundary, the high-pressure build-up in the plasma is transmitted into thewater interface and an intense compression wave (i.e., shock wave) isformed, traveling at a much greater speed than the speed of sound. Notethat the shock waves provide an almost perfect mixing of water to betreated, significantly enhancing the plasma treatment efficiency.

G. PROCESS OF THE ELECTRICAL BREAKDOWN IN WATER

The critical breakdown condition for a gas is described by the Paschencurve, from which one can calculate the breakdown voltage for air, forexample. A value of 30 kV/cm is a well-accepted breakdown voltage of air at1 atm. When one attempted to produce direct plasma discharges in water, itwas believed that a much greater breakdown voltage in the order of30,000 kV/cm might be needed due to the density difference between air andwater. In other words, the density difference of approximately 1000 gives thesame difference in the mean free path. Subsequently, the breakdown voltagein water was thought to be much greater than that in air.

A large body of experimental data on the breakdown voltage in watershows, however, that without special precautions this voltage is of the samemagnitude as for gases. This interesting and practically important effect canbe explained taking into account the fast formation of gas channels in thebody of water under the influence of the applied high voltage. When formed,the gas channels give the space for the gas breakdown inside of the body ofwater. It explains why the voltage required for water breakdown is of thesame magnitude as for gases. The gas channels can be formed by devel-opment and electric expansion of gas bubbles already existing in water aswell as by additional formation of the vapor channel through fast localheating and evaporation. We are going to focus below mostly on the secondmechanism, which is usually referred to as the thermal breakdown.

When a voltage pulse is applied to water, it induces a current in water andthe redistribution of electric field there. More specifically, the voltage pulseonce applied immediately stimulates the rearrangement of electric charges inwater, and the rearrangement of the electric charges results in a fast redis-tribution of electric field in water. Due to the dielectric nature of water, anelectric double layer is formed near the anode surface. The formation ofthe electric double layer results in the localization of the major portion ofthe applied electric field in the vicinity of anode. At some point in time, theelectric field near the anode becomes high enough for the formation of a


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narrow conductive channel, which is then heated up by electric current totemperatures of about 10,000K.

Thermal plasma generated in the channel is rapidly expanded and ejectedfrom the narrow conductive channel into water, forming a plasma bubble inwater. High electric conductivity in the plasma channel leads to shifting ofthe high electric fields from the channel to the bubble. These electric fieldsprovide a drift of negatively charged particles from the bubble into thechannel. Taking into account that the temperature in the plasma bubble isnot large enough to cause thermal ionization, and the electric field at thebubble is not sufficient to cause direct electric impact ionization, the oxygen-containing negative ions from water are believed to make major contribu-tions in the negative charge transfer from the bubble into the channel.

The plasma bubble can be characterized by a very high temperature gra-dient and a large electric field. The energy required to form and sustain theplasma bubble should be provided by Joule heating in the narrow conduc-tive channel in water. High current density in the channel is limited by theconductivity in the relatively cold plasma bubble, where temperature isabout 2000K. The electric conductivity in the bubble is determined not byelectrons but by negative oxygen-containing ions.

Further expansion of the plasma bubble leads to its cooling, decreasingthe density of charged particles into the microchannel. Subsequently, theelectric current decreases, resulting in a significant reduction in Joule heatingin the conductive channel in water and eventual cooling down of the channelitself. Subsequently, the bubble shrinks and reaction products from thebubble move into the plasma channel.

Physical nature of the thermal breakdown can be related to thermal in-stability of local leakage currents through water with respect to the Jouleoverheating. If the leakage current is slightly higher at one point, the Jouleheating and hence temperature also grow there. The temperature increaseresults in a significant growth of local conductivity and the leakage current.Exponential temperature growth to several thousand degrees at a local pointleads to formation of the narrow plasma channel in water, which determinesthe thermal breakdown. The thermal breakdown is a critical thermal-electricphenomenon taking place at the applied voltages exceeding a certainthreshold value, when heat release in the conductive channel cannot becompensated by heat transfer losses to the surroundings. The describedsequence of plasma channel events takes place in frameworks of a singlevoltage pulse. When the next voltage pulse is applied to water, a new ther-mal breakdown and new microarc occur in the other surface spot in theanode.

During the plasma discharge the thermal condition of water is constant,water stays liquid far away from the discharge, and the thermal conductivity


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of water is constant to be approximately 0.6W/mK. When the Joule heatingbetween the two electrodes is larger than a threshold value, one has aninstability, resulting in the instant evaporation of water and a subsequentthermal breakdown. On the other hand, when the Joule heating between thetwo electrodes is smaller than a threshold value, nothing happens but anelectrolysis and the breakdown never takes place. The Joule heating is in-versely proportional to the resistance of matter when a fixed voltage isapplied between the two electrodes. The resistance is inversely proportionalto the electric conductivity of dielectric medium (here initially liquid waterand later water vapor).

To analyze the thermal instability it can be assumed that electricconductivity of water se can be expressed as an exponential function oftemperature:

se ¼ s0e�ðEa=RTÞ (55)

where Ea (approximately 700 kJ/kg) is an activation energy and R the uni-versal gas constant. When the medium temperature increases, the electricconductivity of dielectric medium increases, resulting in the decrease in theresistance. Thus, the Joule heating increases, increasing the temperature ofthe dielectric medium. Subsequently, the increased temperature increases theelectric conductivity, further increasing temperature, leading to a thermal‘‘explosion’’ that can be referred as an instability and described by linearperturbation analysis of the transient energy equation:

rCp@T

@t¼ s0 expðEa=RTÞðE2 � kr2TÞ (56)

where E [V/cm] is the electric field and k is the thermal conductivity ofwater. The thermal conductivity of liquid water at room temperature is0.6W/mK, while that of water vapor at 373K is 0.68W/mK. The secondterm in the right-hand side representing heat conduction, which takes placewith a large temperature gradient along the radial direction, has a minussign because it represents heat loss to the surrounding water. Note that theconvection heat loss is not considered because there is no time for heat todissipate via convection.

The instability is usually described in terms of its increment O, which is anangular frequency [rad/s]. When O is greater than zero, the perturbed tem-perature exponentially increases with time, resulting in thermal explosion,when O is less than zero, the perturbed temperature exponentially decreaseswith time, resulting in the steady-state condition, and when O is complex,the perturbed temperature oscillates with time. The linear perturbation


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analysis of Eq. (56) leads to the following expression for the increment of thethermal breakdown instability:

O ¼ s0ðT0ÞE2

rCp

Ea

RT20

( )� k

rCp

1

R20

¼ s0E2

rCpT0

� �Ea

RT0

� � a

1

R20

(57)

Note that a is the thermal diffusivity of water medium, which becomesapproximately 1.47� 10�7m2/s with Cp of 4179 J/kgK and k of 0.6W/mK.

The first term is made up of the product of the two, [s0E2/rCpT0] and {Ea/

RT0}, where [s0E2/rCpT0] represents the frequency of heating as the nu-

merator is Joule heating, whereas the denominator is the heat stored in thewater medium; {Ea/RT0} represents the activation energy to temperature, asensitivity indicator. The second term in the right-hand side represents theratio of the thermal diffusivity to the square of the radial characteristiclength for radial heat conduction (see Fig. 55), indicating how fast heatdissipates along the radial direction. The first term is only active during theperiod when the pulse power is on, while the second term is active evenduring the period of the pulse power turned off. Hence, there is a balancebetween the Joule heat generation by pulse discharges and heat conductionto the surrounding water. When the heat generation is greater than theconduction loss, the increment O becomes positive, leading to the thermalexplosion. Hence, the critical phenomenon leading to the thermal explosionis given as follows:

s0E2

rCpT0

� �Ea

RT0

� a

1

R20

(58)

Note that O ¼ 0 means the transition from the stabilization to thermalexplosion, a condition that can be defined as the critical phenomenon.

r

L

2Ro

ChannelElectrode 1

Electrode 2

FIG.55. Sketch of a vapor channel between two electrodes surrounded by water.


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Since the electric conductivity s of a dielectric medium is extremely sensi-tive to temperature as manifested in Eq. (55), one can expect that as thetemperature increases, one can expect that the breakdown voltage decreases.

The breakdown voltage V is given by the product of electric field strengthE and the distance between two electrodes L. Thus, one can rewrite theabove equation as

sðELÞ2rCpT0

� �Ea

RT0

� ¼ s0V2

rCpT0

� �Ea

RT0

� a

1

R20=L

2 � (59)

If we introduce a geometry factor, b ¼ L/R0, one can rewrite the aboveequation as

s0V2

rCpT0

� �Ea

RT0

� ab2 (60)

From this equation, the breakdown voltage V can be obtained as

V ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ab2

s0rCpT0

h iEa

RT0

n ovuut ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffik

rCp

� �b2

s0rCpT0

h iEa

RT0

n ovuuut ¼

ffiffiffiffiffiffiffiffiffiffiffiffikRT2

0

s0Ea

sb (61)

For the plasma discharge in water, the breakdown voltage can be nu-merically estimated as follows:

V ffiffiffiffiffiffiffiffiffiffiffiffikRT2

0

s0Ea

sb ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0:613� 461:5� 3002

0:05� 700

sb ¼ 26b (62)

For a case of L ¼ 3 cm, if one assumes that the geometry factor, b ¼ L/R0, isapproximately 100, then the breakdown voltage in water becomes approxi-mately 2600V. If one assumes b ¼ 1000, the breakdown voltage in waterbecomes 26,000V. The breakdown voltage will decrease as the electric con-ductivity of water increases. The breakdown voltage will increase withb ¼ L/R0, the ratio of the distance between two electrodes to the currentchannel radius.

H. NEW DEVELOPMENTS IN PLASMA WATER TREATMENT AT DREXEL PLASMA

INSTITUTE

Based on the previous research, it is clear that plasma discharge in waterhas the ability to effectively inactivate microorganisms [163,184–196, 198].


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There are many different types of electrode configurations that can be usedto generate the plasma discharge in water, including a point-to-plane con-figuration and a coaxial configuration. Furthermore, a plasma-based watertreatment system has many advantages compared to chemical or mechanicalwater treatment methods, such as very minimal maintenance, low operatingpower, and minimal pressure loss through the device. Therefore, a plasma-based water treatment is advantageous in the implementation of a point-of-use water treatment system as well as in a large industrial water treatment.

The present section is based on a recent report prepared by Campbellet al. [204], who examined three functional plasma discharge prototypes(i.e., point-to-plane electrode configuration, magnetic GA and elongatedspark discharge). The spark gap generator was used to produce a pulsedvoltage capable of initiating the desired pulsed plasma discharge.

Validation and characterization of the plasma discharge were conductedby measuring pH, conductivity, temperature, voltage and current. To vali-date whether or not the present design effectively inactivates microorgan-isms, a series of experiments were conducted with active bacterial species.The effectiveness of the present designs was quantified by the amount ofenergy required to achieve a one-log reduction in bacterial concentration. Inaddition, Campbell et al. [204] examined whether or not a four-log reductionof viable microorganisms [159] was feasible using the present plasma designs.

1. Point-to-Plane Electrode Configuration

The first configuration utilized a point-to-plane electrode geometry (seeFig. 56). Initial experiments included stainless steel and tungsten wire

PowerSupply

Spark Gap

FIG.56. Schematic diagram of a point-to-plane plasma discharge system for pulsed corona

discharge and spark in water [204].


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electrodes of varying diameters (0.18–2.5mm) with no insulation. Variancein the plasma from corona to spark discharge was observed to bedependent on the gap distance measured from the anode to the groundedcathode.

Electrodes that were both rigid and electrically insulated were fabricated.This design included a stainless steel electrode (0.18mm) encased in siliconeresiding in a hollow Teflon tube which was inserted in a glass tube, pro-viding the necessary insulation for the electrodes. The stainless steel wirewas chosen as the electrode due to its high melting temperature and relativestability at high pressure. The stainless steel electrode extended approxi-mately 1.6mm beyond the bottom of the glass tube, providing a region forspark discharge initiation. The critical distance between which spark dis-charge and corona discharge exist was observed to be approximately 50mmbetween electrodes. Greater than 50mm resulted in the corona discharge,whereas less than 50mm resulted in the spark discharge.

When the distance between the electrodes was small, the voltage wouldinitiate a channel breakdown in water thus leading to a spark discharge.Conversely, when the distance between the electrodes increased and reacheda critical distance, the plasma would cease being a spark discharge and acorona discharge would initiate.

Figure 57 presents voltage, current and power profiles measured using anoscilloscope during a typical pulsed spark test. The initial steep rise in thevoltage profile indicates the time moment of breakdown in the spark gap,after which the voltage linearly decreased with time over the next 17 ms dueto a long delay time while the corona was formed and transferred to a spark.The rate of the voltage drop over time depends on the capacitance used inthe test. The current and power profiles show the corresponding historieswhich show initially sharp peaks and then very gradual changes over thenext 17 ms. The duration of the initial peak was measured to be approxi-mately 70 ns. At tffi17 ms, there was a sudden drop in the voltage, indicatingthe onset of a spark or the moment of channel appearance, which wasaccompanied by sharp changes in both the current and power profiles. Theduration of the spark was approximately 2 ms, which was much longer thanthe duration of the corona.

The bacteria selected for the biological validation test was a non-pathogenic (i.e., non-infectious) strain of E. coli requiring certain proceduresand equipment to properly grow and obtain experimental results. Biologicaltest laboratory includes an autoclave, centrifuge, incubators, distiller andother pertinent biological equipment. Bacterial growth and measurementtechniques included the production of agar plates, incubating and growingbacteria, and performing bacterial colonies counts on the plates. This


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method of counting bacteria colonies is a widely accepted practice in biologycalled heterotrophic plate counting. The complete procedure used for thegrowth and utilization of E. coli in the present study can be found elsewhere[205]. The results of the biological validation tests are given in Table VIII fortwo different initial conditions. When the initial cell count was high (i.e.,1.8E+8 cells/mL), the spark discharge could produce a four-log reductionat 100 pulses and two-log reduction at about 65–70 pulses. When the initialcell count was an intermediate level (i.e., 2E+6 cells/mL), the spark dis-charge produced a two-log reduction at 50 pulses.

-2.0

-1.5

-1.0

-0.5

0.0

0.5

0 5 10 15

0

5

10

15

20

25

30

0 5 10 15 20

-500

0

500

1000

1500

2000

2500

3000

0 5 10 15 20Time (µs)

Time (µs)

Time (µs)

∆ T = 1.85 µs

AB

Rising time = 80 ns

Corona Spark

17.4 µs

Pow

er (

W)

Cur

rent

(A

)V

olta

ge (

kV)

20

FIG.57. Voltage, current and power profiles measured using an oscilloscope during a typ-

ical pulsed spark test. Period between sparks ¼ 103ms [204].


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2. Magnetic Gliding Arc Configuration

Another configuration was a magnetic gliding arc. This system utilized aconstant DC voltage which created an arc discharge between two coaxialelectrodes This discharge moves with a help of externally applied magneticfields. The schematic diagram given in Fig. 58 shows the design and opera-tional principle of the magnetic GA. The magnetic GA was made up ofconcentric electrodes with a central cathode (1 in Fig. 58) and a groundedcoaxial cylindrical anode (2). Multiple ceramic ring magnets (4) were ori-ented such that one had an axial magnetic field within the grounded coaxialcylindrical anode as indicated by dotted arrows (see B in the figure). A spiralwire (3) was attached to the cathode and was arranged close to the anode inorder to initiate the breakdown. The liquid to be treated was introducedfrom the top of the reactor.

The plasma after initiation was rotated by the magnetic field along thespiral wire and was forced to stabilize in a form that looked like a ‘‘plasmadisc’’. The arc rotated around the cylindrical vessel due to the magnetic andelectrical forces. The Lorentz force can be described by the cross product ofthe charge velocity and magnetic field, and the direction of the force can bedetermined using the right-hand rule.

~F ¼ q~V � ~B (63)

After the initiation of discharge using the spiral wire connected to thecenter electrode, there was an arc, at any given time, between the central

TABLE VIII

BIOLOGICAL VALIDATION EXPERIMENT. BACTERIAL CONCENTRATION FOLLOWING PULSED SPARK

DISCHARGE TREATMENT OF WATER [204]

# of pulses Cells/ml

Run A Run B Run C

Experiment 1

0 1.84E+08 1.76E+08 1.60E+08

20 1.01E+08 7.40E+07 -

40 1.54E+07 1.01E+07 1.85E+07

60 1.67E+06 4.20E+06 3.20E+06

80 2.10E+05 4.80E+05 3.30E+05

100 9.30E+04 2.43E+04 3.05E+04

Experiment 2

0 2.05E+06 2.04E+06 1.96E+06

50 8.70E+03 1.52E+04 1.58E+04


ARTICLE IN PRESS

cylindrical cathode and the outer ring anode Fig. 58). This GA plasmatreated water quasi-uniformly as the water moved along the spiral trajectoryover the internal surface of the anode and fell by the gravity. The powersupply was different from the other two plasma systems for water treatmentbecause it utilized a DC rather than pulsed discharge. A reactive resistancecapacitance power supply (from Quinta Ltd.) was developed such that theinternal reactive resistance mimicked serial active resistance and the effi-ciency of power transfer to the plasma was close to 100%. Figure 59 shows

3

5

(-)

(+)

1 2

Power Supply &Regulator

3

5

B

-2

-

4

-

4

B

E

Ringmagnets

FIG.58. Sketch of a magnetic gliding arc. Multiple ring magnets were used to form a

magnetic field B, which paralleled to the axial direction of the reaction vessel. Electric field E

was in the radial direction of the reactor [204].

FIG.59. Magnetic gliding arc in operation, White arrows indicate water entry. (A) 1/30

shutter speed; (B) 1/640 shutter speed [204].


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photographs of the magnetic GA in operation together with an introductionof water flow into the gliding arc reactor. A high-speed camera was used tocapture the motion of the arc that looked like a disc to a human eye.Photographs were taken with shutter speeds of 1/30 and 1/640 s. At a shutterspeed of 1/640 s, one can clearly see one arc frozen between the two elec-trodes, whereas at a shutter speed of 1/30 s, one can see a plasma disc andbright dots of the electrode spots in the places where they made a short stop.

The bacteria laden solution was introduced into the vessel near the top ofthe cylinder and moved tangentially along the wall creating a complete circleprior to entering the plasma region. After the solution was treated by theGA, it descended to the bottom of the apparatus and was expelled throughtwo exit ports on the side of the base. The power source was a standardplatform power supply in our laboratory, which was rugged, reliable andeasily integrated into the gliding arc system.

It is important to note that the exposure of the water to the gliding arcinduces an initial decrease in pH. We have measured plasma power, andchanges in pH of the water, and water temperature. Table IX shows theresults of the measurements, where the pH value changed once the plasmawas on. No significant fluctuation in water temperature was observed overvariances in power levels. Table X shows the results of biological validationtests using the magnetic gliding arc, where the number of E. coli was countedas a function of the applied power ( instead of the number of pulses). At apower level of 120W, the magnetic GA could completely kill all the E. coliin water, an impressive six-log reduction.

3. Elongated Spark Configuration

Long spark ignition is a process of taking a single spark and elongating itthrough a series of capacitors (see Fig. 60). The long spark has potentially asignificant advantage over increasing the spark gap distance of the standardsystem. In order to increase the spark gap distance, the standard system

TABLE IX

PH AND TEMPERATURE VARIATIONS IN WATER AFTER THE PLASMA TREATMENT WITH A ROTATING

MAGNETIC GLIDING ARC [204]

Plasma Power (W) pH T (1C)

0 7.23 23.8

120.7 6.65 24.6

182 6.64 25.2

239 6.67 25.5

299 6.36 25.4


ARTICLE IN PRESS

would have needed both an increased capacitance and an increased voltagein order to initiate breakdown. The present long spark technology onlyrequires individual capacitors per adjacent electrodes, thus eliminating theneed for an increased supply voltage. The present system utilized a length ofcoaxial cable (RG-8/u) to create a series of high-voltage capacitors. Thecapacitance of the cable was determined to be 93.5 pF/m, with each cablemeasuring approximately 0.9m. The discharge was sustained over three ofthe capacitors with an overall spark length of approximately 25mm (seeFig. 60).

TABLE X

BIOLOGICAL VALIDATION EXPERIMENT. BACTERIAL CONCENTRATION FOLLOWING THE MAGNETIC

GLIDING ARC TREATMENT OF WATER [204]

Power (W) Cells/ml

Run A Run B Run C

0 2.71E+06 3.60E+06 2.79E+06

120.7 0.00E+00 0.00E+00 0.00E+00

182 0.00E+00 0.00E+00 0.00E+00

239 0.00E+00 0.00E+00 0.00E+00

299 0.00E+00 0.00E+00 0.00E+00

Power SupplyHV

Spark Gap

(A)

(C)

(B)

FIG.60. Long arc discharge schematic diagram. A ¼ single ignition; B ¼ double ignition;

and C ¼ full ignition [204].


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4. Comparison of Different Plasma Discharges for Water Treatment

The possible applications for plasma water treatment method span a widerange of areas and industries, including foreign aid and disaster relief, pro-viding a means for developing countries to sustain potable water sources,integrating into American household water delivery systems, and improvingpower plant waste water treatment facilities. Table XI shows a chart com-paring different plasma discharges found in plasma-based water treatmentmethods. The typical discharges applied in research today are found on twoends of the spectrum, either a highly energetic thermal discharge called anarc discharge, or a less energetic non-thermal discharge called a coronadischarge. The pulsed spark discharge used in the present study is foundbetween these two extremes. The properties of this type of discharge arequite unique and beneficial with regards to water treatment. First and mostimportantly, according to the preliminary experiments [204] it requires very

TABLE XI

COMPARISON CHART. DIFFERENT PLASMA DISCHARGES USED IN PLASMA-BASED WATER TREATMENT

METHODS [204]

Pulsed Arc

Discharge

Pulsed Spark

Discharge

(Present study)

Pulsed Corona

Discharge (min-

max)

Energy per liter for 1-log

reduction in E. coli : (J/L)

860 77 30,000–150,000

Power requirement for household

water consumption at 6 gpm :

(kW)

0.326 0.029 11.4–56.8

Power requirement for village

water consumption at

1000 gpm (kW)

54.3 4.9 1892.7–9463.5

Efficiency of power supply

required

Excellent Excellent Poor

Maximum Power available in

small power system

(10� 10� 10 cm overall

system size) : (kW)

30 10 0.3

Maximum water throughput

based on maximum power :

(gpm)

553 2058 0.03–0.16

Central lethal biological agent of

discharge

UV and chemical

radicals

UV and shock

waves

Chemical radicals

(OH, H3O+,

H2O2)

Note: 1 gpm (gallon per min) ¼ 3.786 l/min.


ARTICLE IN PRESS

low power in comparison to other systems. To achieve a four-log reductionfor a typical household flow rate of 6 gpm (22.7 L/min) the electrical energyrequirement was only 120W, less than some light bulbs. Secondly, the pHand temperature of the surrounding water did not significantly change dur-ing the treatment, indicating that the energy of the discharge was used veryeffectively for the treatment of the microorganisms. Thirdly, the flow ratesallowable for small overall system sizes in comparison were significantlylarger than other plasma systems for water treatment.

The present pulsed spark discharge system indicates a potential to accom-modate a 1000 gpm (3,786L/min) water flow rate, while, at the same time,retaining the capability of achieving a four-log reduction in biological con-taminant at a power measuring only 20 kW. This can be an extraordinarybreakthrough in plasma water treatment. It is our hope that the plasmatechnologies will prove to be significant developments in the area of watertreatment and perpetuate new and improved methods of delivering potablewater both nationally and internationally.

XI. Final Remarks

Non-thermal atmospheric plasma sources, becoming so important inmodern technologies, are an interesting and relatively new topic for con-sideration from the standpoint of the classical heat transfer. Even the com-bination of the terms ‘‘heat transfer’’ and ‘‘non-thermal systems’’ looksstrange at the first moment. Looking just a little deeper, we see that the‘‘non-thermal systems’’ actually become non-thermal because of the specialorganization of heat transfer. The heat transfer is a key for the organizationand stabilization of the non-thermal plasma systems, which we tried toemphasize in this chapter.

Non-thermal plasmas contain subsystems with different temperatures(electronic temperature, vibrational temperature, translational temperature,rotational temperature, the temperature of electronic excitation). It is asignificant simplification to even take into account all these temperatures assome subsystems can have non-Boltzmann energy distribution. On the otherhand, the energy transfer within each subsystem and between subsystems isvery intense at atmospheric pressure and defines major properties of non-thermal plasmas and their possible applications.

In this chapter we tried to consider all major types of non-thermalatmospheric plasma sources and their uses with different media that havedefinite influences on the energy transfer within non-thermal plasma andbetween the plasma and environment. These media that have very differentinfluences on energy transfer processes at atmospheric pressure include


ARTICLE IN PRESS

atomic gases, molecular gases and liquids. In addition, the relative speed ofthe media and plasma has a significant influence on the energy transfer. Allthese issues were touched in this chapter. Surely, this area of research is toobroad to be comprehensively considered in one chapter, but we hope that wegave a general idea on the state-of-the-art in this branch of science.

Though the stabilization of the non-thermal state of atmospheric pressureplasma is always a challenge, scientists found multiple approaches in orderto overcome it. A number of atmospheric pressure non-thermal dischargeswere developed, including many of them – recently. The selection of aparticular discharge should be based on a desired application.

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Heat Transfer in Plasma Spray Coating

Processes

J. MOSTAGHIMI and S. CHANDRA

Department of Mechanical and Industrial Engineering, Centre for Advanced Coating

Technologies, University of Toronto, 5 King’s College Road, Toronto, Ontario,

Canada, M5S-3G8

I. Introduction

Plasma spray coating is a process in which high temperature plasma isemployed to melt powders of metallic or non-metallic materials and spraythem onto a substrate, forming a dense deposit. The process is commonlyused to apply protective coatings on components to shield them from wear,corrosion, and high temperatures. Both direct current plasma (dc) and radiofrequency inductively coupled plasma (RF-ICP) are employed as a heatsource for melting and accelerating the powders. Wire-arc spraying is arelated technique in which an electric arc is struck between the tips of twocontinuously fed wires. A high-speed gas jet strips off molten metal dropletsfrom the tips of the wires and propels them onto the surface to be coated.Both these processes may be carried out at either atmospheric pressure or, ifoxidation is to be minimized, under vacuum.

Plasma coatings are built up by agglomeration of splats formed by theimpact, spread and solidification of individual particles. Inspection of aplasma coating cross-section (Figure 1) shows that it is built up of thinlamellae formed by flattened droplets that land on each other and fusetogether. Closer examination shows that the coating is not fully dense:pores are found at the interface between splats. The presence of these poresmay or may not be desirable, depending on the purpose of the coating.Porosity is detrimental to the performance of wear resistant coatings sinceit reduces their structural integrity and adhesion strength. But closed poresare useful in thermal barrier coatings since they reduce thermal conduc-tivity and provide insulation. In either case it is important to be able toproduce the desired level of porosity by controlling the coating depositionprocess.




To ensure strong adhesion of a thermal spray coating it is necessary tocarefully prepare the substrate on which the coating is to be applied. Typ-ically the substrate is grit-blasted, creating a rough surface pitted with tinycraters into which impinging droplets flow before they freeze. Mechanicalinterlocking between solidified droplets and the substrate produces durablebonds. Coating strength is enhanced if droplets penetrate deep into surfacecavities before they freeze. Coating properties are therefore highly depend-ent on fluid flow and heat transfer during droplet impact, and are stronglyaffected by surface temperature.

Pershin et al. [1] plasma-sprayed nickel powder onto a stainless steel plateand found that coating adhesion strength increased by almost an order ofmagnitude as surface temperature was raised from room temperature to6501C. Several explanations were offered: heating the surface clears volatilecontaminants adsorbed on the surface, improving contact between impingingparticles and the substrate; reducing the solidification rate of droplets allowsthem to flow into surface cavities before freezing, enhancing mechanicalbonding. The most visible effect of increasing substrate temperature, though,was to change the shape of splats formed by solidified droplets after impact onthe surface. Figure 2 shows micrographs of splats produced by spraying nickelpowder, sieved to give a size distribution of +63 to –75mm, onto stainlesssteel surfaces maintained at either 2901C (Figure 2a) or 4001C (Figure 2b).Particle temperature in-flight was measured to be 160072201C and impact

a) b)

FIG.1. A typical cross-section of nickel sprayed plasma coating (a), with higher mag-

nification (b).

144 J. MOSTAGHIMI AND S. CHANDRA

velocity 7379m/s. On the colder surface there was evidence of splashing anddroplet break-up, while splats on the hotter surface were circular.

The effect of substrate temperature on splat shape has been well estab-lished in a number of studies, reviewed in detail by Fauchais et al. [2].Bianchi et al. [3] demonstrated that the shape of splats formed by sprayingalumina or zirconia droplets from a plasma torch onto a stainless steel platevaried as substrate temperature was increased. Droplets landing on a coldsubstrate (below 1001C) splashed extensively after impact and had very ir-regular contours while those deposited on a hot surface (above 1501C) weredisk-like, almost perfectly circular. Fukumoto et al. [4] did a statisticalanalysis of splat shapes deposited on a surface and defined a ‘‘transitiontemperature’’ (Tt) as the substrate temperature where half of the splats on thesurface were circular without splashing. Other researchers [5–10] also ob-served this change of splat shape and showed that the transition temperaturewas a complex function of particle and substrate material properties [5,6],surface contamination [7] and surface oxidation [9]. Jiang et al. [8] plasma-sprayed molybdenum onto polished stainless steel coupons and found thatincreasing impact velocity enhanced splashing; removing adsorbed volatilecompounds on the surface reduced splashing. Fukomoto and Huang [10]conjectured that freezing along the bottom of an impinging droplet causessplashing: liquid flowing on top of the solid layer jets off and splashes.

a) b)

FIG.2. Splats formed by spraying molten nickel particles on a stainless steel surface in-

itially at (a) 2901C and (b) 4001C. The particle size distribution was –53 to +63mm, particle

temperature before impact 160072201C, velocity 7379m/s.

145HEAT TRANSFER IN PLASMA SPRAY COATING PROCESSES

Particle impact dynamics depend on the rate at which a droplet solidifiesduring impact, which is a function of the heat flux from the molten dropletto the substrate. When molten metal comes suddenly in contact with arough, solid surface, air may be trapped in crevices at the liquid solidinterface, creating a temperature difference between the molten metal andthe substrate, whose value depends on surface finish, contact pressure andmaterial properties. To quantify the magnitude of this effect, the thermalcontact resistance (Rc) is defined as the temperature difference betweenthe droplet (Td) and substrate (Ts) divided by the heat flux (q00) betweenthe two.

Rc ¼Td � T s

q00ð1Þ

Droplet solidification rate is therefore a function not just of substratetemperature, but also contact resistance and initial droplet temperature.Heating the surface may therefore indirectly affect droplet impact dynam-ics by changing thermal contact resistance, either decreasing it by removingvolatile compounds adsorbed on the surface, or increasing it in the case ofmetallic substrates heated in air, due to the formation of an oxide layer. Ifnickel particles are plasma-sprayed onto a steel surface that is at roomtemperature they will splash, but not on a surface that is maintained at4001C; however, splashing is also suppressed on a surface that is heated to4001C in air, oxidized, and then cooled [1].

Computer simulations of impacting molten metal droplets [11] provideinsight into a mechanism for solidification-induced splashing. A spreadingdrop begins to freeze along its edges, where it first contacts the coldersubstrate. The solid rim formed obstructs further flow, forcing liquid to jetoff the surface so that it becomes unstable and breaks up into satellitedroplets. Reducing heat transfer from the droplet slows solidification andallows the droplet to spread into a disk before freezing. It was found insimulations that the rate of solidification was much more sensitive to valuesof thermal contact resistance than substrate temperature. Simulations ofimpact of nickel particles [12] showed that raising substrate temperaturefrom 290 to 4001C had little effect on impact dynamics, but increasingthermal contact resistance from 10�7 to 10�6m2K/W diminished heattransfer sufficiently to prevent splashing. An oxide layer or adsorbed con-taminants on the surface may, in practice, be the cause of increased thermalcontact resistance.

The state of particles at the point of impact is important in the type ofmicrostructure the coating will have and it is dependent on the trajectory ofparticles and their residence time within the plasma. Thus, the particles may


be fully or partially melted with a few still completely solid. In the case ofwire-arc spray, all particles are fully molten. Coating properties such asporosity, adhesion strength and surface roughness depend on the shape ofthese splats and how they bond together and to the substrate. The splatshape is dependent on material properties of the powder, impact conditions(e.g., impact velocity and temperature) and substrate conditions, e.g., subst-rate roughness, temperature and contact resistance.

Understanding the dependence of the microstructure of spray coatings onoperating conditions of the plasma spray system is of great practical interest.To obtain good quality coatings the spray parameters must be selectedcarefully, and due to the large variety in process parameters, much trial anderror goes into optimizing the process for each specific coating and substratecombinations. A great deal of research is currently devoted to exactly un-derstand how varying spray parameters changes coating properties. To un-derstand coating formation and improve the process, three distinct regionsshould be studied (Figure 3):

(i) Plasma-generation zone,(ii) Particle-heating zone, and(iii) Deposition zone.

The particle-heating region and, to some degree, the plasma-genera-tion zone has been the subject of considerable theoretical and experi-mental research over the past 20 years [13,14]. In contrast, the depositionzone is still not well understood and considerable further research is stillneeded.

This chapter primarily focuses on heat transfer issues in the depositionzone. In Section II, we first briefly describe plasma spray sources mostcommonly used in industry. Sections III–VI describe theoretical and exper-imental studies of droplet impact ad solidification phenomenon.

shrouding gas powdercathode

plasma gas

anode water inshroud nozzle

water out

FIG.3. Schematic of a DC plasma spray coating process.


II. Plasma Spray Sources

A. DIRECT CURRENT (DC) PLASMA GUN

DC plasma (Figure 3) guns consist of a water-cooled cathode and anode.The tubular anode forms the body of the spray gun and is made fromcopper, while the central cathode is normally of tungsten, which has a lowwork function. Plasma gases flow through the anode and around the cath-ode. Plasma formation is initiated by a high voltage discharge that forms anarc between the electrodes. Joule heating is responsible for the high tem-peratures achieved and ionization of the gas. Commercial plasma guns arenormally operated with argon, which is an inert gas with relatively lowionization potential (15.75 eV). However, argon’s thermal conductivity islow, which impedes heat transfer to the injected powders. To enhance heattransfer, either hydrogen or helium, that have the highest thermal conduc-tivity among gases, is mixed with argon. Depending on gas composition,average arc voltage varies between 20 and 50V. The arc current is a con-trolled parameter, typically ranging from 600 to 900A. The high arc currentis responsible for electrode erosion, which over time leads to deterioration intorch performance.

Powder is fed into the plasma jet via an external powder port mountednear the anode nozzle exit. The powder is rapidly heated and acceleratedtowards the substrate. Spray distances can vary between 25 and 150mm.

Plasma spraying is most commonly carried out with the torch open to theatmosphere, and is referred as atmospheric plasma spray (APS). Someplasma spraying is conducted in protective environments, using vacuumchambers back filled with an inert gas at low pressure; this is referred asvacuum plasma spray (VPS) or low pressure plasma spray (LPPS). BothAPS and VPS may be operated in subsonic or supersonic modes.

Plasma spraying is done at much higher temperatures than combustionbased processes, and can spray very high melting point materials such asrefractory metals (tungsten, molybdenum, titanium) and ceramics (alumina,zirconia). Plasma-sprayed coatings are generally much denser, stronger andcleaner than those produced by most other thermal spray processes with theexception of high-velocity oxy-fuel (HVOF) and detonation processes.Plasma spray coatings account for the widest range of thermal spray coat-ings and applications and it is the most versatile spraying process.

B. RADIO-FREQUENCY INDUCTIVELY COUPLED PLASMA (RF-ICP)

RF-ICPs are generated by passing an alternative current through a coilwound around a dielectric tube (Figure 4). Depending on the tube size


and available RF power, the frequency varies from 200 to 60MHz. As thename suggests, the plasma is heated inductively. Electromagnetic fields in-duced by the coil current penetrate the plasma and through joule heatingmaintain it. Much of the power is dissipated in the so-called ‘‘skin-depth’’which is proportional to the square root of the ratio of the electrical con-ductivity of plasma to the induction frequency. For argon plasmas operatedat 4MHz with an average plasma temperature of 8000K, the skin-depth isabout 4mm. The skin-depth dictates the torch diameter, which has to belarger by a factor of at least 4. Compared to DC plasmas, the heatedvolume of RF-ICP is large and temperature and velocity gradients aresmall.

Since no electrodes are needed to generate the plasma, the plasma is freeof impurities and not contaminated by evaporating electrode materials.Since powders are injected along the axis of the torch, there is better controlof heat transfer to the material. In principle, there is no fundamental limiton torch power and powers of up to 500 kW have been reported. Plasmascan be generated with any type of gases. RF-ICP can be operated at at-mospheric pressure or under vacuum.

The disadvantages of RF-ICP include high cost, the inability to mounttorches on robots, and relatively low gas velocities resulting in low particleimpact velocity.

Induction Coil

Plasma

Q3 Q2 Q1

Torch Tube

Gas Flow

FIG.4. Schematic of an RF-ICP torch.


C. WIRE-ARC SPRAYING

Wire-arc is a method for spraying any metal that can be drawn on a wire.Drive rolls feed two electrically charged wires through the gun to its nozzle.The arc is created by the high potential difference maintained between thetips of the two wires. The arc melts the tip of the two wires and a compressedair (or nitrogen) blast atomizes the molten metal and projects it onto apreviously prepared surface (Figure 5).

Wire-arc spraying is excellent for applications that require a thick coatingdeposit. The wire-arc system produces a highly concentrated spray pattern andcan spray at extremely high speeds. This process allows the creation of pseudo-alloy coatings by feeding a different metal through each electrode. Wire-arcspray is an excellent process for the repair of shafts and is relatively inexpensive.

III. Droplet Impact, Spread and Solidification

Individual splats are the building block of thermal spray coatings. Theshape of these splats is a function of particle impact conditions, materials

FIG.5. A photograph of the two wires and the in-flight particles; inversed. Two lasers

illuminate the area from top to bottom. Aluminum wires with 7m/min feed rate, 28.4V,

straight nozzle, HV cap. Some particles are out of focus (a lens system has been ordered to

prevent illuminating the particles that are out of focus).


properties of powder and substrate, substrate temperature and its roughness.Depending on the above parameters, splats may be in the shape of a disk, orthey may break-up and splash. To better understand how coating micro-structure is formed, it is important to find answer to the following questions:

1. What is the relationship between the final splat shape and impactparameters, properties of the powder, substrate thermal properties,and substrate roughness?

2. What causes splashing and break-up?3. How do splats interact with each other?

Prediction of splat shapes involves numerical simulation of fluid flow andheat transfer of an impacting droplet. In general, this is a three-dimensional,time-dependent problem. One challenge is the prediction of rapid and largedeformations of impacting droplets on the surface. In what follows, wedescribe the current state of modeling droplet impact and solidification.

A. AXI-SYMMETRIC IMPACT

Before describing the details of the 3D mathematical model, let us list themost important variables that control the impact phenomenon. Consider theisothermal normal impact of a spherical droplet on a smooth, flat surface, asshown in Fig. 6. Furthermore, assume the gas phase does not influence theimpact. The parameters that influence such impact include: initial dropletdiameter Do, impact velocity Vo, liquid density r, liquid viscosity m, liq-uid–gas surface tension s and liquid–solid contact angle yU Combining theseinto non-dimensional groups reduces the number of variables to three: con-tact angle, the Reynolds and the Weber numbers, defined below:

Re ¼ rVoDo

m; We ¼ rV2

oDo

sð2Þ

Re is a measure of the droplet inertia to viscous force and We is a measureof inertia to the surface tension force. There has been many successful

VO

FIG.6. Schematic of droplet just before impact.


attempts to derive analytical expressions for the extent of maximum spread,xmax ¼ Dmax/Do, as a function of process variables [15–18].

Pasandideh-Fard et al. [17] developed a simple model to predict themaximum spread diameter of an impacting droplet. In their model, theyequated the energy before and after impact, accounting for the energy dis-sipation during impact. The initial kinetic energy (KE1) and surface energy(SE1) of a liquid droplet before impact are

KE1 ¼1

2rV2

o

� �p6D3

o

� �ð3Þ

SE1 ¼ pD2os ð4Þ

After impact, when the droplet is at its maximum extension, the kineticenergy is zero and the surface energy (SE2) is

SE2 ¼p4D2

maxsð1� cos yaÞ ð5Þ

where ya is the advancing liquid–solid contact angle. The work done indeforming the droplet against viscosity (W) is

W ¼ p3rV2

oDoD2max

1ffiffiffiffiffiffiRe

p ð6Þ

The effect of solidification in restricting droplet spread is modeled by as-suming that all the kinetic energy stored in the solidified layer is lost. If thesolid layer has average thickness s and diameter ds when the splat is at itsmaximum extension, then the loss of kinetic energy (DKE) is approximated by

DKE ¼ p4d2s s

� � 1

2rV2

o

� �ð7Þ

ds varies from 0 to Dmax during droplet spread: a reasonable estimate of itsmean value is ds�Dmax/2. Substituting Eqs. (3–7) into the energy balanceKE1+SE1 ¼ SE2+W+DKE yields an expression for the maximum spreadfactor:

xmax ¼Dmax

Do¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiWeþ 12

3

8Wes þ 3ð1� cos yaÞ þ 4

WeffiffiffiffiffiffiRe

p

vuuut ð8Þ

s� is the dimensionless solid layer thickness (s� ¼ s/Do).


There are two unknowns in Eq. (8): advancing contact angle (ya) andsolidified layer thickness (s�). Liquid–solid contact angles during spreadingand recoil of tin droplets on a stainless steel were measured from enlargedphotographs by Aziz and Chandra [18] and the advancing contact angle wasfound to be almost constant at ya ¼ 1401.

The growth in thickness of the solidified layer can be calculated using anapproximate analytical solution developed by Poirier and Poirier [19]. Themodel assumes that heat transfer is by one-dimensional conduction; there isno thermal contact resistance at the droplet–substrate interface; the tem-perature drop across the solid layer is negligible; the substrate is semi-infinitein extent and has constant thermal properties. The dimensionless solidifi-cation thickness was expressed as a function of the Stefan number (Ste ¼ C(Tm�Tw,i)/Hf), Peclet number (Pe ¼ VoDo/a) and g ¼ krC:

s ¼ 2ffiffiffip

p Ste

ffiffiffiffiffiffiffiffiffiffitgwPegd

sð9Þ

Substituting Eq. (9) into (8) gives the maximum spread of a droplet that issolidifying during impact:

xmax ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Weþ 12

WeSteffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3gw=2pPegd

pþ 3ð1� cos yaÞ þ 4 We=

ffiffiffiffiffiffiRe

p �s

ð10Þ

The variation of xmax with impact velocity predicted by Eq. (10) fordroplets falling on a substrate at 251C is shown in Fig. 7, along with meas-ured values. Predictions of xmax from Eq. (10), for a droplet spreadingwithout solidifying, are also compared with measurements for droplets im-pacting a surface at 2401C. Agreement between measured and calculatedvalues is good in both instances. At low impact velocity Eq. (10) predictssomewhat larger values of xmax than were measured: to estimate viscousdissipation the model assumes that there exists a thin boundary layer in thedrop [16] which is not true when the droplet is deposited very gently.

The above analytical relations are quite useful in providing an approx-imate answer to the first question: i.e., the relation between maximumspread and impact variables. But they provide little information about morecomplex scenarios, such as break-up and splashing of droplets and inter-actions between multiple droplets. Modeling such phenomena requires moredetailed numerical models.

To better understand the dynamics of impact, spread, and solidification, anumber of two-dimensional, axi-symmetric models were developed over thelast 15 years. Zhao et al. [20,21] studied, both experimentally and


numerically, heat transfer and fluid flow of an impacting droplet. Solidi-fication was not considered in this work. Bennet and Poulikakos [22] andKang et al. [23] studied droplet deposition assuming solidification to startafter spreading is completed. As discussed above, the validity of this as-sumption depends on both Prandtl and Stefan numbers. Liu et al. [24],Bertagnolli et al. [25] and Trapaga et al. [26] used finite difference techniquesto study solidification and spreading of the impacting drops. The substratewas, however, assumed to be isothermal. Furthermore, the important effectof thermal contact resistance between the drop and the substrate was notconsidered. In these studies, the liquid–solid contact angle was considered tobe constant, with an arbitrarily assigned value. Pasandideh-Fard et al. [16],however, showed that the value of contact angle can have a significant effecton the results.

Pasandideh-Fard and Mostaghimi [27] studied the effect of thermal con-tact resistance between the droplet and the substrate. They showed that itsmagnitude could have a dramatic effect on droplet spreading and solidi-fication. Solidification and heat transfer within the substrate was modeledassuming one-dimensional heat conduction. The model was later completedand a fully two-dimensional axi-symmetric model of droplet impact was

FIG.7. Calculated (lines) and measured (symbols) variation of maximum spread factor

with impact velocity for 2.0mm diameter tin droplets landing on a stainless steel surface with

initial temperature Tw,i [Ref. 18].


developed [17] and impact and solidification of relatively large tin droplets(�2mm diameter) on stainless steel substrates were studied both numeri-cally and experimentally. The model correctly predicted the shape of thedeforming droplet. The values of thermal contact resistance were estimatedby matching the numerical predictions of substrate temperature with thosemeasured experimentally. While thermal contact resistance should, in prin-ciple, vary at different contact points, it was shown that accurate simula-tions of the impact could be done using a constant value. The results alsoshowed the sensitivity of the predicted maximum spread to the value ofthermal contact resistance.

A few experimental studies have investigated impact of molten droplets.Madejski [15] developed a simple model to predict the maximum splat di-ameter of a droplet after impact, and compared his predictions with the sizeof alumina droplets deposited on a cold surface. Inada [28] measured thetemperature variation of a plate on which a molten lead droplet wasdropped, and noted that the droplet cooling rate was a function of impactvelocity. Watanabe et al. [29] photographed impact of n-cetane and n-eico-sane droplets on a cold surface and concluded that in their tests dropletsspread completely before solidifying. Fukanuma and Ohmori [30] photo-graphed the impact of tin and zinc droplets and also found that freezing hadno influence on droplet spread. Inada and Yang [31] used holographic in-terferometry to observe droplet–substrate contact during impact of leaddroplets on a quartz plate. Liu et al. [32] measured the temperature variationon the upper surface of an impacting metal droplet by a pyrometer, andused these results to estimate the thermal resistance under the drop. How-ever, the response time of the pyrometer (25ms) was longer than the timetaken by the droplet to spread, so that their results are applicable to theperiod after the droplet had come to rest rather than the duration of theimpact itself. Pasandideh-Fard et al. [17] photographed the impact of tindroplets on stainless steel substrate and measured the changes in substratetemperature during the impact. They showed that the value of the maximumspread is sensitive to the magnitude of thermal contact resistance, which intheir case was estimated from the measurements.

B. SPLASHING AND BREAK-UP

Two-dimensional models have been very useful in simulating the dynam-ics of impact and solidification of droplets landing normally on a flat sur-face. In reality, most impacts occur under conditions that are not axi-symmetric. Even under axi-symmetric impact conditions, the contact linemay become unstable; fingers develop and grow and may eventually breakaway from the bulk of the splat.


The first experimental study of droplet fingering and splashing – in theabsence of solidification – was that of Worthington [33,34] which was pub-lished over a century ago. Worthington observed that the number of fingersincreased with droplet size and impact speed; observed merging of the fin-gers at or soon after the maximum spread; and found fingering to be morepronounced for fluids that did not wet the substrate. Many researchershave since contributed to the understanding of the fingering and splashing inthe absence of solidification. A review of their findings may be found in theworks of Bussmann et al. [35–37].

Bussmann et al. [35–37] developed a three-dimensional model for theisothermal impact of a droplet on a solid surface. The model was based onthe extension of the two-dimensional RIPPLE [38] algorithm to three di-mensions. The model employs a fixed-grid Eulerian approach along with avolume-tracking algorithm to track fluid deformation and droplet free sur-face. The choice of fixed-grid technique is attractive for several reasons: it isrelatively simple to implement; volume-tracking method is capable to modelgross fluid deformation, including break-up; and the relatively small de-mand on computational resources.

Pasandideh-Fard et al. [17] extended the three-dimensional model ofBussmann et al. [35,36] to include heat transfer and solidification. Thismodel is described in the next section.

IV. Mathematical Model of Impact

A. FLUID FLOW AND FREE SURFACE RECONSTRUCTION

Developing a numerical model requires a few simplifying assumptions. Itis assumed that during the impact of a droplet against a solid surface, thesurrounding gas, the droplet is dynamically inactive, which implies that theimpact may be modeled by following the flow field only in the liquid phase.The droplet is spherical at impact, the liquid is incompressible and fluid flowis modeled as being Newtonian and laminar. And finally, as a consequenceof these assumptions, it is assumed that the only stress at the liquid freesurface is a normal stress, and that any tangential stress is negligible.

Equations of conservation of mass and momentum govern the fluid dy-namics:

= � V ¼ 0 ð11Þ

@V

@tþ ðV � =ÞV ¼ �1

r=pþ n=2Vþ 1

rFb ð12Þ


where V represents the velocity vector, p the pressure, r the density, n thekinematic viscosity and Fb any body forces acting on the fluid.

Boundary conditions for fluid along solid surfaces are the no-slip and no-penetration conditions. At the liquid free surface, Laplace’s equation spec-ifies the surface tension-induced jump in the normal stress ps across theinterface:

ps ¼ sk ð13Þ

where s represents the liquid–air surface tension and k the total curvature ofthe interface.

Finally, a boundary condition is required at the contact line, the line atwhich the solid, liquid and gas phases meet. It is this boundary conditionwhich introduces into the model information regarding the wettability ofthe solid surface. Although it is conceivable that one could formulatethis boundary condition incorporating values of the solid surface tensions,such values are often inaccessible. It is simpler to specify the contact angle,y, the value of which can be a constant or dependent on the contact linespeed.

The basis for the model is RIPPLE [35], a 2D fixed-grid Eulerian codewritten specifically for free surface flows with surface tension. In addition tothree-dimensionalization of the code, significant improvements are incor-porated into the model, including new algorithms for evaluating surfacetension and for interface tracking. These improvements are described inwhat follows.

Equations (11) and (12) are discretized according to typical finite volumeconventions on a rectilinear grid encompassing both the volume occupied bythe droplet prior to impact as well as sufficient volume to accommodate thesubsequent deformation. Velocities and pressures are specified as on a tra-ditional staggered grid [39]. Equations (11) and (12) are solved using a two-step projection method, in which a time discretization of the momentumequation is broken up into two steps [35].

In addition to solving the flow equations within the liquid, the numericalmodel must also track the location of the liquid free surface. Various ap-proaches exist to tracking a sharp discontinuity through a flow field: theapproach chosen here is the first-order accurate 3D volume-tracking methodof Youngs [40] in place of the Hirt–Nichols algorithm [41] implemented inRIPPLE. Although the Hirt–Nichols algorithm can be three-dimensionali-zed, Youngs’ algorithm is a more sophisticated and more accurate ap-proach. A comparison of various 2D algorithms [42], includingHirt–Nichols and Youngs’ equivalent 2D method [43], demonstrated a sig-nificant difference in the accuracy of the two approaches.


Consider a function f defined in a continuous domain as

f ¼ 1 within the liquid phase

0 without

�ð14Þ

For a cell (i, j, k) of volume ui;j;k a ‘‘volume fraction’’ fi,j,k is defined as

f i;j;k ¼1

ui;j;k

Zui;j;k

f du ð15Þ

and a corresponding cell density ri;j;k, which appears in the discretization ofEq. (12), is evaluated as

ri;j;k ¼ rf f i;j;k ð16Þ

where rf represents the (constant) value of the liquid density. Obviously,f i;j;k ¼ 1 for a cell filled with liquid and f i;j;k ¼ 0 for an empty call. When0of i;j;ko1, the cell is deemed to contain a portion of the free surface and istermed an ‘‘interface cell.’’ Note that unlike f, the integrated quantity f i;j;kno longer contains information regarding the exact location of the interface.This is, in fact, the primary drawback of volume tracking as an interfacetracking method, and becomes problematic when dealing with surface ten-sion and contact angles. On the other hand, volume tracking is relativelysimple to implement even in three dimensions, retains this simplicity re-gardless of the complexity of the interface geometry, conserves mass (orvolume, since the fluid is incompressible) exactly, and demands only amodest computational resource beyond that required by the flow solver.

Since the function f is passively advected with the flow, f satisfies theadvection equation:

@f

@tþ ðV � =Þf ¼ 0 ð17Þ

Given the volumetric nature of f i;j;k and in order to maintain a sharpinterface, the discretization of Eq. (17) requires special treatment. As withmost other volume-tracking algorithms, Youngs’ algorithm consists of twosteps: an approximate reconstruction of the interface followed by a geo-metric evaluation of volume fluxes across cell faces.

The interface is reconstructed by locating a plane within each interfacecell, corresponding exactly to the volume fraction f i;j;k and to an estimate ofthe orientation of the interface, specified as a unit normal vector ni;j;k di-rected into the liquid phase. In two dimensions such an interface is simply aline crossing a cell; in three dimensions the line becomes a three- to six-sided


polygon, depending on how the plane slices the cell. To illustrate in twodimensions, Fig. (8b) portrays the volume fractions corresponding to theexact (albeit unknown) interface of Fig. (8a). Note that nothing guaranteesthat interface planes be contiguous. The position of the interface within eachcell and the new velocities at the cell faces are then used to determine volumefluxes across each face during the time step. Figure (8c) illustrates such aflux across one face of a cell. Volume fluxes are evaluated one direction at atime, always followed by an interim interface reconstruction. Alternatingthe order of advection from one time step to the next minimizes directionalbias.

The original RIPPLE code was primarily a vehicle for introducing the‘‘continuum surface force,’’ or CSF, model [44] as a novel approach toevaluating surface tension. The CSF model reformulates surface tensioninto an equivalent volume force FST:

FSTðxÞ ¼ gZS

kðrÞnðrÞdðx� rÞ dr ð18Þ

where d is the Dirac delta function and the integration is performed oversome area of free surface S. Surface tension is then incorporated into theflow equations simply as a component of the body force Fb in Eq. (12).Discretization of Eq. (18) requires an approximation to d which spreads thesurface tension force over fluid in the vicinity of the surface. Unfortunately,the original discretization of Eq. (18) resulted in a surface tension forcedistribution, which induced spurious fluid motion near free surfaces [44].Other discretizations of Eq. (18) have been proposed [45,46] and were testedin both two and three dimensions. The accuracy of our simulations im-proved dramatically when we incorporated these improvements.

What remains is to evaluate ni;j;k, required by the volume-tracking algo-rithm to reconstruct the interface, and essential to the accurate evaluation of

FIG.8. The volume-tracking method. (a) The exact liquid interface. (b) The corresponding

volume fractions and planar interfaces. (c) With velocity u positive, the shaded region to the

right of the dotted line is advected into the neighboring cell during the time step dt.


FSTi;j;k, especially since k is evaluated as

k ¼ �= � n ð19Þ

In a continuous domain,

n ¼ =f

=f�� ð20Þ

But given the volumetric nature of f i;j;k, a simple algebraic discretizationof Eq. (14) leads to poor estimates of ni;j;k. In two dimensions, complexgeometric algorithms have been devised to evaluate n and k [47,48]. Thereare no obvious extensions of these algorithms to three dimensions.

Instead, the approach implemented in this model comes from a suggestioncontained within the original CSF formulation [44]. Analogous to spreadingthe surface tension force to fluid in the vicinity of the free surface, betterestimates of ni;j;k are obtained by evaluating the gradient of a smoothed f i;j;k,equivalent to employing a spatially weighted gradient operator to evaluate=f . In practice the same d2h is employed for smoothing f i;j;k as for smooth-ing FSti;j;k . ni;j;k is first evaluated at cell vertices, to accommodate the eval-uation of the cell-centered ki;j;k; cell-centered ni;j;k are then evaluated as anaverage of eight vertex values.

The particular d2h chosen for the model is a radially symmetric variationof a widely used kernel proposed by Peskin [49]:

d2hðxÞ ¼1þ cos p xj j

2h

� �.c xj j � 2h

0 xj j42h

8<: ð21Þ

where c normalizes the kernel:

c ¼ 32

3h3ðp2 � 6Þ=p ð22Þ

The reason Peskin’s kernel is modified is found in work by Aleinov andPuckett [45], which demonstrates that radial symmetry appears to be anattractive attribute of d2h.

Finally, much has been written of the apparent contradiction of a contactline moving along a no-slip solid surface. Analytical solutions of the Navi-er–Stokes equations yield a force singularity at a contact line unless a slipcondition is imposed near the line [50]. Numerical models, which explicitlytrack the free surface, also require that a slip boundary condition be im-posed on any contact line velocities [51]. This turns out not to be an issue for


this model, precisely because it does not explicitly track the free surface, nordoes it solve for contact line velocities. Instead, since velocities are specifiedat cell faces, the nearest velocity to the contact line is specified one half-cellheight above the solid surface. Again, Fig. 8 provides an illustration. It isthis non-zero velocity which is then used to move fluid near the contact lineat each time step.

B. HEAT TRANSFER AND SOLIDIFICATION

Solidification is assumed to occur at the melting temperature and viscousdissipation is neglected. Densities of liquid and solid are assumed constantand equal to each other. The energy equation can be written as

@h

@tþ ðV � =Þh ¼ 1

r= � ðk=TÞ ð23Þ

The above equation has two dependent variables: temperature T andenthalpy h. The method of Cao et al. [52] is employed to transform theenergy equation in terms of enthalpy alone. The main advantage of thismethod is that it solves the energy equation for both phases simultaneously.The transformed energy equation is as follows:

@h

@tþ ðV � =Þh ¼ 1

r=2ðbhÞ þ 1

r=2f ð24Þ

where in the solid phase

h � 0; b ¼ ks

Cs; f ¼ 0 ð25aÞ

at the liquid–solid interface

0ohoHf ; b ¼ 0; f ¼ 0 ð25bÞ

and in the liquid phase

h Hf ; b ¼ kl

Cl; f ¼ �Hfkl

Clð25cÞ

where f is a new source term, andHf is the latent heat of fusion. Subscripts land s refer to liquid and solid properties, respectively. The energy equationhas now only one dependent variable, the enthalpy, h. The relationshipbetween temperature and enthalpy is given by

T ¼ Tm þ 1

kðbhþ fÞ ð26Þ


in which Tm is the melting point of the droplet. Heat transfer within thesubstrate is by conduction only. The governing equation is

rwCw@Tw

@t¼ = � ðkw=TwÞ ð27Þ

where subscript w indicates the substrate. The free surface is assumed to beadiabatic. Note that, initially, the dominant heat loss from the droplet is dueto heat conduction to the substrate, and later on, conduction and convectionto the solidified layer. Estimates of heat loss by convection from the dropletsurface to the surrounding gas showed that it is three orders of magnitudelower than heat conduction to the substrate. Therefore, the adiabatic con-dition at the free surface is reasonable. This condition can, however, beeasily modified to a convective, radiative or mixed boundary condition.

C. THERMAL CONTACT RESISTANCE

The incomplete contact between the drop and the substrate results in atemperature discontinuity across the contact surface. The effect can be in-corporated in the model via the definition of the thermal contact resistance,Rc (Eq. (1)). Values of Rc are provided as an input to the model. Although inprinciple Rc could vary with time and/or position on the interface, for sim-plicity it is assumed to be a constant. From the results of experiments de-scribed in Section V, Rc typically varies between 10�6 and 10�7m2K/W.

D. EFFECT OF SOLIDIFICATION ON FLUID FLOW

Computation of the velocity field has to account for the presence of amoving, irregularly shaped solidification front on which the relevant bound-ary conditions are applied. We treat the solidified regions by a modifiedversion of the fixed velocity method. In this approach, a liquid volumefraction Y is defined such that Y ¼ 1 for a cell completely filled with liquid;Y ¼ 0 for a cell filled with solid; and, 0oYo1 for a cell containing aportion of the solidification front. Normal and tangential velocities on thefaces of cells containing only solidified material are set to 0. The modifiedcontinuity and momentum equations are then given by [53]

= � ðYVÞ ¼ 0 ð28Þ

@ðYVÞ@t

þ ðYV � =ÞV ¼ �Yr

=pþYu=2VþYrFb ð29Þ

@f

@tþ ðYV � =Þf ¼ 0 ð30Þ


E. NUMERICAL PROCEDURE

The modified Navier–Stokes, volume of fluid, and energy equations aresolved on an Eulerian, rectangular, staggered mesh in a 3D Cartesian co-ordinate system. The computational procedure for advancing the solutionthrough one time step is as follows:

1. From time level n values, the velocity and pressure fields as well as fare calculated at time level n+1 in accordance with the 3D model ofBussmann et al. [35,36].

2. Given droplet enthalpy and substrate temperature fields at timelevel n, Eqs. (24) and (27) are solved implicitly to obtain the newenthalpy field in the droplet and the new temperature field in thesubstrate. Temperatures in the droplet can then be calculated fromEq. (26).

3. New values of the liquid volume fraction Y are calculated from theenthalpy field in the droplet by using Eq. (25a–c) in conjunction withan algorithm described by Voller and Cross [54]. In this algorithm, asphase change proceeds in a computational cell, the rate of change inthe cell enthalpy is the product of the speed of the phase change frontand the latent heat of fusion.

4. Flow and thermal boundary conditions are imposed on the free sur-face, at the solidification front, and other boundaries of the compu-tational domain. In particular, the thermal contact resistance at thedroplet–substrate interface is applied by using Eq. (1) and the heatflux to the substrate is calculated. This value of ‘‘q’’ is then used toupdate temperature boundary conditions along the bottom surface ofthe droplet and the upper plane of the substrate.

Repetition of these steps allowed advancing the solution through a giventime interval.

F. SIMULATION OF SPLAT FORMATION IN THERMAL SPRAY

Figure 9 shows the simulation views of a 73m/s normal impact of a 60 mmnickel droplet on a stainless steel substrate at 2901C initial temperature (thesurface of droplets in this figure correspond to the f ¼ 0.5 plane). The initialdroplet temperature was 16001C (i.e., 1501C of superheat) and the contactresistance was low at 10�7m2K/W. Considering nickel properties (Table I),this case corresponds to Re ¼ 7892, We ¼ 1419, Ste ¼ 1.67 and Pr ¼ 0.043.Figure 10 shows a cross-sectional view through the same drop, showingliquid (white) and solid (black) regions.

Immediately following impact, liquid jets out from under the drop andspreads in the radial direction. Solidification is however fast enough that all


parts of the droplet in contact with the substrate freeze 0.5 ms after impact(see Figures 9 and 10). When the bottom layer is solidified, the remainingliquid jets out over the rim of the splat. Shortly after the impact, the contactline becomes unstable leading to the liquid break-up. The shape of liquidligaments detached from the bulk of the splat changes due to surface tensioneffects. During this shape oscillation, most ligaments touch the surface be-cause they move close to the substrate. When this occurs, the liquid is

0.15 µs

0.5 µs

0.8 µs

1.4 µs

1.7 µs

2.2 µs

3.0 µs

10. µs

FIG.9. Simulations showing the impact of a 60 mm diameter molten nickel particle at

16001C landing with a velocity of 73m/s on a stainless steel plate initially at a temperature of

2901C. The contact resistance at the substrate surface was assumed to be 10�7m2K/W.

Adapted from Ref. [26].


dragged on the substrate (no-slip condition) making a finger around thebulk of the splat (Figure 9 at 10 ms). Small parts of the detached liquid thatfly away from the splat will eventually descend onto the substrate due togravity. The final shape of the simulated splat resembles those observed inexperiments under similar conditions.

In the absence of solidification, Rayleigh–Taylor instability [36] plays thedominant role in the break-up of an impacting droplet. To show that Ray-leigh–Taylor instability is not responsible for the break-up described above,and it is in fact solidification that causes splashing, we simulated the aboveimpact without heat transfer and solidification. Results showed no splash-ing; even when we initially induced formation of fingers, they merged later

TABLE I

PROPERTIES OF NICKEL, ALUMINA AND STAINLESS STEEL. FOR SUBSTRATE MATERIAL (STAINLESS

STEEL) THE ONLY PROPERTIES NEEDED ARE DENSITY, THERMAL CONDUCTIVITY AND SPECIFIC HEAT

Material Nickel Alumina Stainless steel

Properties

Density (kg/m3) 7.9E3 3.0E3 6.97E3

Melting point (1C) 1453 2050 –

Heat of fusion (J/kg) 3.1E5 1.075E6 –

Kinematic viscosity (m2/s) 1C1453 6.7E–7 1.026E–5 –

1477 6.4E–7

1527 6.0E–7

1577 5.7E–7

1627 5.4E–7

1727 5.0E–7

Liquid thermal conductivity (W/(mK)) 45 6 –

Liquid specific heat (J/(kgK)) 444 1300 –

Surface tension (N/m) 1.78 0.69 –

Solid thermal conductivity (W/(mK)) 1C 6 1C527 67.6 127 16.6

727 71.8 327 19.8

927 76.2 527 22.6

1227 82.6 727 25.4

927 28.0

1227 31.7

Solid specific heat (J/(kgK)) 1C 1C527 530 1273 127 515

727 562 327 557

927 594 527 582

1227 616 727 611

927 640

1227 682


on and the final shape was circular. Extensive trials with the numericalmodel confirmed that solidification is necessary to trigger splashing in anickel droplet of the size used in thermal spray coatings (o100 mm).

To model the effect of substrate temperature on final splat shape, initialsubstrate temperature was increased to 4001C. Figure 11a shows two images

0.15 µs

0.5 µs

0.8 µs

1.1 µs

1.4 µs

1.7 µs

2.2 µs

10. µs

FIG.10. A cross-sectional view of the images in Fig. 5. Black shows the solidified portion

of the droplet and white represent liquid. Adapted from Ref. [26].

a)

c)

b)

FIG.11. Nickel splat shapes on a steel plate initially at 4001C from (a) experiments (b)

numerical model assuming a contact resistance of 10�7m2K/W and (c) numerical model

assuming a contact resistance of 10�6m2K/W. Adapted from Ref. [26].


of disk splats that collected after spraying a stainless steel surface initially at4001C. Figure 11b shows the final shape of the simulated splat, calculatedassuming an initial surface temperature of 4001C and a thermal contactresistance Rc ¼ 10�7m2K/W. The droplet showed less splashing than it didin the previous simulation of impact on a surface at 2901C (see Figure 9),but there are still a significant number of fingers around it. The reasonsplashing diminishes on a hotter surface is that solidification is delayed andtherefore the fluid flow is not disturbed as much by a thinner frozen layer. Inother words, increasing the substrate temperature reduces Stefan number,while Prandtl number remains unchanged. As was stated before the ratio ofStefan number to Prandtl number reflects the importance of solidificationeffect on spreading.

Splashing could be eliminated completely in our simulations if the dropletdid not start solidifying until it had finished spreading. The onset of solid-ification could be delayed, the value of the thermal contact resistance be-tween the drop and the substrate was increased, thereby reducing heattransfer. Figure 11c shows the final splat shape on a surface at a temperatureof 4001C assuming a thermal contact resistance Rc ¼ 10�6m2K/W, which isan order of magnitude larger than that used previously. The splat was diskshaped, with no splashing, looking much like those observed experimentally(Figure 11a). The increase in thermal contact resistance is expected, sinceraising stainless steel substrate temperature thickens the surface oxide layer,hence increasing thermal contact resistance. Measurement of oxide layerthickness has confirmed this statement [55]. These results agree well with theprevious study of Fukomoto et al. [56], who also observed a sharp transitionfrom splashing to disk splats when spraying nickel particles on stainless steel.

Solidification inside a spreading droplet can trigger splashing. However,other protrusions on the surface can also make a droplet splash, such asscratches on the surface. The presence of an already solid splat under animpacting droplet can also create an instability that causes droplet splash-ing. Figure 12 shows simulations of the sequential impact of two nickeldroplets, both 60 mm in diameter and with impact velocities of 48m/s land-ing on a stainless steel surface at 1941C. The second droplet landed 5ms afterthe first, with its center offset by 140 mm from that of the first droplet.Contact resistance was assumed to be 5� 10�7m2K/W. The first dropletlanded, spread, and solidified without any significant splashing, forming adisk splat. The second droplet, introduced after the first one was completelysolidified, landed near the edge of the first splat. The spreading sheet ofliquid hit the solidified splat and was in part directed sideways; the remain-der of the liquid sheet jetted upward over the previously deposited splat andfragments with small droplets flying on top of the splats. Evidence of thistype of behavior is seen in experiments: Fig. 13 shows two splats deposited


next to each other on a surface at 4001C. The first splat is disk-like, but thesecond splashed after hitting the edge of the first. Streaks of splashed ma-terial are visible on the surface of the first splat.

Droplet and substrate materials properties are obviously important in deter-mining the splat shapes. Pershin et al. [1] studied both experimentally and nu-merically, the effect of substrate temperature on alumina splat shapes. Twosubstrate materials, glass and stainless steel, were employed. As shown in Ta-ble I, alumina and nickel have substantially different properties. Compared tonickel, alumina is substantially more viscous, less dense, has higher melting pointtemperature and higher heat of fusion, as well as much larger specific heat.

Figure 14 shows the predicted splat shape for the case of a 25-mm, 22601Calumina droplet impacting normally at 105m/s on a stainless steel substrate

0.3 µs 5.5 µs

0.8 µs 6.5 µs

2.2 µs 7.5 µs

5.0 µs 10 µs

FIG.12. Simulation images of the impact of two nickel particles (60mm diameter; 48m/s

impact velocity; initial temperature 20501C) on a stainless steel substrate initially at a temper-

ature of 1941C. The contact resistance below the droplets was assumed to be 5� 10�7m2K/W.

Adapted from Ref. [26].


initially at 251C (Figure 14a) and 5001C (Figure 14b). No break-up is pre-dicted. The non-dimensional parameters for this case are: Re ¼ 267.5,We ¼ 1198, Pr ¼ 6.67, and Ste ¼ 2.7 (for 251C) and 2.13 (for 5001C). Forboth substrate temperatures the first term in the denominator of Eq. (10),which gives the extent of solidification, is small and solidification does notplay a significant role on droplet spreading. In addition, for the given con-ditions, Rayleigh–Taylor instability does not cause break-up. Hence, in thecase of atmospheric sprayed alumina, the extent of break-up is much less

FIG.13. Micrograph of two nickel particles deposited on a stainless steel surface at 4001C.Adapted from Ref. [26].

a) b)

FIG.14. Final shapes of a 25 mm alumina particle at 2101C above melting point following

its 105m/s impact on a stainless steel plate initially at a temperature of (a) 251C and (b) 5001C.Adapted from Ref. [45].


than that for nickel, and perhaps other metals. Pershin et al. [1], however,report that a minority of alumina droplets break-up when substrate is atroom temperature. Figure 15 shows an example of these break-ups. Thefigure suggests that the nature of this break-up is different than that fornickel; there is no particular pattern to it or any symmetry. Presently, themodel cannot account for this behavior. It is probable that, in this case,break-up is related to substrate contamination, which can considerably altercontact angle and wettability. Alumina might be more sensitive to contam-ination than nickel. It is likely that when substrate temperature is raised, thecontamination evaporates, and a clean surface results. Finally, note that, inthe absence of contact angle information, a constant contact angle of 901was used for all simulations.

db

a c

FIG.15. Two types of alumina splats on glass (a, b) and stainless steel (c, d) substrates at

201C. Adapted from Ref. [45].


G. EFFECT OF ROUGHNESS

The three-dimensional model of droplet impact and solidification hasbeen used to simulate the effect of surface roughness on the impact dy-namics and the splat shape of an alumina droplet impinging onto a substrate[57]. The substrate surface was patterned with a regular array of cubesspaced at an interval twice their size. Three different cube sizes were con-sidered, and the results were compared to the case of droplet impact onto asmooth substrate. To understand the effect of solidification on the dropletimpact dynamics and splat morphology, the simulations were run with andwithout considering solidification.

Figure 16 shows simulated images of 40mm diameter alumina droplets,initially at 20551C, impinging with an impact velocity of 65m/s onto smoothand rough alumina substrates. Each column shows a droplet during successivestages of impact. For the rough substrates, the surface is patterned with cubeswhich are regularly spaced at an interval twice their side length. Three differentcube sizes, of side length 1, 2 and 3mm, were considered. In Fig. 16(a) to (d),the fluid flow, heat transfer and phase change are modeled. The splat shape onthe smooth substrate (Figure 16(a)) differs little from the shape on the 1mmrough substrate (Figure 16(b)). But as the roughness size increases further to 2and 3mm, the splat shape changes substantially. In particular, on the 3mmrough substrate, the droplet is blocked at t ¼ 0.8ms from spreading along the451 diagonal and effectively the liquid flow is channeled in two directions. To

FIG.16. Computer generated images of 40mm diameter alumina droplets at 20551C im-

pacting with a velocity of 65m/s onto alumina substrates initially at 251C, characterized by

different values of surface roughness.


understand the effect of solidification, Fig. 16(e) presents results of fluid flowwithout solidification for the case of 3mm roughness.

In Fig. 17(a), a quarter of the final shape of the alumina splats is depictedfor different substrate surface conditions. As the size of the surface rough-ness increases from 0 (smooth) to 1 and 2 mm, the splat radius also increases.However, on the 3 mm rough substrate, the extent of spreading along thehorizontal and vertical axes is approximately equal to that on the smoothsubstrate. Figure 17(a) also clearly depicts the effect of roughness size on thesplat morphology.

The upper half of Fig. 17(b) shows an alumina splat on the substrate of3 mm roughness at t ¼ 5 ms, for the case when solidification is modeled. Forcomparison, the lower half of Fig. 17(b) shows the droplet shape on thesame substrate and at the same time, but without solidification. Comparingthe two cases, the effect of solidification on the splat shape is very well seen.It must be mentioned that without solidification, the droplet recoils furtheruntil it reaches its equilibrium configuration which is not shown here.

Finally, Fig. 18 shows the cross-sections of the alumina splat on the 3 mmrough substrate, along directions A–A (horizontal) and B–B (451 diagonal)shown in Fig. 17(b). The cubes on the substrate and the splat are shown inblue and red, respectively. The splat appears to bond more completely withthe substrate along the diagonals, as the voids beneath the splat are smalleralong section B–B than along section A–A.

FIG.17. (a) Comparison of alumina splats on different surface conditions in the presence

of solidification. (b) Comparison of splat shape on a substrate with 3mm roughness with and

without solidification.


V. Laboratory Experiments on Droplet Impact

A. LARGE DROPLETS

Early attempts to understand heat transfer and fluid flow during moltendroplet impact relied on laboratory experiments in which the impact ofrelatively large (2–4mm) molten metal droplets was photographed andsubstrate temperature under impacting droplets was measured. Aziz andChandra [18] used an experimental apparatus that consisted of a dropletgenerator, a test surface on which droplets landed, photography equipmentand temperature measurement instrumentation. Droplets fell after detach-ment from the droplet generator nozzle through a heated tube onto astainless steel plate mounted on a heated copper block. The droplet gen-erator height above the test surface could be adjusted, allowing dropletimpact velocity to be varied from 1 to 4m/s. The test surface was housed in achamber filled with inert gas to prevent oxidation of droplets. A single-shotphotographic technique was used to capture droplet impact. As a dropletfell to the surface it interrupted a laser beam, tripping a timing circuit thatopened the shutter of a camera and triggered an electronic flash, taking asingle photograph of an impacting droplet. By adjusting the time delaydifferent stages of droplet deformation were captured, and the entire impactpieced together from this sequence of photographs.

The effect of increasing droplet velocity on impact dynamics is visible inFig. 19, which shows molten tin droplets landing on a 251C stainless steelsubstrate with impact velocities of 1m/s (Figure 19a), 2m/s (Figure 19b) and4m/s (Figure 19c). Each row in Fig. 19 represents the same dimensionlesstime (t� ¼ tVo/Do); the real time (t) from the instant of impact is indicatednext to each frame. At a low impact velocity Vo ¼ 1m/s (Figure 19a), thedroplet reached its maximum spread a little after t� ¼ 1.0. The molten layerwas pulled back by surface tension, and recoiled above the surface(t� ¼ 4.5). The drop finally subsided and solidified to form a rounded splat(t� ¼ 7.5). Increasing the impact velocity to 2m/s (Figure 19b) increased thesplat diameter and reduced the splat thickness. The recoil of the droplet was

FIG.18. Cross-section of an alumina splat on a substrate with 3 mm roughness in the

directions shown in Fig. 17(b). The cubes on the substrate and the splat are shown in blue and

red, respectively.


also greatly diminished, so that there was only a small flow of liquid backfrom the edges of the splat towards its center. There was also evidence of theformation of fingers around the edges of the splat (t� ¼ 1.0). At the highestvelocity, 4m/s (Figure 19c), the fingers were large, and visible very earlyduring impact. The tips of the fingers had enough inertia to detach as smallsatellite droplets (t� ¼ 4.5). The growth of the fingers was stopped by thedroplet solidifying so that the final splat shape was reached by

FIG.19. Impact of molten tin droplets on a stainless steel surface at temperature 251Cwith velocity (a) 1m/s, (b) 2m/s and (c) 4m/s [Ref. 18].


approximately t� ¼ 4.5, with little change after that time. On a surface thatwas maintained at 2401C, above the melting point of tin (2321C), there wasextensive splashing in droplets impacting at a velocity of 4m/s, so that theyshattered upon impact [18].

Figure 20 shows the effect of increasing surface roughness on dropletimpact [58]. Each column in the figure shows the impact of a 2.2mm di-ameter tin droplet impacting with 4m/s velocity on surfaces of differentaverage roughness, having Ra 0.07, 0.56 and 3.45 mm, respectively. The timeafter impact is indicated on the left side of the images. The first column,impact on a surface with roughness 0.07 mm was the same case as that seenin Fig. 19c. Small fingers were observed around the periphery of the dropimmediately after impact with some of these detaching to form satellitedroplets. Increasing the roughness of the stainless steel substrate toRa ¼ 0.56 mm produced significant changes in droplet spreading (see Fig-ure 20b). Instead of thin fingers there were large, triangular projectionsaround the periphery of the drop early during spreading (t ¼ 0.3ms) whichthen broke loose (t ¼ 0.6ms) and continued to travel outwards, leavingbehind a solidified circular splat (t ¼ 7.9ms). Increasing the roughness evenfurther to Ra ¼ 3.45 mm produced further changes in the droplet shapeduring spreading (Figure 20c). Again there were triangular projectionsaround the drop (t ¼ 0.3ms), but these did not detach (t ¼ 1.1ms). In thiscase solidification of the droplet was much slower, so that it remained liquidand surface tension forces pulled back the edge of the droplet (t ¼ 7.9ms).The final splat had a distinctive star-like shape.

On a smooth surface the thermal contact resistance between the dropletand surface is low because little air is trapped in surface cavities. Thereforesolidification is rapid, starting before the droplet has fully spread. Increas-ing the surface roughness raises contact resistance, and lets the dropletspread to a greater extent before it freezes. Therefore droplets spread fur-ther on a rough surface than on a smooth surface when the substratetemperature was low enough to cause freezing. On a hot surface, wherethere was no solidification, surface roughness had little effect on dropletspread [58].

B. SMALL DROPLETS

Studies of large molten metal droplet landing at low velocity give insightinto the dynamics of spreading; however, they do not seem adequately sim-ulate the splashing of plasma particles. Splashing of droplets increases withboth Reynolds and Weber numbers. The impact Weber and Reynoldsnumber of such droplets is much lower than those in typical plasma sprayapplications (We�102 and Re�103 in experiments, compared to Re and


FIG.20. The impact of 2.2mm diameter molten tin droplets with 4.0m/s velocity on a

stainless steel plate at a temperature of 2401C with surface roughness Ra (a) 0.07mm, (b)

0.56mm and (c) 3.45mm [Ref. 58].


We�103–104 in applications). For low We and Re droplet solidificationsuppresses splashing, since the impacting liquid does not have enough mo-mentum to jet over the solidified layer near the edges of droplets and splash.

Droplet size also affects heat transfer, since it alters the relative resistanceto heat conduction of the droplet itself, relative to the thermal contactresistance between the particle and substrate. The ratio between the two isgiven by the Biot number (Bi ¼ Do/(Rckd)). For the 2.2mm diameter tindroplets of Fig. 19 Bi�102 (assuming Rc ¼ 10�6m2K/W), and thermalcontact resistance can be neglected; for a thermal spray particle with di-ameter two orders of magnitude smaller, Bi�1, and contact resistance con-trols heat transfer from the particle to the substrate.

Mehdizadeh et al. [11] built an apparatus in which molten tin dropletsimpinged on a steel plate mounted on the rim of a rotating flywheel, givingimpact velocities of up to 40m/s and We�103. Photographs of splashingdroplets were compared with predictions from computer simulations thatshowed that freezing around the edges of a spreading droplet obstructsliquid flow and causes splashing. Figure 21 shows a schematic diagram ofthe experimental apparatus used. It consisted of a molten metal dropletgenerator that produced uniform-sized tin droplets (0.6mm diameter) ondemand. In order to achieve high impact velocities, the substrate wasmounted on the rim of a rotating flywheel. The substrates could be heatedand maintained at a desired temperature by means of cartridge heatersinserted into the plate on which the substrate was mounted. Substrate tem-perature was allowed to reach steady value while rotating before drops weredeposited. An optical sensor ascertained the position of the flywheel andactivated a timing unit that synchronized droplet ejection with triggering ofa high-resolution digital camera and flash so that a single photograph wastaken when a falling droplet collided with the horizontally moving substrate.By varying the time delay before triggering the camera different stages ofimpact were photographed. Flywheel rotation was monitored by means of adigital motion controller and feedback system that controlled angular ve-locity within70.5%. The vertical velocity of the droplet was less than 1m/s,whereas the linear velocity of impact varied between 10 and 30m/s: impactwas therefore essentially normal. The entire droplet impact process tookapproximately 100–200 ms, depending on impact velocity.

Dhiman and Chandra [59] used the same apparatus to photograph impactof tin droplets on solid plates for a range of impact velocities (10–30m/s),substrate temperature (25–2001C) and substrate materials (stainless steel,aluminum and glass). Droplet Reynolds number ranged from 2.2� 104 to6.5� 104 and Weber number from 8.0� 102 to 7.2� 103. Figure 22 showsimages of 0.6mm diameter tin droplets impacting on a mirror-polishedstainless steel substrate with 20m/s velocity. Each column shows successive


stages of droplet impact on a substrate at initial temperature (Ts,i) varyingfrom 25 to 2001C (indicated at the top of the column). The first picture ineach sequence shows a droplet prior to impact, and the last shows the finalsplat shape. Droplets hitting a cold substrate (Ts,i ¼ 25�1501C) splashedextensively, producing small satellite droplets and leaving a splat with ir-regular edges. The final splat surface was rough along the periphery, show-ing the region where it first solidified very rapidly; the center was smoother,marking the area where surface tension forces had enough time to smoothenthe surface before the onset of solidification. The extent of splashing

FIG.21. Schematic of droplet impact apparatus.


decreased and eventually disappeared as substrate temperature was in-creased. No splashing was visible on a surface at 1801C. Solidification didnot start until fairly late during spreading; localized freezing at several spotsacted to obstruct spreading of the splat and produced an irregular shapedsplat even though there was no splashing. At Ts,i ¼ 2001C solidification wassufficiently delayed that droplets spread to form thin disks. Computer sim-ulations [11] have shown that freezing around the droplet periphery duringspreading on a substrate at low temperature obstructs liquid flow and trig-gers splashing. When substrate temperature is increased, freezing is sloweddown and the droplet spreads in the form of a thin liquid sheet without anysplashing. The transition temperature, though difficult to identify exactly,lies between Ts,i ¼ 150 and 1801C.

C. TRANSITION TEMPERATURE MODEL

Heat transfer from the spreading splat to the substrate can reasonably beassumed to be one-dimensional: numerical simulations of molten metaldroplet impact [11,17] have shown that temperature gradients in the subst-rate normal to the surface are several orders of magnitude greater than those

FIG.22. Impact of molten tin drops with velocity 20m/s on a stainless steel surface at

temperature, Ts,i. Re ¼ 43,636, We ¼ 3180 [Ref. 59].


in the radial direction. Poirier and Poirier [19] developed an analytical modelfor solidification of a molten metal in contact with a solid, semi-infinitesubstrate that accounts for thermal contact resistance at the droplet–subst-rate interface. The substrate is assumed to be isotropic with constant ther-mal properties. At time t ¼ 0, the molten droplet at its melting point issuddenly brought into contact with the substrate whose initial surface tem-perature (Ts,i) is below the melting point of the droplet (Tm).

The contact resistance (Rc) at the melt–substrate interface is assumed tobe constant so the surface temperature Ts is given by

T s ¼ Tm � qoRc ð31Þ

where qo is the heat flux leaving the bottom surface of the splat. It is as-sumed that there is no temperature drop across the solidified layer. Cal-culations of the temperature drop across the solid layer shows that itincreases from 0 to a maximum of 121C while the molten tin is at its meltingpoint of 2321C.

The thickness of the solid layer as a function of time (t) is given by [19]:

s ¼ 2ffiffiffip

p ðTm � T s;iÞrdHf ;d

ffiffiffiffiffiffigst

p1� Rc

ffiffiffiffiffigspt

rln 1þ 1

Rc

ffiffiffiffiffiptgs

r� �� ð32Þ

Equation (11) can be written in non-dimensional form as

s ¼ 2ffiffiffip

p Ste

ffiffiffiffiffiffiffiffiffiffigst

gdPe

s1� 1

Bi

ffiffiffiffiffiffiffiffiffiffiffigsPegdpt

sln 1þ Bi

ffiffiffiffiffiffiffiffiffiffiffigdpt

gsPe

s" #( )ð33Þ

Splat thickness is estimated by assuming that the solidified splat is a thincylindrical disk with a volume equal to that of the initially spherical droplet.The splat thickness (h) is [19]

h ¼ 2Do

3x2max

ð34Þ

where xmax is the maximum splat diameter (Dmax) non-dimensionalized bythe initial droplet diameter (Do) which can be calculated from the followinganalytical expression [10]:

xmax ¼Dmax

Do¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiWeþ 12

3

8Wes þ 3ð1� cos yaÞ þ 4

WeffiffiffiffiffiffiRe

p

vuuut ð35Þ


Substituting xmax from Eq. (14) into Eq. (13) gives an expression for thedimensionless splat thickness:

h ¼ h

Do¼

23

8Wes þ 3ð1� cos yaÞ þ

4WeffiffiffiffiffiffiRe

p� �

3ðWeþ 12Þ ð36Þ

The dimensionless time taken by an impacting droplet to reach its max-imum extension ðtc Þ has been estimated by Pasandideh-Fard et al. [16] as

tc ¼8

3ð37Þ

Equation (16) is valid, in principle, for all values of Re and We, and hasbeen shown [10–12,19] to agree reasonably well with experimental meas-urements.

The criterion we use to determine the transition temperature is that it isthe surface temperature for which the solid layer grows as thick as the splatin the time the droplet takes to spread to its maximum extent: in dimen-sionless form, h ¼ s at time t ¼ tc . Using h ¼ s in Eq. (15) gives thefollowing expression for dimensionless solid layer thickness:

s ¼ 8 ð1� cos yÞ þ ð4We=3ffiffiffiffiffiffiRe

pÞ �

3ðWeþ 16Þ ð38Þ

Substituting Eqs. (7) and (8) in Eq. (3) we obtain the following expressionfor critical Stefan number (Stec, the Stefan number at which Ts,i ¼ Tt):

Stec ¼APe

2ðWeþ 16Þ ð1� cos yaÞ þ4We

3ffiffiffiffiffiffiRe

p� �

1

1� lnð1þ BiAÞ=BiA �ð39Þ

where

A ¼ffiffiffiffiffiffiffiffiffiffiffiffi8pgd3Pegs

sð40Þ

The transition temperature (Tt) is given by

T t ¼ Tm � StecHf ;d

cdð41Þ

Figure 23 shows the calculated variation of transition temperature withimpact velocity for 0.6mm diameter tin droplets. Aziz and Chandra [10]


measured the advancing contact angle (ya) of molten tin on a smooth pol-ished stainless steel surface to be around 1401, which was used in all cal-culations; a variation of 7201 in the magnitude of ya led to a variation ofless than 70.5% in the prediction of transition temperature. Since the con-tact resistance was unknown, curves are shown for three different values ofRc (10�6, 10�7 and 0m2K/W). The shaded region in Fig. 23 shows theobserved range of transition temperature values. Assuming Rc ¼ 10�7m2K/W gives predictions for the transition temperature in the range 155–1601C,which agree reasonably with experimental observations.

Droplet impact velocity may either increase or decrease transition tem-perature, depending upon the value of the contact resistance; forRco10�7m2K/W, Tt increases slightly with impact velocity, whereas forRc ¼ 10�6m2K/W, Tt decreases. Increasing impact velocity has two effects:it decreases both droplet spreading time and splat thickness. A smallerdroplet spreading time implies that the solid layer has to grow faster toobstruct flow, so the transition temperature is lowered. However, as impactvelocity increases, splat thickness diminishes and the solid layer has to growto a smaller thickness, which increases transition temperature. The magni-tude of contact resistance determines which of these two competing effectsdominates. When Rc is low, the solid layer grows rapidly and spreading timevariation is less important; for higher Rc, solid layer growth is slow andtherefore transition temperature is determined by the time of droplet

FIG.23. Variation of transition temperature, Tt for stainless steel substrate with impact

velocity, Vo for different values of contact resistance, Rc at the droplet–substrate interface

[Ref. 59].


spreading. In either case the magnitude of the change is small, less than101C, and difficult to detect in our experiments.

D. EFFECT OF SUBSTRATE MATERIAL

The model for transition temperature predicts that it is a function of thesubstrate thermal property gs ¼ (rskscs). Aluminum has a much higher value ofgs (5.8� 108 J2m�4 s�1K�2) than stainless steel (gs ¼ 5.8� 107 J2m�4 s�1K�2),while g for glass is much lower (2.6� 106 J2m�4 s�1K�2). Calculated values ofTt are shown in Fig. 24 for all three materials. Assuming that Rc ¼ 10�7m2K/W in all cases, the transition temperature on aluminum substrates is higherthan that on stainless steel. The model predicts that we will never observesolidification-induced splashing on a glass substrate maintained at room tem-perature, since the transition temperature is always far below that. Changingthermal contact resistance had little effect: setting Rc ¼ 0 for glass raised Tt byonly about 201C.

Figure 25 shows three sequences of images showing the effect of substratematerial on droplet impact dynamics. Substrate temperature was 251C andimpact velocity was 10m/s in all cases. The first column shows differentstages of droplet impact on an aluminum substrate. The droplet splashedafter impact and left a small splat that had a rough surface and edges.

FIG.24. Variation of transition temperature, Tt with impact velocity, Vo for aluminum,

glass and stainless steel surfaces. Rc ¼ 10�7m2K/W [Ref. 59].


Splashing occurred on a stainless steel surface as well, but the final splat wasa little larger and the center of it was smooth, showing that solidificationwas slow enough for surface tension to smoothen the splat surface. Therewas no splashing on the glass surface, as predicted by the model.

FIG.25. Impact of molten tin drops with velocity 10m/s on substrates of different ma-

terials at an initial temperature, Ts,i ¼ 251C. The last picture in each column is the final

solidified shape of the droplet. Re ¼ 21,818, We ¼ 795 [Ref. 59].


VI. Thermal Spray Splats

A. WIRE-ARC

Figure 26 shows images of aluminum splats formed on stainless steelsubstrates held at temperature (Ts) ranging from 25 to 3001C, and corre-sponding cross-sections through coatings formed at the same conditions.The two columns on the left show splats and coatings formed with a higheratomizing gas pressure, where mean particle velocity was 143m/s, whilethose on the right were formed with a lower gas pressure and mean impactvelocity of 109m/s. At surface temperatures below 1001C splats showedsigns of having undergone extensive splashing, with long fingers radiating

FIG.26. Splat morphology and coating microstructure of aluminum deposited onto pol-

ished stainless steel (type AISI304L) held at various temperatures.


out from a central core of solidified metal. Computer simulations of dropletsplashing [11,55] have shown that solidification starts at the periphery of thespreading droplet, creating a solid rim that forces the liquid to jet off thesurface, where it becomes unstable and breaks into fingers. Voids betweenfragments of the drop and in the central splat itself create pores in thecoating: cross-sections through coatings formed on surfaces at 251C showlarge voids and pores (see Figure 26). The voids were largest at the lowerimpact velocity (V ¼ 109m/s), especially at the substrate–coating interface,and decreased when impact velocity increased to 143m/s.

Increasing substrate temperature produced a change in splat shape. As Ts

was increased above 1001C splats became rounder and fingers becameshorter until they disappeared almost entirely. The change was progressive,but there was a sharp transition in the range 1001CoTso1501C for splatswith mean velocity 143m/s. At lower impact velocity (109m/s) the transitiontemperature was in a higher range 2151CoTso2501C. The number of voidsin splats decreased as substrate temperature was elevated (see Figure 26) andas a consequence the density of pores in the coating also decreased.

Judging the transition temperature from photographs of individual splatsis subjective, since the decrease in splashing is gradual. A more reliabletechnique for determining transition temperature, proposed by Fukomoto[60], is to photograph an area of the substrate with 20–30 splats on it andcount the fraction of disk splats. The frequency of disk splats was countedfor three different substrates at each temperature and their average calcu-lated. Figure 27 shows the variation of disk splat frequency with substrate

FIG.27. Frequency of disk splats increases with increasing substrate temperature.


temperature, at two different impact velocities. Less than 10% of dropletslanding with average velocity 143m/s formed disk splats at Ts ¼ 1001C,increasing to more than 80% at Ts ¼ 2001C. The transition temperature,corresponding to a disk splat frequency of 50%, was 1401C. When impactvelocity was reduced to 109m/s the transition temperature increased to2301C.

An alternate method of identifying the transition temperature is to cal-culate the degree of splashing (DS) as defined by Sampath et al. [61]

DS ¼ P2splat

4pAsplatð42Þ

where the splat area (Asplat) and the length of the periphery (Psplat) of eachsplat are determined using the image analysis software. Figure 28 shows thevariation of DS as a function of substrate temperature. As splashing de-creases so does DS approaching DS ¼ 1 for perfectly circular splats. Se-lecting a threshold of DS ¼ 1.5, above which splats were noticeablydistorted, gives values of transition temperature close to those obtainedby counting the frequency of disk splats.

Figure 29 shows the variation of transition temperature with impact ve-locity for aluminum droplets impacting stainless steel surfaces. Results areshown for four different values of Rc ¼ 0, 10�7, 1.4� 10�7 and1.7� 10�7m2K/W, as well as the three experimentally determined values

FIG.28. Degree of splashing decreases with increasing substrate temperature.


of Tt. Transition temperature decreased significantly with increasing contactresistance. For Rc ¼ 0 there was little effect of impact velocity on transitiontemperature; at higher values of contact resistance transition temperaturedecreased with impact velocity. As impact velocity increases droplet spread-ing time and splat thickness both decrease. As a consequence of shorterdroplet spreading time the solid layer has to grow faster to obstruct flow,resulting in a lower transition temperature. However, reduced splat thick-ness means that the solid layer has to grow less to obstruct flow, whichincreases transition temperature. The contact resistance determines the rel-ative magnitude of these two competing effects. For Rc ¼ 0, solidificationprogresses rapidly and changes in spreading time have little impact; forhigher Rc, solid layer growth is slow and therefore transition temperaturedecreases with increasing droplet velocity.

The experimentally observed decrease in transition temperature, from2301C at Vo ¼ 109m/s to 1401C at Vo ¼ 143m/s, was more than that pre-dicted by the model if Rc was assumed the same at both temperatures.However, it seems quite likely that contact resistance increases with surfacetemperature due to the growth of an oxide layer when steel plates are heatedin air. Heating test coupons to 3001C changed their color to a golden hue,which turned brown under further heating. The oxygen content of thestainless steel substrates, measured using X-ray Photoelectron Scanning(XPS) to determine the elemental composition, increased from 35% of thetotal at room temperature to over 60% at 3501C, indicating increasedoxidation.

FIG.29. Prediction of transition temperature.


B. PLASMA PARTICLE IMPACT

McDonald et al. [62] photographed impact of plasma-sprayed particles onboth hot and cold glass substrates. A schematic diagram of the experimentalsetup used is shown in Fig. 30. A SG100 torch (Praxair Surface Technol-ogies, Indianapolis, IN) was used to melt and accelerate dense, sphericalmolybdenum and amorphous steel powder particles, sieved to +38–60 mm,with an average diameter of 40 mm. In order to heat the substrate, the glasswas placed in a copper substrate holder that included resistance heaterwires.

The plasma torch was passed rapidly across the glass substrate. In orderto protect the substrate from an excess of particles and heat, a V-shapedbarrier was placed in front of the torch. This V-shaped shield had a 3.5mmhole in it through which particles could pass. To reduce the number ofparticles landing on the substrate, two additional barriers were placed infront of the substrate, the first of which had a 1mm hole and the second, a0.6mm hole. All the holes were aligned to permit passage of the particleswith a horizontal trajectory.

After exiting the third barrier and just before impacting the substrate, thethermal radiation of the particle was measured with a rapid two-color pyro-metric system. This system included an optical sensor head that consisted ofa custom-made lens, which focused the collected radiation, with 0.21 mag-nification, on an optical fiber with an 800mm core [63]. This optical fiber wascovered with an optical mask that was opaque to near infrared radiation,except for three slits (see Figure 31a). The two smaller slits (slits b and c inFigure 31a), with dimensions of 30mm� 150mm and 30mm� 300mm, wereused to detect the thermal radiation of the particles in-flight. The radiationwas used to calculate the temperature, velocity and diameter of the in-flightparticle [63,64]. The largest slit (slit e in Figure 31a), measuring150mm� 300mm, was used to collect thermal radiation of the particle as itimpacted and spread on the substrate. With the thermal radiation from thisslit, the splat temperature, diameter and cooling rate were calculated at100 ns intervals after impact.

The collected thermal radiation was transmitted through the optical fiberto a detection unit that contained optical filters and two photodetectors. Theradiation beam was divided into two equal parts by a beam splitter. Eachsignal was transmitted through a bandpass filter with wavelength of either785 or 995 nm and then detected using an avalanche silicon photodetector.The ratio of the radiation intensity at these wavelengths (referred to as D1

and D2, respectively) was used to calculate the particle temperatures with anaccuracy of 71001C [64]. The signals were recorded and stored by thedigital oscilloscope. A signal from the laser diode in Fig. 30 was also stored


FIG.30. Schematic of the experimental assembly.

190

J.MOSTAGHIM

IAND

S.CHANDRA

by the oscilloscope. This indicated the time in which the splat image wascaptured, relative to the pyrometric signals.

Figure 31b shows a typical signal captured by a photodetector. The labels,a–f, correspond to the position of a particle (shown in Figure 31c) as itpasses through the fields of view of each of the optical slits. At points a andd, the particle was not in the optical field of view of any of the slits, so thesignal voltage was zero. The two peaks at points b and c were produced bythermal emissions from the particle as it passed through the first two smallslits. The droplet average in-flight velocity was calculated by dividing the

FIG.31. (a) Details of the three-slit mask. (b) A typical signal collected by the three-slit

mask. (c) Schematic of the optical detector fields of view.


known distance between the centres of the two slits by the measured time offlight. At point e the droplet entered the field of view of the third and largestoptical slit. This is shown on the thermal signal by a plateau in the profile.Upon impact at f, the signal increased as the particle spread and eventuallydecreased as the particle cooled down and/or splashed out of the field ofview.

To illuminate an impacting particle, a 572 ns duration pulse of light froma Nd:YAG laser was used. When the particle entered the large slit field ofview (labeled e in Figure 31a) of the optical fiber, a signal was sent to triggerthe laser after a controlled time delay. This permitted illumination of thesubstrate at different time intervals after impact and during spreading of thedroplet. A 12-bit CCD camera was used to capture images of the spreadingparticles from the back of the glass substrate.

Figure 32 shows images of molybdenum splats at different times afterimpact on glass held at room temperature or at 4001C. The figure also showstypical D1 thermal emission signals; D2 thermal emission signals have thesame shape and are not shown. For molybdenum, the average droplet di-ameter was 40 mm, the average impact velocity was 135m/s, and the averagetemperature of the particles in-flight was 29801C, well above the meltingpoint (26171C).

The photodetector signal of impact and spread on the glass held at roomtemperature was subdivided into four intervals (indicated by labels a–e inFigure 31a) and photographs taken in each of these time periods aregrouped together in Fig. 32a. The approximate time after impact that cor-responds to each interval is shown in the figure. To demonstrate the re-peatability of the process, two splat images are shown during each timeinterval. The a to b range represents splats immediately before or uponachieving the maximum spread diameter of 400 mm. Beyond point b, theliquid portion of the splats begin to disintegrate, initially from the solidifiedcentral core and later, from sites within the liquid film. After point d, thesplat is almost totally disintegrated and only a central solidified core remainson the glass.

Figure 32b shows the results after impact on a glass substrate at 4001C.There was almost no splat break-up or splashing, unlike that seen inFig. 31a. Also, the diameter of the splat increased to a maximum of 140 mmafter impact, much less than that on a cold surface (400 mm). At point h onthe pyrometric signal, there is a voltage decrease, followed by an increasethat begins about 4 ms after impact. This is typical of the spreading splats onthe hot glass and represents the onset of liquid solidification. Pyrometricmeasurements of the splat temperature during spreading on the heated glass(Fig. 33b) showed that the time period around point h corresponded to aperiod of almost constant splat temperature, indicating recalescence and


solidification, which began about 4 ms after impact. In this case, duringrecalescence, the splat temperature fell below the melting point and wasraised, as the latent heat of fusion is released, until solidification was com-plete, instead of until reaching the fusion point [65]. After complete solid-ification, the temperature began to decrease again as the splat cooledfurther. This phenomenon is not observed on the pyrometric signal of thesplats on non-heated glass (Figure 31a). Moreau et al. [66] have shown that,for molybdenum, splat material loss begins approximately 3 ms after impact,when the molten material exits the pyrometric field of view. Pyrometricmeasurements of the splat temperature (Figure 33a) show that the splattemperature at this time is approximately 28001C, well above the

FIG.32. Typical thermal emission signals and images of molybdenum splats at different

times after impact on glass held at (a) room temperature and (b) 4001C [Ref. 62].


molybdenum melting point (26171C). From the pyrometric signals, rec-alescence is not observed because a large portion of the splat has exited thefield of view before solidifying.

The time required for the splat to spread to its maximum diameter af-ter impact was measured starting at the instant the pyrometric thermalemission signals began to increase after the plateau (point f of Figure 31b)to the maximum voltage on the thermal emission signal profile. For mo-lybdenum on glass held at room temperature, the maximum spread time was2 ms and on glass held at 4001C, it was 1ms. Analysis of the images indicatesthat the maximum spread diameter of the splats on the cold glass are ap-proximately three times that on the hot glass for both the pure metal and thealloy.

The evolution of the liquid temperature during the spreading of molyb-denum on cold and hot glass is shown in Fig. 33. The temperatures were

FIG.33. Typical cooling curves of molybdenum splats on glass held at (a) room tem-

perature and (b) 4001C [Ref. 62].


calculated from the ratio of signals from the photodetectors, D1 and D2, anda calibration equation determined experimentally. In the figures, the slope ofthe curves, dT/dt, represents the average splat cooling rate calculated fromall available splats. Since, on glass held at room temperature, fragmentationand splashing were observed after achieving the maximum spread diameter(Figure 31), the cooling rate of the liquid splat was calculated from the timeof impact to the point of initial disintegration of the splat (�2–3 ms afterimpact). On glass held at 4001C, the degree of splashing was small, so thecooling rate of the liquid splat was calculated from the time of impact to thesolidification plateau. Table II shows the average cooling rates of plasma-sprayed molybdenum and amorphous steel on glass held at room temper-ature and at 4001C.

For both materials, the liquid cooling rates on glass held at 4001C isapproximately an order of magnitude larger (order of 108K/s) than on theglass held at room temperature (order of 107K/s). This suggests that thermalcontact resistance between the cold glass and the splat is greater than thatbetween the hot glass and splat. The cause of the increased thermal contactresistance on the cold surface is probably a gas barrier, formed after evap-oration of adsorbed substances on the substrate beneath the splat. It ispossible that heating the surface removes the adsorbed substances and gasbarrier, producing better contact [8].

The cooling curves of the splats on glass held at 4001C show the solid-ification plateau at temperatures lower than the melting point of the ma-terials. For molybdenum, with melting point at 26171C, the solidificationplateau occurs at approximately 22001C. For amorphous steel, completesolidification occurs at approximately 7001C, but the temperature requiredis 15501C. The occurrence of solidification at temperatures lower thanthe equilibrium melting point is evidence that undercooling of the splatsoccurred. Moreau et al. [67] found that undercooling occurred when amolybdenum particle impacted a previously deposited, hot splat. The cool-ing rate was larger than that of a particle that impacted the bare, coldsubstrate.

TABLE II

AVERAGE COOLING RATES OF MOLYBDENUM AND AMORPHOUS STEEL SPLATS

Material Glass temperature (1C) No. of samples dT=dt� 107 (K/s)

Molybdenum 27 17 3.370.2

400 21 2271.2

Amorphous steel 27 12 5.870.8

400 6 3271.7


VII. Simulating Coating Formation

In spite of the extensive literature published on processes such as plasmaspraying or HVOF spraying, thermal spray coating still remains as much anart as a science. The user has to select suitable values for a large number ofvariables, including the power of the torch, gas flow rates, substrate standoffdistance, powder feed rate and speed of torch movement. Coating qualitydepends a great deal on the skill of the operator in selecting these param-eters, which differ for each coating material. Typically a lengthy process oftrial-and-error goes into optimizing thermal spray operations for any givenapplication. Since the equipment is expensive to operate, the cost of devel-oping new coatings can be very high. A computer model capable of pre-dicting coating properties as a function of process parameters could, inprinciple, greatly reduce development time. However, the physical mecha-nism by which a thermal spray coating is formed is so complex that fewattempts have been made to simulate it.

Simulating impact of droplets on an uneven surface requires a fully three-dimensional model, which places severe demands on computing resources.Modeling the impact and solidification of just a single drop requires manyhours of computer time [55]; simulating the build-up of even a small area ofcoating, which may consist of several thousand droplets, is extremely timeconsuming.

A. DIRECT COATING MODEL

Figure 34 shows the deposition of alumina droplets on a stainless steelsubstrate. Droplet diameter was set to 2876 mm, velocity to 105716m/s,while droplet temperatures varied between 250075001C. Droplet propertieswere assigned randomly by the computer: a random number between 0and 1 was generated, and multiplied by twice the standard deviation of aspecific parameter and added to the minimum value of that parameter toobtain range of values evenly distributed between the maximum and min-imum values. The time interval between the deposition of two successivedroplets was set to 1 ms. All droplets impacted downward, in a directionperpendicular to the substrate surface. Since the melting point of alumina is20521C, some unmelted particles were introduced into the coating. Thecomputational domain was 1mm long, 0.25mm wide and 0.125mm highdivided into a mesh with 302� 52� 52 nodes. The 0.05mm thick substratehad 22 node points. This was the finest resolution that could be tried, giventhe limitation of 1.5G computer memory. A value of Rc ¼ 1.5� 10�6m2K/W was used at all interfaces. Numerical computations were performed on aSun Ultra Enterprise 9.1 workstation. Typical CPU time for the deposition


of the first 20 alumina droplet was 350min. As droplets accumulatedand coatings became thicker, computing times became longer. For the sec-ond set of simulations, it took almost 2 weeks to model impact of the last20 droplets (of a total of 300). The deposition of 300 droplets took about81 days.

Figure 35 shows the final coating produced by 300 droplets depositedrandomly on the surface. Coating porosity (59%), roughness (2.4 mm) andaverage thickness (31 mm) were evaluated from cross-sections throughthe coating. The values of porosity are much higher than those obtainedtypically in plasma coating processes, which are less than 15%. The reasonfor this discrepancy appears to be the relatively low resolution used in

FIG.34. Deposition of alumina droplets on a stainless steel substrate. (a) An unmelted

particle lands on the surface at t ¼ 28.0ms; (b) coating profile at t ¼ 28.8ms; (c) coating profile

at t ¼ 100ms; (d) a coating cross-section passing through the center of the unmelted particle at

t ¼ 100ms.


our simulations. The mesh spacing was such, that even at the highestresolutions, a typical droplet diameter corresponded to 8–10 node points.High-resolution simulations of single droplet impact [17] have used up to 44node points per droplet diameter. Achieving more realistic results will re-quire higher resolution computations than those done here.

B. STOCHASTIC COATING MODEL

Since direct simulation of coating formation is prohibitively time con-suming, it is necessary to develop stochastic models in which the final splatshape is determined from a set of prescribed rules, as a function of dropletimpact conditions. Knotek and Elsing [68] developed a model of thermalspray deposition that used the Monte Carlo method, in which particles withrandomly varying diameter and velocity were deposited on a surface. Thesize of lamellae and pores formed by impacting droplets were determinedaccording to simple guidelines, and the overall coating structure determined.The model was two-dimensional, so that it predicted only the structure of asingle cross-section through the deposited layer. Cirolini et al. [69,70] alsosimulated coating deposition with a two-dimensional stochastic model, andpostulated a much more complex set of rules to represent interactions be-tween splats landing on each other. Kanouff et al. [71] modeled coating by athermal spray inclined at an angle to the substrate, and calculated the sur-face roughness of the coating.

Ghafouri-Azar et al. [72] developed a stochastic model of coating for-mation that dispersed molten droplets on the substrate by generating ran-dom values of process parameters, assuming that these properties followappropriate distributions with user-specified means and standard deviations.Measurement of these parameters for every particle in a spray is extremelydifficult, but their statistical distributions can be quite easily determined

FIG.35. Coating formed by the deposition of 300 alumina droplets on a stainless steel

substrate during the second simulation. (a) Three-dimensional view; (b) the top view; (c) the

side view.


experimentally using commercially available instruments. In the stochasticmodel of coating formation, it was assumed that the particle speed V, di-ameter D, temperature T and particle trajectory (defined by the angles be-tween particle velocity and the spray axis) have random, continuouslyvarying values. Measurements of particle properties in thermal sprays haveshown that the variation of velocity and temperature can be representedreasonably well by a normal probability distribution with probability den-sity function (PDF) given by

gðxÞ ¼ 1

sffiffiffiffiffiffi2p

p exp � 1

2s2ðx� mÞ2

� �ð43Þ

where g represents any distributed variable, m the mean value and s thestandard deviation. Particle size distributions are better described by a log-normal PDF.

Having assigned a velocity, size and temperature to each droplet in thespray, the diameter of the splat formed by it after impacting on a solidsurface can be calculated from equation (35) and the thickness from equa-tion (36). Based on experimental results, and some simulations of sequentialdroplet impact using a three-dimensional model, four possible scenarios asto the splat shape formed by droplet interactions were developed, based onthe distances between the droplet impact point and the center point theclosest previously deposited splats. It was assumed that splat curvature wasthe only mechanism creating porosity. Based on experimental evidence,splats were assumed to detach from the substrate starting at a distance 0.6Rfrom the center where R is the splat radius (see Figure 36).

Figure 36 illustrates how a splat was transformed when it was depositedonto the irregular surface of the coating. The shape of the splat was mod-ified to conform to the surface under it, while keeping its thickness the same,and the splat material added to that of the existing coating.

The average time ðdtÞ between deposition of two particles was calculatedby dividing the average mass of a droplet by the mass flow rate of powderthrough the gun ð _mgunÞ:

dt ¼ rp �D3

6 _mgunð44Þ

Since the time required for a droplet to spread and solidify is much lessthan the average time between deposition of two particles, it was assumedthat they impact on the substrate sequentially and that no two land at thesame time.


Figure 37 shows results from the simulation of plasma spraying nickelparticles with average velocity 60m/s, average diameter 58 mm and averagetemperature 1609K onto a substrate with the spray gun held stationary at adistance of 150mm from the substrate, with a powder mass flow rate of0.126 g/s. To keep the size of the computational data stored at a manageablelevel, only the coating deposited on a 1mm� 1mm area centered along thegun axis was modeled.

Figure 37 shows the predicted coating shape after 2mg of powder was fedinto the gun, which required 0.016 s of spraying time. Only 38.7% of thetotal mass sprayed from the gun landed on the 1mm� 1mm area con-sidered in the computation. The simulation was performed on a grid with252 points in both x and y directions (Dx ¼ Dy ¼ 4 mm) and 220 points inthe z direction (Dz ¼ 2.5 mm). As expected, the surface of the deposit followsa Gaussian distribution, with its thickness maximum at the center of thedeposit and decreasing with distance from this point.

Figure 38a shows a cross-section through a coating made with a guntraveling with constant velocity 1m/s, moving back and forth in the x di-rection only, on a substrate 1mm� 0.1mm in size. The total mass depositedwas 5mg, which took 0.039 s to spray. The cross-section shown was madethrough the center-plane of the coating, at y ¼ 0.05mm. Calculations gaveporosity 11.1%, average thickness 0.422mm and average surface roughness52 mm. The to-and-fro motion of the gun means that it spends twice the time

FIG.36. Curl-up of splats after impact. Splats were assumed to detach from the substrate,

starting at a distance 0.6R from the center, with an angle a.


at the center of the substrate that it does at its edges, so that the coating wasthickest at the center.

A more uniform coating can be obtained by varying the gun velocity in asinusoidal fashion. This ensures that gun speed is lowest near the ends of thesubstrate (increasing the mass deposited) and maximum at its middle. Fig-ure 38b shows the cross-section through a coating deposited with a gunmoving sinusoidally with a maximum velocity U0 ¼ 1m/s. The total massdeposited, and all other parameters were the same as that in Fig. 16a. Theporosity did not change significantly (10.6%), but both average thickness(0.373mm), and surface roughness (41 mm) were reduced, reflecting the moreeven coating distribution.

FIG.37. Deposition of nickel particles in plasma spray by a spray gun held stationary over

the substrate.


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Thi

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0.2

0.0

Thi

ckne

ss,m

m

0.2 1.00.4 0.6 0.8

0.0Substrate length, mm

0.2 1.00.4 0.6 0.8

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Spray Technol. 12, 53–69.


Plasma Spraying: From Plasma Generation to

Coating Structure

P. FAUCHAIS and G. MONTAVON

SPCTS – UMR CNRS 6638, Faculty of Sciences, University of Limoges, 123 Avenue Albert

Thomas, 87060 Limoges Cedex, France; E-mail: [email protected]

I. Introduction

Thermal plasmas produced by direct current (d.c.) arcs or radio-fre-quency (RF) discharges at atmospheric pressure or close to it (between 10and 300 kPa) are now used since the 1960s for surface treatment (at least ford.c. torches, RF ones appearing later). They belong to thermal spray tech-niques among with flame spraying (diffuse flame, deflagration or detona-tion) and electric arc spraying.

In 2005, these techniques represent about US$5 b (about h4.8 b) of salesworld-wide [1]. Table I lists the estimated geographical repartition of thisactivity as well as the estimated evolution of the market related to eachthermal spray process.

Typical equipment prices, to the exclusion of those of the spray booth androbot, are as follows:

� wire arcs: 10–25 kh;� plasma at atmospheric pressure: 75–185 kh;� plasma under controlled pressure: 600–1500 kh depending on the

considered range of pressures at which the system operates and thesize of the controlled atmosphere chamber;

� plasma transferred arcs (PTA): 50–75 kh.

It is worth noting that powder spheroidization by RF plasma can beconsidered to be related to surface treatments (the particle treatment beingthe same as that for RF spraying except that the substrate is replaced by along enough particle collector to let them cool down and avoid their stickingbetween themselves).

Plasma spraying is a process in which finely divided metallic and non-metallic materials are deposited in a molten or semi-molten state on a pre-pared substrate [3]. The base material/coating combination can be tailored

Advances in Heat TransferVolume 40 ISSN 0065-2717DOI: 10.1016/S0065-2717(07)40003-X



to provide resistance to heat, wear, erosion and/or corrosion as well asunique sets of surface characteristics. Coatings are also used to restore wornor poorly machined parts to original dimensions or manufacture near-net-shape of high-performance ceramics, composites, refractory metals andfunctionally graded materials. Plasmas are mainly used to spray refractorymaterials as the jet temperature is over 8000K at atmospheric pressure or,more generally, high-added value coatings in air or controlled atmosphere.Numerous industries, in recognition of the versatility and cost–efficiency ofplasma spraying have introduced this technology in the manufacturing

TABLE I

ECONOMICAL BENCHMARK

Global Worldwide Market in 2005–US$5b; (about h4.8b)

Geographical repartition (%)

USA 35

Europe (15) 30

Japan 15

Asia and Pacific Rim 15

Rest of the World 5

Evolution of the market from 1960 to 2005

1960(%) 1980(%) 2005(%)

Plasma� 15 55 48

Wire flame 35 11 4

Powder flame 35 28 8

Supersonic flame (HVOF) Non-existing Non-existing 25

Electric arc 15 6 15

�Among plasma processes, more than 97% are d.c. plasmas and less than 3% RFplasmas [2].

plasma flow and mixing

withsurroundingatmosphere

particle.injection,

accelerationand heating

substrateheating

coating formation

(1)

(2)

(3)(4)

plasma jet formation

FIG.1. Various sub-systems of the plasma-spraying process.

206 P. FAUCHAIS AND G. MONTAVON

environment. This is especially in the case of aeronautic industries, energyproduction industries, steel industries, petrol industries, etc., and for a lesslong time the automotive industries.

The plasma-spraying process can be divided into four sub-systems asshown in Fig. 1. They encompass: (1) plasma jet formation inside the torch;(2) plasma jet issuing from the torch and mixing with the surrounding gas;(3) particle injection, acceleration and heating in the gas flow; (4) particleimpact on the substrate and coating formation. The following presentationwill follow these divisions, parts 1 and 2 being gathered.

II. Plasma Spray Torches

Figure 2 gives a sketch of a d.c. plasma-spraying process with a low-power (o60 kW) plasma torch. Feedstock particles are injected normally(or close to the normal direction) to the plasma jet downstream of the arcroot, thanks to a carrier gas. They experience heat and momentum transfersfrom the plasma jet resulting in heating/melting and acceleration toward thesurface to cover (substrate). The molten or semi-molten particles impact onthe substrate where they very rapidly flatten and solidify (in the ms range ford.c. plasmas). Then, the successive resulting splats stack up on top of eachother to form the coating, each incoming particle impacting on an alreadysolidified splat.

A. GENERAL REMARKS

The operating conditions of thermal plasma devices are highly linkedto the plasma thermodynamic and transport properties. At local

feedstock injector

air entrapment

plasma jet

coating

particle flow pattern

FIG.2. Schematic of the d.c. plasma-spraying process.

207FROM PLASMA GENERATION TO COATING STRUCTURE

thermodynamic equilibrium (LTE), the calculation of thermodynamic prop-erties is straightforward [4,5] except for minor species (i.e., for molar frac-tions below 10�4) where the precision becomes very poor due to the lack ofprecise data. The LTE transport properties of the main plasma-forminggases as well as that of air are now well-known [4,5]. For the mixing of thesurrounding atmosphere with the plasma jet, mixing rules are generally used[4]. However, if these data are quite sufficient for flow modeling, two-temperature properties are needed to model the plasma behavior close toelectrodes or when a cold gas or a liquid is injected within a plasma jet [4].

The mandatory condition to achieve sustainable plasma is such that, atatmospheric pressure, its electrical conductivity is higher than 103 Sm�1

(i.e., ionization mechanisms begin when about 1–3% of electrons appearwithin the species mixture). Such a condition is achieved, at atmosphericpressure, for plasma spray gases and gas mixtures (Ar, Ar–He, N2–H2,Ar–H2, etc.) as soon as the plasma temperature is higher than 8000K.The plasma temperature depends on its enthalpy calculated by dividing thepower dissipated in the gas, Pg (Pg ¼ VI–Qe, where V is the arc voltage, I thearc current and Qe the losses in the cooling unit), by the plasma-forming gasmass flow rate _mg (kg s�1). A temperature of 8000K corresponds to a min-imum critical enthalpy (hc) dissipated into the gas [6]. This enthalpy stronglydepends on the plasma gas composition that has to be tailored to the mo-mentum and heat to be imparted to the particles injected in the flow. This isillustrated in Fig. 3 that displays the electrical conductivity evolution as afunction of the enthalpy at atmospheric pressure for three gas species: pure

6000

4000

2000

0

7000

5000

3000

1000elec

tric

al c

ondu

ctiv

ity

[S.m

-1]

enthalpy [MJ.kg-1]

0 10 20 30 40 50 60 70 80

Ar

Ar-H2

N2

FIG.3. Evolution of the electrical conductivity (s [Sm�1]) of Ar, Ar–H2 (25 vol. %) and

N2 versus the mass enthalpy.


argon, argon–hydrogen mixture (25 vol. %) and pure nitrogen. It clearlyappears here that operating a nitrogen plasma requires an enthalpy seventimes higher than the one required for pure argon.

Figure 4 illustrates the evolution of the enthalpy of pure argon andhydrogen and mixtures of both gas species (i.e., 10, 20 and 30 vol. %) versusits temperature. The addition of hydrogen as secondary plasma-forming gasto primary argon plasma-forming gas leads to an increase of the mixtureenthalpy due to two mechanisms:

� hydrogen molecular dissociation around 3500K requires energy whilepure argon begins to ionize only at 8000K. Argon ionization becomessignificant between 10,000 and 15,000K, temperature at which it isalmost achieved (Ar and H exhibit ionization energies very close toeach other: 15.8 and 13.6 eV, respectively);

� plasma gas mixture specific mass is reduced by adding hydrogen(argon molecular weight is 40 g whereas hydrogen molecular weight isonly 2 g, or in other words 1 kg of Ar represents 25mol whereas 1 kgof H2 represents 500mol).

Under these conditions, the temperature of an Ar–H2 mixture (30 vol. %)is about 10,000K with an enthalpy of 20MJkg�1. To increase this temper-ature up to 15,000K (50% higher), an enthalpy of 70MJkg�1 is required(350% higher). Thus, the gas species ionization acts as an inertia wheel. Thisexplains why when operating d.c. plasma torches, the maximum tempera-ture of the jets varies between 12,000 and 14,000K when operating RF

200

150

100

50

0

enth

alpy

[M

J.kg

-1]

0 5 10 15 20 25

temperature [103 K]

pure H2 pure Ar

30% H2

20% H2

10% H2

argon – hydrogen mixturespressure: 100 kPa

FIG.4. Evolution of the mass enthalpy (h [J kg�1]) of Ar, H2 and Ar–H2 (10, 20 and 30 vol.

%) versus the plasma temperature [5].


plasma torches, the maximum temperature of the flow varies between 9000and 11,000K due to the larger plasma volume for an almost same dissipatedpower.

The mass of the plasma gas species plays also a relevant role in the plasmajet momentum which in turn drives the acceleration of the injected feedstockparticles as well as pushing down the arc attachment column at the anodewall.

The plasma jet momentum depends upon the gas jet velocity, vg, linked tothe nozzle internal diameter, d (vgEd�2, in a first approximation), theplasma gas composition and the mass flow rate depend on the gas molarmass. The d.c. torch nozzle internal diameters usually vary between 6 and10mm while conventional RF ones range from 35 to 50mm, thus inducing asignificantly lower gas velocity (ratio of � 70 for a RF torch with an internaldiameter of 50mm compared to a d.c. torch with an internal diameter of6mm). ‘‘Heavy’’ gas species such as Ar, N2 and air are often used as primaryplasma-forming gas. In fact, the choice of the plasma source (d.c. or RF) isdictated mostly by the required particle velocity (vp) order of magnitude atimpact with values, for the same feedstock nature and identical particle-sizedistribution (22–45 mm, for example, a typical particle-size distribution),ranging from a few tens of meters per second (RF torch) to about400–500ms�1 (d.c. high-power vortex torch) for particles fully or partiallymelted at impact.

The heat transfer to particles is essentially controlled by the plasma gasthermal conductivity (K), the particle size and its residence time in theplasma flow. The increase of K is ensured by the secondary plasma-forminggas [5]. Indeed, the heat transfer to particles is driven by the mean integratedthermal conductivity �k defined as follows:

�k ¼ 1

T1 � Tp

Z T1

Tp

kðsÞds ðWm�1K�1Þ (1)

where TN is the plasma temperature outside the thermal boundary layersurrounding the particle which surface temperature is Tp.

When adding H2 to Ar, �k drastically increases at temperatures higher than4000K (i.e., temperature at which the molecular dissociation of H2 iscompleted). For example, considering a plasma temperature of 10,000Kcontaining 20 vol. % of H2, �k equals approximately 1Wm�1K�1. AddingHe leads to an almost linear evolution of �k with TN and for conditionsidentical to the previously mentioned ones (20 vol. % of secondary plasmagas), �k equals approximately 0.5Wm�1K�1. It is worth noticed that con-sidering a pure Ar plasma at a temperature of about 10,000K, �k is below0.2Wm�1K�1. Such values explain why H2 or He is added as secondary


plasma gas to the Ar primary plasma gas to promote the heat transfer tofeedstock particles.

However, all these parameters are strongly interrelated implying that therange in which the working conditions of a plasma spray device can bevaried is rather narrow and each process will have its specific applications.

B. PLASMA JET CHARACTERIZATION

To compare plasma torch working conditions or back models, in situdiagnostics and measurements are mandatory.

The plasma jet temperature and its surrounding atmosphere entrainmentare usually characterized by

� Emission spectroscopy (mostly from atomic lines 8000oTo14,000K);

� Rayleigh scattering (To10,000 or 16,000K depending on theresolution);

� Coherent anti-Stokes Raman spectroscopy – CARS (To10,000K).

For details regarding these techniques, please refer to the review papers[7–9].

In most cases, and due to the plasma torch exit nozzle geometries, plasmajets are assumed to have a cylindrical symmetry but tomography proce-dures, if necessary simplified with measurements only along two orthogonaldirections [10], can be also used. This latter approach is required when aplasma jet perturbed by a cold carrier gas injected orthogonally to it or by aliquid carrier of nano-sized particles has to be analyzed. A very importantpoint regarding the accuracy of these measurements is also to account forthe arc root fluctuations to determine the plasma jet stationary temperatureprofile from the time-averaged volumetric emission coefficients [7]. In con-ventional emission spectroscopy, the recording characteristic time of theatomic lines used to determine the plasma temperature is between 10�1 and10�2 s. Thus, the plasma jet fluctuations (see Section II.C.1) in the 5 kHzrange are integrated and a time-averaged temperature derives from themeasurements. To increase the frequency at which spectroscopy measure-ments are carried out, photomultipliers with characteristic recording timesof about 10�6 s must be implemented.

Velocities of d.c. plasma jets are measured by using a non-intrusive opti-cal method based on the propagation between two measuring points [7,11]of the plasma jet luminosity fluctuations (induced by arc root fluctuations).

Water-cooled enthalpy probes, which nevertheless perturb the plasmaflow (their mean diameter is about 3mm), are also used [12,13]. However, asthey cannot sustain heat fluxes higher than 108W.m�2, they are mainly used


at temperatures below 8000K in pure argon plasmas and 6000K inargon–hydrogen ones. Coupled with a mass spectrometer, they lead to thedetermination of the gas temperature, its global composition (and thusthe air entrainment and the dimixing phenomenon) and its velocity [14]. Theresulting temperature is a Favre averaged one, generally different from thetime-averaged temperatures obtained by spectroscopy.

Schelieren imaging is also used to study the turbulence around the plasmajet [7].

The transient behavior of d.c. plasma jets is generally studied thanks tofast cameras synchronized with a transient signal such as the voltage fluc-tuations [7,8] such as:

� basic digital video cameras with very short shutter times (� 10�5 s);� motion analyzers;� digital or video cameras coupled with laser flashes.

Whatever the measuring method used, LTE is generally assumed becausemost of the required data are comparative values related to torch workingconditions [8]. Nevertheless, the existence of LTE is very questionable in thefollowing considered cases: at the jet fringes, at the jet core extremity (wherethe jet becomes fully turbulent) or when a cold gas or a liquid is injected.

C. DIRECT CURRENT STICK-TYPE CATHODE

The arc strikes between a thermoionic cathode and an anode (Fig. 5). Thislatter has the passive function to collect the electrons and so to ensurecurrent continuity. The stick-type cathode (8–12mm in diameter) has aconical tip and is made of thoriated (2 wt. %) tungsten while the anode isusually made of oxygen-free high purity (OFHP) copper meanwhile some ofthem can have an insert made of tungsten to limit the anode wear. The arcattaches to the anode via a high-temperature, low-density gas columnthrough the cold gas boundary layer that develops on the water-cooled(under a pressure of 1.5–2MPa) anode wall.

Downstream the arc column (which fluctuates with time), the plasmaslowly extinguishes due to the exothermic recombination phenomena (i.e.,electrons with ions to form atoms, atoms with atoms to form molecules). Assoon as the plasma flow exits the anode-nozzle at high velocity(600–2300m s�1 depending on the operating parameters and the torchdesign), the plasma jet generates vortex rings (i.e., where one of the tur-bulent velocity components is almost one order of magnitude higher thanthe two others), which will rapidly coalesce. This results in an engulfment-type process [15] of the surrounding atmosphere within the plasma flow. Themixing between the cold entrapped atmosphere and the warm plasma flow is


not instantaneous but a contrario takes time due to the flow-specific massmismatch (i.e., a ratio of 20–40). The flow can be considered here as a two-phase mixture. The mixing develops when the cold air or cold gas pocketsare heated up enough and the plasma cooled down enough. Figure 6 sche-matically illustrates the mechanisms.

1. Arc Root Instabilities

The cold gas flow in the boundary layer exerts a pulling down drag forceon the warm connecting column while the Lorentz forces may act in thesame or opposite direction depending on the local curvature of the arcconnecting column (Fig. 7). Under the combined actions of these forces andof thermal effects, the connecting column lengthens and the voltage drop inthe column increases up to a value where breakdown occurs leading to thecreation of a new arc root of lower voltage drop. It has to be kept in mindthat within the boundary layer temperatures are over 3000K, temperaturewhich is closely related to the H2 vol. %, resulting in much lower breakdownvoltages than in cold gas. This movement induces periodic variations in arcvoltage. Such variations result in fluctuations of the enthalpy input to thegas, of the plasma jet velocity, of its length, width and position, and of theway it mixes with the surrounding atmosphere when exiting from the torch.

cathode

gas

gas

anode nozzle

cooling fluid (H2O)

plasma jet

anode (+)

cooling structure

cathode (-)

W-ThO2 (3%)

(a)

(b)

FIG.5. (a) Schematic of a d.c. stick-type cathode plasma torch. (b) Cathode and anode of a

PT F4 Sulzer-Metco torch.


air entrapment

entrained eddies of cold air

transitionalflow with

engulfmentof cold

eddies into plasma jet

andincomplete

mixing

cold eddies and plasma gas eddies

arebreaking down

turbulentflow: eddieshave brokendown andfluid has

thoroughlymixed

FIG.6. Engulfment process of the surrounding atmosphere within a plasma jet exiting

from a nozzle [15].

B

j x BFd

Ff

j x B

j

FIG.7. Scheme of the forces acting on the connecting column between the arc column and

the anodic arc root attachment (Fd, drag force; jxB, Lorentz forces; Ff, friction force) (after

[17]).


Indeed, four different arc fluctuation modes have been identified [2,16,17](Fig. 8):

� the steady mode for which the anode lifetime is very poor;� the takeover mode occurring mostly with monatomic plasma gas

species;� the restrike mode occurring mostly with diatomic plasma gas species;� the mixed modes.

These different modes differ in the movement of the arc root at the anodewall and therefore in the time-evolution and amplitude of the arc voltage.

The restrike mode corresponds to a large range of plasma spray operatingparameters with diatomic primary (N2) or secondary (H2) plasma gases.Under these conditions, the arc is stretched out by the cold gas flow until anelectric breakdown occurs through the colder and electrically insulating layersurrounding the arc. Each breakdown initiates a short circuit and a new arc

100

90

80

70

60

50

40

30

20

volt

age

[V]

0 0.5 1.0 1.5 2.0

time [ms]

restrike

takeover

steady

FIG.8. Different modes of voltage–time evolution linked to arc root fluctuations at the

anode: restrike (mainly with diatomic gas mixtures), takeover (mostly with monoatomic gas

mixtures) and steady modes [17].


attachment at the nozzle wall. Thus, the arc voltage V exhibits large fluc-tuations (DV/Vm 4 0.8) and a high-mean voltage value Vm (60–90V). In thismode, the frequency of arc root fluctuation ranges between 2 and 8kHz [16].As d.c. torches are supplied with current sources (i.e., the arc current intensityI remains almost constant and close to the selected value for any voltage), thissignifies that the dissipated power varies linearly with the arc voltage. Indeed,the losses in cooling water depend mostly upon the arc current intensity [18].As an example, considering Vm ¼ 60V, DV ¼ 60V and I ¼ 600 A, the dis-sipated power in the torch varies between 18 and 54kW. In such conditions,it is not surprising that the plasma jet fluctuates in length and position atthese characteristic frequencies (Fig. 9). Here, the plasma flow can be con-sidered as successions of warm and cold puffs [19]. As it will be shown later,this dramatically affects the transfers to injected feedstock particles.

The takeover mode, for which DV/Vmo0.6, is observed generally whenoperating plasma torches with monatomic species. In this case, the arc rootfluctuation is drastically reduced.

The work of Duan and Heberlein [20] has clearly shown that for anyplasma-forming gas species, restrike and takeover modes could take placesimultaneously to form a mixed mode.

FIG.9. Typical fluctuations of a d.c. plasma spray jet working in the restrike mode (delay

between each view: 10�4 s; time delay between images: 10�2 s).


In fact, the mode depends upon the characteristics of the cold boundarylayer which develops between the anode-nozzle and the arc column.Figure 10 for Ar–He mixtures displays for example the evolution of themode value (m.v.) versus the cold gas boundary layer thickness (measuredby end-on imaging of the arc), where m.v. ¼ 2 corresponds to the restrikemode, m.v. ¼ 1 to the takeover mode and m.v. ¼ 0 to the steady mode.When the boundary layer thickness decreases (for example by increasing thearc current intensity [19]), the arc column characteristic diameter increasesleading to a decrease of the cold gas mass flow rate and hence to the Heratio. In this case, m.v. tends to 1 (takeover mode). On the opposite, whenthe boundary layer thickness increases (for example by decreasing the arccurrent intensity), the arc column characteristic diameter decreases leadingto increases of both the cold gas mass flow rate and the He ratio. In thiscase, m.v. tends to 2 (restrike mode). As already underlined, operating aplasma spray torch under the takeover mode is preferable regarding thecoating overall characteristics.

2. Anode Erosion

The wear of the electrodes resulting to the electric arc attachment spoterosion is not negligible and drives their mean lifetime (which can evolvebetween 30 and 100 h depending on the working conditions and the number

Ar = 60 SLPM

Ar = 100 SLPM

Ar/He = 58/20 SLPM

Ar/He = 98/20 SLPM

2.0

1.5

1.0

0.5

0

mod

e va

lue

boundary layer thickness [mm]

0.6 0.8 1.0 1.2 1.4 1.6

FIG.10. Evolution of the mode value versus the cold boundary layer thickness for Ar and

Ar–He operated d.c. plasma torches [20].


of restarts). This wear affects ultimately in a drastic manner the heat andmomentum transfers to particles [21]. Thus it has to be compensated,especially during the spraying of large parts (which lasts longer) in order tokeep as constant as possible the operating conditions and hence as homo-geneous as possible the resulting coating microstructure.

Indeed, erosion wear of both electrodes is quite different. The majorerosion wear of the cathode occurs during the very first working hours. Thecathode erodes due to the diffusion and evaporation of thoria [16] and thisleads to a lower plasma flow velocity [22]. The erosion wear mechanisms ofthe anode are by far more complex than for cathode and many works, oftencontradictory, have been devoted to them [15–17,21,23,24]. The generaltrend, however, is an almost regular voltage drop during a few tens of hoursworking time. Then, this drop increases drastically and this leads to theejection of tungsten or copper particles issuing from the anode. This phe-nomenon is of course totally detrimental to the coating characteristics dueto particle embedding. This is why in industrial spray booths the electrodesare usually systematically replaced long before (i.e., only a few tens of hoursworking time) this event occurs. Rigot et al. [24] have shown that the erosionis due, for given operating conditions, to the shortening of the arc columntogether with a smaller area of the arc root attachment. This results inlonger arc root lifetimes (i.e., for new electrodes, stagnation time is below160 ms while for worn ones, stagnation times can reach 200 ms) leading to themelting and evaporation of the anode. Another predominant factor isalso the way the plasma-forming gas mixture is injected within the anode(i.e., axially, radially or in vortex) and the number of gas injectors [25].

When the anode wear develops, the plasma flow becomes more instable,the fluctuation frequencies increase and the jet average length shortens. Tocompensate the lower arc average voltage resulting from the anode erosion,one way is to increase either the arc current intensity or the secondaryplasma gas flow rate. Nevertheless, it has to be kept in mind that selectingthe second option, that is to say increasing the secondary plasma gas flowrate, the cold boundary layer thickness will rise amplifying hence thearc instabilities. Indeed, as it will be shown in the section devoted to theplasma–particle interactions, the best way to keep constant the power dis-sipated in the plasma torch is to compensate the anode erosion by increasingthe arc current intensity only, reducing in such a way the instabilities andtheir consequences on the resulting coating structure.

3. Some Torch Characteristics

Torch characteristics are usually related to voltage V and arc currentintensity I operating values. They depend strongly upon the anode-nozzle


internal diameter, the design of the arc chamber, the cathode tip morphol-ogy and the manner the plasma gas mixture is injected into the chamber.

Three types of injection are encountered (Fig. 11 (a)): radial injection (i.e.,orthogonal to the cathode geometric axis), axial injection (i.e., parallel to thecathode geometric axis) and vortex injection (i.e., according to the charac-teristics of the plasma gas mixture injector mounted on these torches, theswirl number is generally below 3).

The selection of the plasma gas mixture injection mode, promoting moreor less turbulences close to the cathode tip and to the anode-nozzle wall,plays a significant role on the arc voltage for a given arc current intensityand an anode-nozzle internal diameter (Fig. 11 (b)) [18,26]. Consideringradial injection, the arc length is the shortest compared to other injectionmodes and thus the arc voltage is the lowest. With axial injection, and in thecase depicted in Fig. 11 (b), the arc length is on the opposite the longestcompared to other injection modes. Nevertheless, an important vortexinjection can promote the development of an even thicker cold gas boundarylayer close to the anode wall. This will result in a slightly higher arc voltagethan axial injection. It has to be kept in mind that the cold gas velocity closeto cathode tip has to be lower than 50m s�1 to avoid, once the arc is ignited,the blowing out of the molten cathode tip [27]. In Fig. 11 (b), the voltagedecreases when the arc current intensity increases. In such a way, the lossestoward the anode wall increases resulting in a higher electric field.

anode

radial injection

anode

axial injection

radial injection

vortex injectionaxial injection

200 400 600

arc current intensity [A]

arc

volt

age

[V]

plasma gases: Ar-H2 (30-12 SLPM) anode internal diameter: 7 mm

40

50

60

70

anode

vortex injection

FIG.11. (a) Scheme of the plasma–gas mixture injection mode. (b) Average voltage

evolution versus arc current intensity for different injection modes [18,26].


Correlatively, the arc root average position at the anode wall tendsnevertheless to move toward the cathode. Finally, the balance between thesetwo opposite phenomena results in an almost constant voltage for currentintensities higher than 600A under conditions depicted in Fig. 11.

The effect of the anode-nozzle internal diameter on the voltage and arccurrent intensity for an Ar–H2 (45–15 SLPM) plasma gas mixture axiallyinjected is depicted in Fig. 12 [28,29]. For a nozzle internal diameter higheror equal to 7mm, the torch characteristics are decreasing. For a given arccurrent intensity and when the anode internal diameter increases, the arccolumn constriction decreases reducing the electric field. In this case, andeven if the arc length increases, this is by far insufficient to compensatethe voltage decrease. Thus, the negative slope of the torch characteristicseven more decreases with an increase in the anode internal diameter. Forexample, for an anode-nozzle internal diameter of 6mm and an arc currentintensity over 500A, the losses toward the wall increases drastically risingthe electric field faster than the arc column length: the torch characteristicsevolve following a positive slope.

In a d.c. plasma torch, the losses in the cathode-cooling water are alwaysbelow 5% of the total losses. In fact, the predominant cathode-coolingmechanism is electron emission [30]. Losses in cooling water are mostlyencountered in the anode-nozzle. As shown in Fig. 13, these losses increasealmost linearly with the arc current intensity whereas the nozzle internaldiameter does not have a significant effect (i.e., a decrease in losses of about

70

66

62

58

54300 400 500 600


arc

volt

age

[V]

plasma gases: Ar-H2(45-15 SLPM)

d = 6 mmd = 7 mmd = 8 mmd = 10 mm

FIG.12. Evolution of the average voltage of a d.c. plasma torch versus the arc current

intensity for different anode-nozzle internal diameters: 6, 7, 8 and 10mm [28,29,10].


only 12% when considering a 10mm diameter anode compared to a 6mmdiameter one). Despite the lower thermal losses for higher nozzle internaldiameter, the thermal efficiency of the 10mm anode is smaller than the oneof the 6mm one mostly due to the higher voltage required to operate thistorch (i.e., 55V for 10mm against 68V for 6mm).

A general important remark has to be done at this stage regarding arcvoltage: the cathode (VK) and anode (VA) voltage drops correspond to anenergy loss which is not anymore available in the plasma jet and whichcannot be hence anymore transferred to particles to heat and acceleratethem: the energy available in the plasma jet depends in fact on the torchvoltage minus the sum of the VK+VA voltages (i.e., about 12–20V).

When increasing the H2 volume fraction of a binary Ar-H2 plasma gasmixture, the voltage increases very rapidly as displayed in Fig. 14 (a) [18,26].This is due to the very fast diffusion mechanisms associated to the use ofsuch light gas species. As demonstrated by the calculations of Murphy [31],H2 diffuses very rapidly to the jet fringes of the arc column, increasing itscooling by conduction and inducing in such a way a strong constriction.

The phenomena are quite different when considering a binary Ar–Heplasma gas mixture. Due to the high difference in ionization potentials betweenHe and Ar (i.e., 15.8 eV and 24.6 eV, respectively), most of the ions come fromAr atoms. This results in an ambipolar diffusive separation (or dimixing) inpresence of the temperature gradient. In addition, the ambipolar diffusionleads to a decrease of the He molar concentration since from Ar ionization


300 400 500 600

20

18

16

14

12

10

ther

mal

loss

es [

kW]

plasma gases: Ar-H2(45-15 SLPM)

d = 6 mmd = 7 mmd = 8 mmd = 10 mm

FIG.13. Evolution of the average thermal losses of a d.c. plasma torch versus the arc

current intensity for different anode-nozzle internal diameters: 6, 7, 8 and 10mm [28,29].


results two particles (an ion and an electron). This He molar concentrationdecrease generates a He atom gradient which tends to activate He diffusiontoward the jet core [32]. These reasons explain why the voltage of an Ar–Hemixture increases slowly with the He percentage than for an Ar–H2 mixture.

The plasma torch thermal efficiency, as previously mentioned, is stronglylinked to the torch voltage. Figure 14 (b) displays the evolutions of the

80

60

40

20

arc

volt

age

[V]

volume fraction of secondary gas [%]

0 20 40 60 80 100

Ar-H2

Ar-He

0

volume fraction of secondary gas [%]

Ar-H2

Ar-He

0

20

40

60

0 20 40 60 80 100

torc

h ef

fici

ency

[%

]

(a)

(b)

FIG.14. Evolution of (a) Arc voltage versus the volume fraction of the secondary gas and

of (b) The volume fraction of the secondary gas versus the torch efficiency for two plasma-

forming gas mixtures: Ar–H2 and Ar–He [18,26].


thermal efficiency for two plasma gas mixtures: Ar–He and Ar–H2, respec-tively. Thermal efficiency evolves faster when considering Ar–H2 instead ofAr–He. However, as soon as the secondary plasma gas ratio becomes toohigh, the thermal conductivity increase raises the losses and lead to thethermal efficiency decrease.

When increasing H2 volume fraction, the electric arc constricts at thecathode tip and the maximum current it can sustain is reduced. Consecutiveto the arc constriction, the cathode temperature increases by a few hundredsKelvin and, as the tip is in a molten state for electronic emission, its erosionbecomes very significant [17,33–35]. This is why for example when operatingthe plasma torch with Ar–H2 plasma gas mixtures (with H2 vol. %4 5), arccurrent intensities are usually limited to about 700A while when operatingthe plasma torch with Ar–He mixtures, arc current intensities can reachabout 900 A and even 1000A when operating the plasma torch with pure Ar(Table II).

It has also to be underlined that due to the very high temperature gradientat the cathode tip, thoria diffuses and evaporates, transforming after a fewhours of operation the thoriated tungsten cathode in a pure tungsten one[17]. This is an additional reason why the size of the cathode (i.e., its externalapparent surface) has to be limited: even if the size does not drive thecathode temperature, it drives the temperature gradients [17].

Finally, it must be underlined that exhibiting initially a conical morphol-ogy, the cathode tip is rounded very rapidly (a few hours of operation).

Major working characteristics of stick-type cathode torches are summa-rized in Table II.

D. VELOCITY AND TEMPERATURE DISTRIBUTIONS

As already mentioned, when the enthalpy dissipated into the plasma isincreased, the plasma temperature does not vary significantly. Its velocitydoes however, as illustrated in Fig. 15 [11,36] where an increase in the arccurrent intensity from 304 to 591A leads to an increase of the maximal jetvelocity of about 750m s�1 (i.e., from 1588 to 2330m s�1). In the consideredcase, the velocity still remains subsonic because at the local temperature(about 13,000K) and pressure (about atmospheric pressure), the soundvelocity in an Ar–H2 plasma is close to 3000m s�1 [37].

According to the plasma jet expansion and the surrounding atmosphereentrapment which cools down the jet, the axial velocity drops rather fast asdepicted in Fig. 16 (considering the same operating conditions than those ofFig. 15). Planche [36,38], by the way of a dimensionless analysis, has es-tablished a relationship correlating some predominant plasma torch oper-ating parameters and the jet maximum velocity on the axis of the nozzle exit.


TABLE II

D.C. ARC PLASMA SPRAY TORCH MAIN CHARACTERISTICS

Plasma torch type Conventional [35] High power [61] Triplex [55,56]

Cathode (W+2wt%ThO2) morphology and number Stick cathode (1) Button cathode (1)

one

Stick cathodes (3)

Plasma gas injection and swirl number S

(dimensionless)

Axial or vortex (So4) Vortex (S48) Vortex (So4)

Anode material and internal diameter OFHP� copper or sintered

W (6–8mm)

OFHP� copper

(8mm)

Segmented OFHP� copper

(6–8mm)

Ar

Ar–He Ar–He

Plasma gases Ar–H2 N2–H2

Ar–He Ar

N2–H2

Plasma gas flow rate (SLPM) 40–100 40–200 30–60

Maximum arc current intensity (A) (depending on the

plasma gas mixture nature)

1000 (Ar)

900 (Ar–He)

700 (Ar–H2) 500 300

700 (Ar–He)

500 (N2–H2)

Maximum arc voltage (V) (depending on the plasma

gas mixture nature)

30 (Ar)

50 (Ar–He)

80 (Ar–H2) 500 80–90

90 (Ar–He)

80 (N2–H2)

Maximum plasma torch electric power (kW)

(depending on the plasma gas mixture nature)

30 (Ar)

45 (Ar–He)

55 (Ar–H2) 250 20–55

60 (Ar–He)

40 (Ar–H2)

�Oxygen free high purity.

224

P.FAUCHAIS

AND

G.MONTAVON

2000

1500

1000

500

-2 0 2 -2 0 2

I = 305 A

I = 591 A

Vmax = 1588 m.s-1

Vmax = 2330 m.s-1


2.4 mm

2.9 mm

jet

velo

city

[m

.s-1

]

jet radius [mm] jet radius [mm]

FIG.15. Radial velocity profiles obtained at 2mm from the plasma torch exit (anode-

nozzle internal diameter of 6mm, plasma gas Ar–H2 mixture flow rate of 45–15 SLPM), axial

injection). (a) I ¼ 305A. (b) 591A [37].

2500

2000

1500

1000

500

00 10 20 30 40 50 60

distance from torch exit [mm]

jet

velo

city

at

the

torc

h ax

is [

m.s

-1]


I = 591 AI = 305 A

FIG.16. Axial velocity profiles obtained at 2mm from the plasma torch exit (anode-

nozzle internal diameter of 6mm, plasma gas Ar–H2 mixture flow rate of 45–15 SLPM), axial

injection). (a) I ¼ 304A. (b) 591A [38].


For example, considering a Ar–H2 (25 vol. %) plasma gas mixture axialinjection, the relationship is, in SI units, as follows:

vmax ¼ 24:3� 10�3I0:43d�1:96G0:21 (2)

where G represents the gas mixture mass flow rate (kg � s�1), d the anode-nozzle internal diameter (m) and I the arc current intensity (A).

It clearly appears from such a relationship that the most significant para-meter is the anode-nozzle internal diameter. Similar results were obtained bycalculating vmax with a Barre de Saint Venant-type equation considering theplasma jet as an isentropic flow of constant isentropic coefficient g [39].

At last, it is worth to underline that the cathode tip erosion also reducesthe plasma flow maximal axial velocity by a few hundreds meters per second.

As already mentioned, the plasma flow temperature does not vary sig-nificantly with the power dissipated in the torch, for given plasma gas mix-ture and flow rate. However, the power increase promotes the jet velocityenhancing the surrounding atmosphere entrapment which in turn coolsdown the jet.

The effect of air entrainment with increasing plasma jet velocity is shownin Fig. 17 in terms of the plasma jet temperature distribution for two differ-ent power levels: 35 and 50 kW. The length of the jet seems not to increasebeyond 35 kW although its diameter increases slightly. When the plasma gasflow rate increases beyond 60 SLPM, with a 7mm i.d. anode-nozzle Ar–H2

(45–15 vol. %) 600A, the length of the jet decreases somewhat. This is ingood agreement with velocity measurements. This result is due to the almostconstant jet velocity because of the increase of flow turbulence with in-creasing plasma gas flow rate.

Moreover, the air entrainment by turbulences occurs about at leastbeyond 30mm. For plasmas produced with diatomic gases, the restrikemode induces severe voltage fluctuations compared to those obtained withthe takeover mode occurring in Ar and Ar–He. In case of the restrike mode,Lagnoux [40,41] has recently shown that the resulting ‘‘back and forth’’ flowinduces also air entrainment with oxygen appearing in the jet core at dis-tances as close as 20mm downstream from the nozzle exit. This is illustratedin Fig. 18 showing radial distributions of the ratio O/Ar determined byspectroscopy from atomic lines ratios at z ¼ 20mm.

The velocity and temperature distributions of the plasma jet dependstrongly on the entrainment of the surrounding atmosphere. When a mono-atomic gas is entrained into the plasma jet, energy will be extracted from theplasma at the rate of:

m0gcpDT (3)


where m0g is the mass flow rate of the entrained atmosphere, cp its specific heat

and DT the temperature difference between the plasma flow and the coldentrained gas. In most cases, the cold gas will however not penetrate into thecore of the jet but will mix in zones where the plasma temperature remainsbelow 10,000K, at the maximum. Thus, ionization of the cold gas will benegligible. When a diatomic gas is entrained, the temperatures will however besufficient to dissociate it and the corresponding cooling rate (CR) is as follows:

m0gðcpDT þ EDÞ (4)

where ED is the dissociation energy. Thus, plasma flow cooling is by far moreimportant in the case of molecular gases especially when air is entrained(oxygen starts to dissociate at T42500K and nitrogen at T47000K). Thisfact is illustrated in Fig. 19 showing the isotherms of a plasma jet under

5

4

3

2

1

0

10 20 30 40 50 60 70

8000 K10000K12000 K


radi

us [

mm

]

plasma gas mixture : Ar-H2

P = 35 kW

5

4

3

2

1

0

10 20 30 40 50 60 70

radi

us [

mm

]


8000 K10000K12000 K

plasma gas mixture : Ar-H2

P = 50 kW

(a)

(b)

FIG.17. Temperature distributions in Ar–H2 plasma jets (Ar–H2, 75.6–14.4 SLPM, anode-

nozzle internal diameter: 7mm). (a) P ¼ 35 kW. (b) P ¼ 50 kW [18,26].


identical conditions in a chamber with controlled atmosphere filled up withair, nitrogen and argon, respectively. The jet is rather short and slim whenemanating into air. A rather long and wide jet is obtained with pure Ar, withN2 in between.

When working under ambient atmosphere and to limit the air entrain-ment, a few works have been devoted to the improvement of torch nozzlegeometries to adapt the flow characteristics via de Laval nozzles [42,43].Such nozzle geometries induce indeed more uniform temperature andvelocity radial distributions resulting from both less air entrainment and amore uniform acceleration and heating of particles.

A long (50–90mm) nozzle shield (‘‘shroud’’) can also be used. Theinternal contour of the nozzle has to be designed to avoid penetration ofambient air between the nozzle wall and the hot plasma jet. Even by using asimple conical profile as shield, the plasma jet isotherms lengthen and widen.Considering for example an Ar–H2 plasma jet (Ar–H2, 45–15 SLPM,d ¼ 10mm, I ¼ 600A) and a plasma torch equipped with a nozzle shield50mm long and having a cone angle of 61, 5.27 kW are lost to the coolingwater of the shield and the total torch plus nozzle shield efficiency dropsfrom 58–41%. In spite of this fact, measurements performed 2mm down-stream of the nozzle shield (i.e., 52mm from the plasma torch nozzle exit)show that the temperature only drops by 2000K on the axis (i.e., 14,000K atthe torch exit) and that the velocity distribution remains similar to the onewithout the nozzle shield but nevertheless with a 200m s�1 drop.

0.01

0.02

0.03

0.04

00 321 4 6

plasma jet radius [mm]

O /

Ar

conc

entr

atio

n ra

tio

[-]

plasma gases: Ar

5

d = 6mmd = 7 mmd = 8 mm

FIG.18. Radial distributions of the ratio O/Ar (determined by spectroscopy from atomic

lines ratios at z ¼ 20mm) versus the plasma jet radius [40,41].


0 20 40 60

0 20 40 60

0

1

2

3

4

radi

us [

mm

]


8000

10000

13000

0

1

2

3

4

radi

us [

mm

]


8000

10000

13000

(a)

(b)

0 20 40 60

radi

us [

mm

]

distance from torch exit [mm](c)

0

1

2

3

4

5

8000

10000

13000

FIG.19. Plasma (Ar–H2, 45–15 SLPM, 1:500 A, anode internal diameter: 6 mm) temper-

ature profiles when flows exit in several surrounding atmospheres at ambient pressure: (a)Air,

(b) Nitrogen, (c) Argon [18,26].


Considering plasma spraying, the problem of operating the plasma torchequipped with such an attached shield is the sticking of molten particles onthe internal walls. To circumvent such a problem, long nozzle shields with awider angle of divergence have been developed. In this case however andsince air entrainment has to be avoided argon as shroud gas is injectedwithin the shield [41]. Unfortunately, high-flow rates (i.e., 200–400 SLPM)are required in this case.

Different nozzle shields have been developed by Okada [44], Guest [45],Houben [46] and Borisov [47]. Industrially, a nozzle shield called GatorGard is commonly used to spray super alloys in particular [48].

E. SOFT VACUUM OR CONTROLLED ATMOSPHERE

A sure way to avoid in-flight particle oxidation is to suppress the sur-rounding air atmosphere by spraying in a controlled atmosphere chamber.Industrial chambers with volumes between a few and 10–20m3 are complexdevices and will not be described here. The ambient pressure usually variesfrom atmospheric pressure to soft vacuum (p410 kPa) using argon as am-bient gas. The advantage of soft vacuum is the possibility to keep thesubstrate at high temperatures (i.e., up to 9501C for superalloys) thanks tothe limited convective cooling without oxidation. Such temperatures pro-mote interdiffusion between sprayed coatings and substrates and thus en-hance the coating adhesion.

1. Soft Vacuum

When the pressure in the chamber is progressively reduced, the plasma jetlength and diameter increase accordingly due to the reduction of turbulenceat the jet fringes. The jet length can under such conditions reach 0.6m at12 kPa (Fig. 20 (a)), but the plasma jet temperature decreases substantially((Fig. 20 (b)). Moreover, the Knudsen effect increases (see Section IV.F.1) asthe pressure decreases and at pressures below 20 kPa it is impossible to meltceramic or refractory materials. The gas velocity depends strongly on thenozzle design, but also on the chamber pressure. For example, with theSG100 Plasmadyne Gun working with an Ar-He mixture at 900A, 31 kW,the exit velocity of the plasma is 1700m/s at 80 kPa, 2455m/s at 40 kPa and3300m/s at 6.7 kPa [49,50]. But here again the Knudsen effect plays animportant role in terms of particle velocities. The maximum acceleration ofparticles occurs at a pressure around 40–45 kPa. However, at low pressuresparticles are less decelerated (less drag to slow them down) [51]. The designof the divergent part of the nozzle is important for the jet temperature andvelocity distributions [43].


2. Atmospheric and Higher Pressure

To spray refractory materials very sensitive to oxidation such as carbides,borides, silicides and a few nitrides, the chamber pressure has to be kept atatmospheric pressure or above. The high-pressure atmosphere (compared tosoft vacuum) improves the deposition efficiency and the hardness of therefractory material coatings [52–54]. However, due to higher electrode ero-sion and the radiation enhancement as the pressure increases, it seemsdifficult to run torches over 300 kPa. The torch thermal efficiency as well asthe plasma jet length decrease as the pressure surpasses 100 kPa (up to 40%decrease between 100 and 300 kPa).

F. OTHER D.C. TORCHES

Triplex I and IITM systems from Sulzer-Metco1 [55,56] (Fig. 21) based onthree counter insulated cathodes (supplied by independent sources and dis-tributing the electrical energy to three parallel arcs sticking at a unique anode

10 cm

5 kPa

20 kPa

95 kPa

195 kPa

4000

3000

2000

1000

0

tem

pera

ture

[°C

]


200 400

101.3 kPa

39.4 kPa

6.6 kPa

5.3 kPa

0

FIG.20. (a) Plasma jet envelope evolution versus surrounding atmosphere pressure [52].

(b) Plasma jet axial temperature versus distance from torch nozzle exit for several surrounding

atmosphere pressures.

1 Sulzer-Metco, Rigackerstrasse 16, 5160 Wohlen, Switzerland.


preceded by insulating rings) permit the generation of a long arc of highvoltage. This long arc reduces significantly the voltage fluctuations percentage(i.e., 4–5 times less than those of conventional d.c. torches). Moreover, thethree-fold symmetry can be used advantageously by means of three-foldfeedstock injectors, the powder flow through the nozzle being aligned either inthe warmest or coldest parts of the plasma jet, depending on the material to besprayed and permitting hence an increase of the intrinsic deposition efficiency.

Torches with axial injection permit to improve the heat transfer to par-ticles, especially to refractory feedstock difficult to melt implementing usualsystems (i.e., zirconia-type ceramics). Such types of torches are well illus-trated by the Axial III torch from Northwest Mettech Corp2 [57,58]. Thisgun is constituted of three cathodes and three anodes (Fig. 22 showing one-third of the torch) operated by three power supplies of total power rangingfrom 50 to 150 kW. The feedstock powder is injected axially between thethree plasma jets converging within an interchangeable plasma nozzle thatcan be equipped with an internal shroud limiting the surrounding atmos-phere entrapment within the plasma jet.

Rotating mini-torches (Fig. 23) permit internal sprayings within cylinderswhile the substrates remain stationary [59,60]. They hence permit coatingthe inner surfaces of cylinder bores of an engine block since the plasma torchand its support structures fit into cylinders of typical diameters rangingfrom 60 to 150mm. These plasma torches operates at lower power levelscompared to conventional systems, in the order of 10–25 kW usually(i.e., compared to 40–50 kW for conventional systems).

insulated rings

adjustable triple feedstock injectors

schematic internal architecture front view

anode

cathode

FIG.21. Triplex IITM plasma-spray gun schematic architecture [55,56].

2 Northwest Mettech Corp. 120-1200 Valmont Way, Richmond, BC V6V 1Y4 Canada.


Figure 24 displays a schematic of the 250 kW Plazjet Torch [61] used tospray up to 20 kg/h of powder. The anode is frequently convergent conicalwith an inlet diameter of 14mm and an outlet diameter of 8mm with a totallength of 120mm. It can also be equipped with a cylindrical anode with a

nozzleexit

cathode / anode arrangement

front viewschematic internal architecture

cathode anode

exit

nozzle

convergent

axialfeedstock

injector

FIG.22. Axial III plasma-spray gun schematic architecture [57,58].

motor

plasma torch

connection block

feedstock powder

slip ring for power

power connection

plasma gas mixture

FIG.23. Rotating mini-torch for internal spraying of cylinder bores [59,60].


step change in its diameter. The cathode holder consists of a truncated coneand the anode-nozzle inlet has a conical or a convergent shape. It workswith high-gas flow rates: up to 300 SLPM of N2 and 150 SLPM of H2

resulting in average jet enthalpies in the range of 10–30MJ kg�1. The highpower is achieved by high voltages (up to 400V) with arc currents typicallybelow 550A. Only a few measurements have been published for this type ofplasma torch. It should be emphasized nevertheless that temperatures arelower (Tmaxo9000K) than those measured with torches equipped withstick-type cathodes (Tmaxp14,000K) [26]. On this type of torch also, theaxial velocity at the nozzle exit (for a torch with a constant diameter anode)increases with arc current and plasma-forming gas flow rate increase [62].

Previously described plasma torches produce low or moderate plasma jetenthalpies (i.e., most of them below 20kWkg�1). To achieve higher enthalpyvalues, the plasma-forming mass flow rate has to be reduced for the sameinput of power level, but still with electrode lifetimes compatible with in-dustrial requirements. Water-stabilized torches have been developed in thisobjective in the 1960s in the Czech Republic [63–65]. They comprise a cath-ode made of a graphite rod which is automatically adjusted to compensateelectrode erosion (i.e., life-time of about 90min). The anode, in the form of arotating, internally water-cooled copper or iron disk, is positioned outside ofthe arc chamber, a few millimeters downstream of the nozzle exit. The O2-H2

plasma jet is generated in the torch chamber where the arc is stabilized by thewater swirl. The power level of this torch ranges from 80 to 180 kW. Forexample, the exit nozzle of the WSP-500 type torch has a diameter of 6mmand the water flow rate from which issues the plasma gas is between 0.2 and

coolingwaterinlet

coolingwateroutlet

powder or wire

feeding

plasma gas inlet

D.C.power

(-)

D.C.power

(+)

plasma jet

extended arc

FIG.24. Scheme of the Plazjet d.c. torch [61].


0.3 g s�1. This leads to enthalpies up to 500MJkg�1, temperatures between12,000 and 23,000K and velocities up to 6000m s�1. These torches are wellsuited to spray ceramics with feedstock up to 20 kg h�1.

A hybrid torch (Fig. 25) [66,67] has also been developed by Czech re-searchers. It is divided into two parts: an upstream part based on an argongas stabilized plasma (i.e., around a thoriated tungsten cathode) and adownstream part based on water stabilized flow with an external rotatingcopper anode. Water is evaporated, as in the water-stabilized torch, andsteam flows into the arc column where it is heated and ionized. As theenthalpy of argon is low, energy balance in the arc column is almost com-pletely controlled by steam inflow and the arc has electrical characteristicsand power balances very close to those of water-stabilized torches. How-ever, the mass flow rate and momentum flux are strongly influenced by theargon flow rate and can be thus controlled almost independently of thepower balance. As a consequence, plasma velocity, enthalpy and otherthermodynamic properties can be varied in a wide range by controlling theargon flow rate [67]. At last one advantage of this hybrid torch is that thecathode is no more consumable.

plasma jet

electric arc

cathodecooling

tangential

waterinlets

waterout

anodecooling

anode

FIG.25. Scheme of the hybrid plasma torch [66].


III. RF Plasma Spray Torches

A. CONVENTIONAL TORCHES

The basic phenomena governing the operation of the inductively coupledRF plasma is essentially similar to that of the induction heating of metals,which is well known since the beginning of the 20th century. The fact that,with induction plasmas, the ‘‘load’’ is a conducting gas with a substantiallylower electrical conductivity than most metals, has a direct influence on therange of oscillator frequencies required to sustaining such discharges. Throughthe solution of the standard electromagnetic induction heating problem,Freeman and Chase [68] demonstrated that the energy will be coupled into theouter shell of the load over a thickness of, dt , known as the skin depth, whichis function of the electrical conductivity of the load, s0 , the oscillator fre-quency, f, and the magnetic permeability of the medium, m0. Based on stand-ard electromagnetic formulation, the skin depth can be calculated as follows:

dt ¼1

ðpm0s0f Þ12

(5)

It is generally accepted that the magnetic permeability of the medium can betaken as that of free space (m0 ¼ 4p� 10–7Hym�1). For pure argon plasma atatmospheric pressure with an average temperature of 8000K, the correspond-ing average electrical conductivity, s0, will be equal to 990.3A.V�1m�1. Theskin depth in this case will be equal to approximately 8mm for an oscillatorfrequency of 4MHz. The significant difference between the results for theplasmas and that for metals such as copper and steel clearly underline the needto operate induction plasma generation systems at substantially higher fre-quencies than those commonly used for the induction heating of metals. Var-iations of the skin depth associated with changes of the operating frequencyhave also a significant influence on the overall energy coupling efficiency andthe minimum power required to sustain the discharge. Historically, the firstconfinement tubes were made of quartz, air cooled for power levels below15kW and water cooled for higher power levels [69,70].

In the spray torches supplied by Tekna,3 the conventional quartz tube hasbeen replaced by a ceramic tube of higher thermal conductivity (Fig. 26).The coil is inserted in the torch body. This allows a perfect alignment and acloser distance between the coil and the discharge and, thus, a better cou-pling [69]. A sheath gas, which can contain oxygen, nitrogen, hydrogen withno effect on the electromagnetic coupling, is used to protect the ceramicconfinement wall. The combination of these elements with a careful

3 TEKNA Systemes Plasma inc., Sherbrooke, QC, CA, J1L 2T9.


aerodynamic design of gas injectors and laminar high-velocity water coolingflow allows reliable operation with a high power varying between 30 and100 kW.This design allows also the addition of different torch nozzles tocontrol the flow pattern in the emerging plasma jet. Table III summarizesthe main characteristics of such torches.

exchangeable plasma discharge nozzle

coil cast (polymer base composite)

ceramic plasma confining tube

feedstock injector aerodynamic design ofthe plasma gas distribution head

high velocity film cooling

FIG.26. Scheme of TEKNA ceramic-wall induction plasma torch (U.S. Patent # 5 200 595

and International PCT/CA92/00156).

TABLE III

RF SPRAY TORCH MAIN CHARACTERISTICS

Type Conventional [69, 70] Supersonic [72, 73]

Torch internal diameter (mm) 35–50 35–50

Plasma gas mixture composition Ar Ar

Plasma gas mixture flow rate (SLPM) 30–60 25

Ar–H2

Ar–O2

Sheath gas nature Ar–air Ar

air

O2

Sheath gas flow rate (SLPM) 90–150 80

Plasma gas injection mode Axial Axial

Coil chamber pressure (kPa) 10–50 30–50

Spray chamber pressure (kPa) idem coil chamber pressure 5–10

Power level (kW) 30–100 30–50

Maximum feedstock flow rate (kg h�1) 6–8 2


These systems are also used for feedstock particle spheroidization: aftertheir flight in the warm plasma flow, particles are collected in a long (1m ormore) water-cooled container where they cool down below their plastic statetemperature to avoid their sticking. Torches operating at power levels up to400 kW are used for such operations. The main advantages of sphericalparticles consist in the improvement of the feedstock flowability, lowerporosity and higher powder density, less friable and abrasive particles,increased purity.

Plasma temperatures are the highest out of the axis where no electro-magnetic coupling takes place, the central part of the torch being heatedonly by conductive–convective transfers. Of course, downstream of the coilgas mixing homogenizes the plasma and the temperature reaches its max-imum at the torch centerline axis. The temperature ranges in such a casebetween 7000 and 10,000K. As the gas velocity is in a first approximationinversely proportional to the square of the torch internal diameter, it meansthat plasma gas velocity is below 100m s�1, corresponding to particle ve-locities below 60m s�1. Of course, this increases the residence times (i.e., inthe tens millisecond range) compared to d.c. plasma torches (few tenths ofms) for example. This permits with spray torches, generally working at

ceramic tube (higher thermal conductivity than usually selected

quartz)

coil

coolingsystem

zone of relatively low

velocity(plasma and particles)

dc

d0

Ld c

d 0

L

M1.5

12.85

13.88

18.38

M3

4.57

7.96

21.5

FIG.27. Supersonic induction plasma torch from TEKNA.


3.6MHz at power levels up to100 kW, to process metallic particles up to150 mm with argon in spite of its low thermal conductivity. Argon as plasma-forming gas allows achieving an easy coupling at reasonable power levels[69,70] but the sheath gas can be pure oxygen if necessary, allowing forexample to spray materials very sensitive to oxygen losses such as perovs-kites [71].

B. SUPERSONIC TORCHES

The adaptation of supersonic nozzles to Tekna RF torches [72,73](Fig. 27) has permitted in a first time to uniformly heat and melt particles inthe coil region where their velocity is low (i.e., a few tens of meters persecond) and so their residence time long thank to argon base plasma in-ducing no heat propagation phenomenon and in a second time to acceleratethem in a divergent nozzle. Gas velocities between 1500 and 2500m s�1 canbe easily reached in such a way in the gas expansion area (i.e., pressure ofa few tens of Pascal) leading ultimately to high particle velocities of, forexample, 600m s�1 for zirconia particles of 20 mm diameter.

IV. Modeling

A. INTRODUCTION

A realistic model must be as close as possible to reality. For example,models related to the d.c. spray process should be 3-D to enable taking intoconsideration the radial injection of the powder, the effect of the carrier gason the plasma jet, the 3-D turbulence structures and the turbulent dispersionof particles. It should also take into account the effect of arc root fluctu-ations on the plasma flow and subsequently of the particle behavior. How-ever, such models are rather complex to handle and CPU time-consumingwhile 2-D steady models are simpler and faster. They nevertheless do notprovide the user with the same level of knowledge about the process. In fact,the type of model must be chosen according to the application under con-sideration:

� better understanding of specific phenomena [74] that cannot be easilymeasured, such as the melting degree and evaporation of feedstockparticles during their flight;

� education and training using simple and fast but reliable models helpto understand the major effects of the operating conditions;

� optimal experimental design using models to limit the number ofexperiments and derive full benefit from them [75];


� process control where models can help to establish relationships be-tween process operating conditions and in-flight particle character-istics and thus can suggest the optimal actions to implement to resetthe measured properties at the desired level.

B. GENERAL REMARKS

Numerous mathematical models of the plasma-spraying process have beenproposed in the literature over the last twenty years [76–81]. Most of themadopt 2-D geometries and steady state and use practically the same meth-odology for the calculation of the turbulent plasma jet and particle behavior.

A 2-D approach is usually sufficient for RF torches: the plasma is fullyaxi-symmetric, including the axial injection of particles with a carrier gasand there is almost no fluctuation (i.e., stationary model).

The most advanced models for d.c. plasma flows deal with 3-D geometries,multiple particle injection, time-dependent phenomena such as arc fluctua-tions and their effects on particle treatment in the jet and coating buildingmechanisms on the substrate. Some of them take also into account chemicalkinetics of multi-component plasmas and non-LTE effects [82,83]. Finally,the first models that try to predict the dynamics of the arc inside the nozzleand plasma jet formation have appeared in the literature [84]. Although thesedevelopments are indicative of the continuous need for more realistic pre-dictions, they also make the models more complex to understand and use.

C. RF PLASMA MODELS

Viscous dissipation and pressure work terms in the energy equation areusually neglected and the displacement current is negligible [85]. The Lorenzforces and electromagnetic power dissipation in the plasma are added to thefluid-governing equations as source terms. A few novel electromagneticmodels, such as the extended field model [86], ferrite effects [87,88], coilinput impedance and coil angle effects [89], have been recently developed.Various turbulence models (i.e., Spallart-Allmaras, standard k-e, Re-Normalization Group k-e, Realizable k-e and Reynolds Stress Models)along with standard two-zonal wall functions are used to simulate theinductively coupled plasma flow. The major results [90] are as follows:

� all turbulent models which include low Reynolds number effect givesimilar modeling results and predict heat fluxes to a substrate close tomeasurements;

� models with no low Reynolds number effect predict results thatdeviate greatly from experimental results;

� RSM model appears to be the best prediction model.


D. D.C. PLASMAS

The complexity of modeling d.c. plasma flows is linked to:

� the arc root fluctuations which require a 3-D transient model;� the particle carrier gas injection orthogonally to the jet perturbing it;� the high velocity of the plasma exiting from the nozzle which creates

vortex rings those coalescence results in an engulfment-type process[15] where the turbulent plasma jet must be considered as a two-phaseplasma (Fig. 6) as confirmed by the measurements of Fincke et al. [91].

With this engulfment process, one of the turbulent velocity components isone order of magnitude larger than the two others. Moreover, the mixingbetween the entrained cold gas and the plasma takes time due to difference inmass densities (i.e., in a ratio 20–40) and thus a two-fluid or two-phase mixtureturbulence model should be applied, as it has been done [92,93] for an argonplasma flowing in a stagnant argon environment. At last, the engulfmentprocess is promoted by the arc root fluctuations resulting in some sort ofpiston flow [22]. The last point to be emphasized is that all models actuallyused are incompressible while the Mach numbers of the flow can be largelymore than 0.3! 2-D or 3-D stationary models calculate, at the nozzle exit,velocity and temperature distributions matching with the plasma gas mass flowrate and enthalpy. The properties are generally written as follows [77,93–96]:

fðrÞ � fw

fc � fw

¼ 1� r

R

� �nh i(6)

where f(r) represents the considered variable (i.e., temperature, velocity orenthalpy) at the distance r, fc the value of this variable at the torch axis andfw its value at the wall, R the torch radius and n an exponent which permits todefine the variable profile (i.e., n ¼ 0 correspond to a ‘‘top-hat’’ profile).

1. 3-D Models

The calculation results are strongly linked to the choice of inlet profiles aswell as of the grid characteristics [97–101]. The turbulence is taken intoaccount by using the k-e model, Re-Normalization Group k-e, Transport ofReynolds tension Rij-e. One has to note that all of these models take intoaccount low Reynolds numbers. Moreover constants used in these equationshave been established for flows at temperatures generally below 2000K andthus are not necessarily adapted to plasmas.

A typical example of results is shown in Fig. 28 for an Ar–H2 d.c. plasmajet expending in air where radial temperature, velocity and N2 volumetric


fraction (corresponding to the air entrainment) distributions are displayedat a stand-off distance of 80mm.

The radial velocity profiles deduced from experiment are close to thosecalculated. The agreement is not as good for the temperature profile and theair entrainment is underestimated by the calculations. Similar results areobtained for the temperature and velocity evolutions along the torch axis,the model underestimating the temperature in the transition area from

0-20 -10 0 10 20 -20 -10 0 10 20

plasma jet radius [mm] plasma jet radius [mm]

flow

vel

ocit

y [m

.s-1

]

flow

tem

pera

ture

[°C

]

250

150

100

50

0

2003000

2000

1000

plasma jet radius [mm]

-20 -10 0 10 20

0.8

0.7

0.6

0.5

N2

volu

me

frac

tion

[-]

keps_BCu

keps_BCv

Rij_BCu

Rij_BCv

Rij_BCv_thin

experiments

FIG.28. Ar–H2 (45–15 SLPM) d.c. plasma jet (I ¼ 600A, U ¼ 65V, thermal effi-

ciency ¼ 55%, nozzle internal diameter ¼ 7mm) radial distribution of temperature, velocity

and nitrogen molar fraction due to air entrainment at 80mm down stream of the nozzle exit

[99].


laminar to turbulent flow. It is thus mandatory to validate models bymeasurements [101].

These 3-D models have nevertheless permitted to adequately describe theperturbations of the plasma jet by the cold carrier gas. Such perturbationsmay be important as soon as the carrier gas flow rate is over 4–6 SLPM forinjectors of internal diameters ranging from 1.2 to 2mm [98].

The effect of the powder carrier gas is more noticeable for internal in-jection, as can be seen by comparing the computed data displayed in Fig. 29.It should be noted that for internal injection of 22–45 mm alumina particles,the optimum carrier gas injection flow rate is 6 SLPM. This flow rate in-duces a relatively high deviation of the plasma jet. On the other hand, theoptimum flow rate for external injection is only 4.5 SLPM. Such resultsexplain why it is not possible to inject particles below 5 mm in diameter: the

0 20 40 60 80 100

plasma jet axis [mm]

plas

ma

jet

radi

us [

mm

]1000 K

3000 K

11000 K

20

10

0

-10

-20

0 20 40 60 80 100

plasma jet axis [mm]

plas

ma

jet

radi

us [

mm

]

20

10

0

-10

-20

EXTERNAL INJECTION (8 SLPM)

1000 K

3000 K

INTERNAL INJECTION (8 SLPM)

11000 K

FIG.29. (a) Isothermal lines at intervals of 2000K for powder external injection (plasma

forming gas: Ar–H2, 27–7 SLPM; carrier gas flow rate: 8 SLPM, I ¼ 600A, V ¼ 65V, thermal

efficiency ¼ 56% and plasma gun internal diameter ¼ 6mm). (b) Isothermal lines at intervals of

2000K for powder internal injection (same conditions as in (a)) [98].


carrier gas flow rate should be a few tens of liters per minute inducing adrastic perturbation of the plasma jet.

At last, the most difficult problem is the arc column modeling within theanode-nozzle. As for RF modeling, electromagnetic equations have to be cou-pled to flow equations. Li et al. [102] have proposed to solve the problem byapplying the Steenberg’s minimum principle. In his recent work, Baudry [103]as well, as Vardelle and Mariaux did [104], proposed the first solution permit-ting to reproduce the arc root fluctuations. The arc is initiated by a hot column,1mm thick at 10,000K with a cathode spot of 3mm2 and an arc current of 200A. Then, the arc current is progressively raised up to 600A and the Ar–H2 flowrate increases from 30 to 60 SLPM. The arc breakdown and restrike is based onthe local value of the electric field E at the anode wall. If E 4 Ec, Ec being acritical value comprised between 150,000 and 300,000Vm�1, a new arc root iscreated (i.e., corresponding to a warm column orthogonal to the arc column)and a condition of the form qPot/qn ¼ 0 is imposed at the previous arc rootduring 10 iterations corresponding to 10�6 s. Figure 30 depicts the temperaturefields in the axial plane of the plasma torch at different time steps.

FIG.30. Temperature fields in the axial plane of the d.c. arc torch at different times (same

working conditions as those considered in Fig. 28) with a time step of 10�7 s [103]. (a) Before

breakdown of the arc. (b) Just after the restriking of the arc. (c) 40 iterations after restriking.


2. 2-D Models

Usually, 2-D steady models are based on a parabolic form of theNavier–Stokes equations (i.e., velocities in positive coordinate’s directiononly). It makes hence possible a very short calculation (i.e., in less than 1 s)the velocity, temperature and entrained air fields of the plasma jet flow.In addition to the spray parameters fixed by the operator, the 2-D modelrequires to be run the temperature and velocity profiles of the gas at theexit plane of the nozzle. The equations, assumptions and boundary condi-tions are usually similar to those of 3-D models. For more details, see[105,106].

To take into account the arc root fluctuations, a simple method consistsalso in defining an inlet enthalpy profile weighted by a time-dependent co-efficient [104,105] or a uniform power generation in a given volume V insidethe nozzle [100] (U(t)� I/V) where U(t) is the fluctuating voltage and I thearc current supposed to be constant with the current power source. Thetransient volumetric rate is used as a source term in the flow energy equa-tion. For the same spray conditions as those described in Fig. 29, Fig. 31presents the time evolution of the input power and the resulting velocity andtemperature evolutions at the nozzle exit on the torch axis. It clearly appearsthat such temperature and velocity fluctuations will significantly modify themomentum and heat transfers to particles.

25000

20000

15000

100000 0.0002 0.0004 0.0006 0.0008

times [s]

pow

er –

velo

city

-te

mpe

ratu

re

30000power [W]10xV [m.s-1]T [°C]

FIG.31. Unsteady profiles of effective power, temperature and velocity at nozzle exit

resulting from model of energy conversion in the nozzle (spray conditions: Ar–H2 (45–15

SLPM) d.c. plasma jet (I ¼ 600A, U ¼ 65V, thermal efficiency ¼ 55%, nozzle internal

diameter ¼ 7mm, voltage fluctuation ¼ 7 15%)) [99].


E. IN-FLIGHT PARTICLES INTERACTION WITH THE PLASMA JET

The understanding of the plasma–particle interactions is a key issue tocontrol the spray process as well as its reliability and its reproducibility. It is,however, a very complex problem due to the large particle size range (i.e.,5–140 mm), particle velocity range (i.e., 50–500m s�1), particle temperaturerange (i.e., 1200–4500K), the number of injected particles (i.e., 107–109 s�1)and the plasma volumetric emission which is very high in its core(i.e., 108–109W/m3) [5] and which drastically enhanced as soon as particlevaporization occurs [5].

In the following, the modeling of a single-particle behavior, the particledistributions including their injection and particle measurements and/oron-line monitorings will be successfully described.

1. Modeling of the Plasma Interactions with a Single Particle

a. Basic Equations Related to Momentum Transfer. For a single particleinjected with a known velocity vector, some effects specific to thermalplasma environment must be taken into account. Most of them are sum-marized in the review papers [107–113].

During its flight in a plasma flow, a single particle is subjected to anumber of forces which act simultaneously on it and have varying influenceon the particle trajectory and its residence time in the flow.

Among the most important forces acting on the particle are:

� the drag force imposed by the flow,� the gravity force important only in RF reactors where the flow ve-

locity is rather low and particles ones rather high,� the thermophoresis force which effect is important for particles below

about 1 mm.

Writing the force balance around a single particle in motion, its trajectorycan be determined provided its injection velocity vector is known (which isespecially important for d.c. plasma spraying). All equations are written forspherical particles which is rather realistic, the fast melting particles (a fewtens ms), rounding them even when they are blocky and angular wheninjected. The force balance results in the following equations:

dup

dt¼ � 3

4CDðup �UÞuR

rrpdp

!�gð Þn (7)

dvp

dt¼ � 3

4CDðvp � VÞvR

rrpdp

!�gð Þn (8)


where r is the fluid specific mass (kgm�3), m the fluid viscosity (Pa.s), dp theparticle diameter (m), up the particle velocity (m s�1) in the plasma jet axisdirection z, U the plasma velocity (m s�1) in the z-direction, vp the particlevelocity (m s�1) in the direction r normal to z, V the plasma velocity (m s�1)in the r-direction, uR the relative plasma–particle velocity (m s�1) and g thegravitational acceleration (m s�2).

The gravity force has to be added or subtracted from either the axial orradial velocity (*). In the case of RF, plasmas flows generally with verticalaxis, the +or – sign in front of the gravitational acceleration corresponds toa flow in axial direction with the positive direction for the velocity of theparticles being downwards or upwards, respectively.

The particle trajectory depends mainly on the drag coefficient expressedas a function of the Reynolds number related to the particle as follows:

NRe ¼rURdp

m(9)

where UR is the relative velocity between the particle and the surroundingflow (m s�1) and is expressed as follows:

UR ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðU �UpÞ2 þ ðV � VpÞ2

q(10)

CD is expressed as function of the Reynolds number NRe. However, theresults relative to the evolution of CD versus NRe are very dispersed ac-cording to the flow conditions and authors [114]. The plasma gas compo-sition plays a drastic role in particle acceleration: it can be demonstrated byconsidering the following simple expression:

CD ¼ 24

NRefor NReo0:2 (11)

and by calculating the characteristic time of dynamic transfer [115] as follows:

t ¼ rpd2p

18m(12)

Besides the importance of the particle diameter and its specific mass, thisexpression depicts why in the jet core, at least for conventional d.c. plasmajets with temperatures up to 14,000K, plasma gas containing helium delaysthe decrease of m for T 4 10,000K (Fig. 32).

b. Basic Equations for Heat Transfers. Once the particle trajectory has beencalculated, the temperatures of the plasma within which the particle travelsalong its trajectory can be determined in order to calculate the particletemperature evolution.


The particle temperature is governed by a balance between conductionand convection heat transfers between the plasma and the particle minusradiative heat losses from the particle to the surrounding atmosphere (theselosses are only important for refractory particles of large diameters; i.e.,4100 mm at temperatures 42000K). In most cases, the radiative transferfrom the plasma gas can be neglected because the plasma is optically thin [5].The heat transfer to the particle Q (W) can be hence expressed as follows:

Q ¼ h pd2p

� �T1 � T sð Þ � pd2

p

� ��ss T4

s � T4a

�(13)

where Ts and dp are the surface temperature (K) and diameter of the particle(m), respectively, e the particle emissivity (dimensionless), ss the Stephan-Boltzmann constant (Wm�2K�4) and TN the temperature of the sur-rounding (K).

Assuming a uniform particle temperature implies that the thermal conduc-tivity of the particle material kp is much higher than that of the gas k, as follows:

Bi ¼ kkp

o0:01 (14)

where Bi is the dimensionless Biot number.The heat transfer coefficient is calculated through the Nusselt, Reynolds

and Prandlt dimensionless numbers (for convection) – For details, see for

5.0x10-5

1.5x10-4

2.5x10-4

3.5x10-4

4.5x10-4

1000 4000 8000 12000 16000 20000

temperature [K]

visc

osit

y [k

g.m

-1.s

-1]

1

0.8

0.6

0.4

0.2

0

FIG.32. Molecular viscosity evolution versus temperature at atmospheric pressure of

Ar–He mixtures with different vol. % [116].


example [110]. These numbers can be correlated for Reynolds numberslower than 200 as follows:

Nu ¼ 2:0þ 0:6�N0:5Re �N0:33

Pr for NReo200 and 0:5oNPro1:0 (15)

Neglecting the convective term (generally below 30% of that of conduc-tion), it comes:

h ¼ 2kdp

ðW=m2KÞ (16)

According to the strong non-linearity of k with temperature, the questionwhich arises is to define at which temperature k has to be calculated? Manysolutions have been proposed [110].

To illustrate the importance of the choice of plasma-forming gas on theheat transfer to the particle, the method proposed by Bourdin et al. [117] isconsidered here. It showed that the heat transfer equation holds even underplasma conditions provided that the thermal conductivity is evaluated as anintegrated mean value defined as:

�k ¼ I

ðT1 � T sÞZ T1

T s

kðTÞdT (17)

It is interesting to note that if the thermal conductivity k is a linearfunction of temperature, Eq. (17) can be reduced to the commonly usedpractice of evaluating the property values at the arithmetic film averagetemperature k(Tf). Such an approach can be implemented to the charac-teristic time of dynamic transfers. A characteristic time for heat transfer canbe hence defined as follows [115]:

tth ¼ rpcpdp

6H 0 (18)

According to Eq. (18), this time will be the shortest for the highest value of k.Figure 33 [118] illustrates the effect of the plasma gas mixture (Ar–H2,

Ar–He and N2–H2, respectively). It is worth noting that the choice is alsolimited by the selected torch. Conventional d.c. plasma torches can be runwith Ar and 30 vol. % H2 at the maximum and He up to 80 vol. %.Concerning N2, 6–8 vol. % of H2 is a maximum ratio. With button-typecathode (i.e., Plazjet torch) nevertheless, N2–H2 mixture with up to 30 vol.% H2 can be used. RF torches work only with pure Ar while Triplex torchesare recommended to be operated with Ar–He.

Figure 33 (a) shows that, compared to pure Ar, pure H2 mean-integratedthermal conductivity is about 5 times higher below 3000K and as soondissociation occurs it is more than 20 times. Practically even with 5 vol. %H2, k� increases by a factor of almost 5. This factor is even doubled with 25


6

5

4

3

2

1

00 5000 10000 15000 20000

temperature [K]

0 5000 10000 15000 20000

temperature [K]

0 5000 10000 15000 20000

temperature [K]

mea

n in

tegr

ated

the

rmal

cond

ucti

vity

[W

.m-1

.K-1

]m

ean

inte

grat

ed t

herm

alco

nduc

tivi

ty [

W.m

-1.K

-1]

mea

n in

tegr

ated

the

rmal

cond

ucti

vity

[W

.m-1

.K-1

]

H2-Ar (5/95)

H2 (100)

H2-Ar (25/75)

H2-Ar (15/85)

He (100)

4

3

2

1

0

Ar (100)

He-Ar (60/40)

He-Ar (30/70)

6

5

4

3

2

1

0

N2 (100)

H2 (100)

H2-N2 (30/70)

H2-N2 (5/95)

(a)

(b)

(c)

FIG.33. Evolution of the mean integrated thermal conductivity versus temperature at

atmospheric pressure (a) Ar, Ar–H2. (b) Ar, Ar–He. (c) N2, N2–H2 [118].


vol. % H2. Such results explain why H2 is used as secondary plasma-forminggas as soon as refractory materials have to be sprayed; however forlow thermal conductivity materials Biot number can be higher than 0.01(see Eq. (14)) promoting heat propagation within particles.

That is why He is used as secondary plasma-forming gas. He improvessmoothly Ar mean integrated thermal conductivity, almost linearly (seeFig. 33 (b)), however, at least 10,000K must be reached with 60 vol. % Heto achieve the same �k as with 25 vol. % H2 at 4000K.

With pure N2, dissociation occurs at about 7000K (see Fig. 33 (c)) andK increases up to 1.6W/m.K (more than the 1W/m.K with 25 vol. % H2 at4000K). The improvement of �k with 5 vol. % H2 is not important at all,while it becomes significant with 30 vol. %. However, for plasma generation(T47000K) N2 mean integrated thermal conductivity, with or without H2,constricts drastically the arc column and stick-type cathodes can be run onlywith less than 7–8 vol. % H2 and arc currents below 500A. Torches withbutton-type cathode sustain H2 vol. % up to 25–30 and thus the heattransfer to particles is good, in spite of higher velocities than with stick-typecathode torches. However the arc current must be below 500A.

F. CORRECTIONS SPECIFIC TO PLASMAS

The aforementioned conventional equations must be modified when cal-culating the drag and Nusselt coefficients to take into account-specificeffects occurring within plasma flows [110]. These corrections are related tothe momentum and heat transfer equations.

1. Momentum Transfer

Corrections to the drag coefficient have to take into account the followingphenomena:

� the tremendous temperature gradients in the boundary layer sur-rounding a particle;

� the non-continuum effect related to the gas mean free path ‘ relativelyto the particle diameter dp, known as Knudsen effect characterized bythe Knudsen number, Kn which has to be taken into account as soonas Kn40.01. For example, at atmospheric pressure ‘ � a few mm inthe d.c. plasma core while particle diameters may be as low as 5 mmresulting in 0.1o Kno1;

� the turbulent dispersion of small particles (dpo20 mm);� the thermophoresis effect which can be neglected for particles higher

than 2 mm diameter;� the particle evaporation diminishing its mass when occurring.


For example, the calculation presented in Fig. 34 was obtained with alu-mina particles injected internally into an Ar–H2 d.c. plasma jet using theisotherms and velocities measured by Vardelle et al. [119]. Correcting thedrag coefficient plays a very significant role on the 20 mm alumina particletrajectory (for a given injection velocity).

Once the correction for the steep gradients has been chosen, the othercorrections have to be determined. Generally the most important ones (i.e.,for particles over 10 mm but below 30 mm) are those for non-continuum andvaporization effects. This is illustrated for example in Fig. 35 for 20 mmdiameter alumina particles (to have significant non-continuum and vapor-ization effects) injected at 25m s�1 within the plasma flow. Here again, thedifferent types of corrections used exhibit an important effect on the cal-culated particle trajectory and thus on its temperature and velocity.

The injection velocity plays also a relevant role in particle trajectories.Figure 36 shows for given plasma jet the different trajectories of a 30 mmdiameter zirconia particle injected with velocities ranging from 4.71 to47.15m s�1 (all previously mentioned corrections taken into account). Ob-viously, the particle momentum is too low for a velocity of 4.71m s�1 andthe particle crosses the torch axis only 5 cm downstream the nozzle exit (i.e.,practically downstream the plasma core). To achieve appropriate heat and

0 30 60 90 120 150

spray distance [mm]

radi

al d

ista

nce

[mm

]

-10

-5

0

5

10alumina – 20 µm – Ar-H2

Lee-PfenderLewis-Gauvinintegrated properties

FIG.34. Effect of the drag coefficient on the trajectories of 20mm diameter alumina par-

ticles injected at 8m s�1 into a plasma jet (Ar–H2: 75 SLPM – 15 SLPM, P ¼ 29 kW, thermal

efficiency ¼ 63%, nozzle internal diameter ¼ 8mm): Lee et al. [112] Lewis and Gauvin [120],

integrated properties [117].


0 30 60 90 120 150

spray distance [mm]

radi

al d

ista

nce

[mm

]

10

5

0

-5

-10

alumina – 20 µm – Ar-H2

without correctionvaporization correctionrarefaction correctionrarefaction + vaporization corrections

FIG.35. Trajectories of 20 mm average diameter alumina particles injected at 25m s�1 in the

plasma jet depicted in Fig. 34. The temperature gradient correction has been calculated using

the mean integrated properties [110].

-80 20 40 60 80 100

axial distance [mm]

radi

al d

ista

nce

[mm

]

-4

0

4

8

12

47.15 m.s-1

20.00 m.s-1

18.60 m.s-1

9.40 m.s-1

4.71 m.s-1

FIG.36. Trajectories of 20mm average diameter alumina particles injected in the plasma jet

depicted in Fig. 34 at several injection velocities. The temperature gradient correction has been

calculated using the mean integrated properties [121].


momentum transfers in spray conditions, an angle of 3.5–41 between theparticle trajectory and the centerline torch axis seems to be the most adapted[119]. As a thumb of rule, it corresponds to the momentum imparted to theparticle by the plasma flow about the same as that of the particle (mpvp).In Fig. 36, it corresponds to a particle velocity of about 20m s�1 whichcorrelatively corresponds to optimized momentum and heat transfers(i.e., the highest particle velocity and temperature). Vardelle et al. [121]have calculated, for an Ar–H2 (45–15 SLPM) d.c. plasma jet with an effec-tive power level of 21.5 kW and a nozzle internal diameter of 7mm, therequired injection velocity for the different particles to impact on nearly thesame location on the substrate surface. Results are plotted on the right-handy-abscissa of Fig. 37. It can be seen that, for a given plasma jet, the injectionvelocity varies drastically with the particle size and its specific mass.

2. Heat Transfer

Major corrections to apply to heat transfer result mainly from:

� the thermal buffer constituted by the vapor resulting from the particleevaporation and traveling with the particle because of the lowReynolds number of the latter (NRepo50);

� the non-continuum effect;

TaC

Si

0 20 40 60

particle diameter [µm]

inje

ctio

n ve

loci

ty [

m.s

-1]

resi

denc

e ti

me

[ms]

0

50

100

150

200

3

2

1

0

W

Mo

Al2O3

FIG.37. Particle residence time as a function of particle size and material specific mass

(plasma forming gas: Ar–H2, 45–15 SLPM, effective power ¼ 21.5 kW, nozzle internal diam-

eter ¼ 7mm) [121].


� the heat conduction within the particle which takes place as soon asthe Biot number Bi 4 0.01. For example, it is the case with ceramicparticles and Ar–H2 (410 vol. %) plasma gas mixtures;

� the radiation emitted by the metallic vapor.

To illustrate these effects, a few examples are detailed hereafter.

a. Vapor Buffer Effect. Typical results for a tungsten particle immersed inan infinite plasma are given in Fig. 38 [122] representing the evolution of theratio of the heat flux to the particles in the presence of vaporization, Q1, tothe ratio in the absence of vaporization, Q0 versus the plasma temperaturefor different plasma mixture compositions. One can note a substantial re-duction of the heat flux transmitted to the particle when the vaporizationrate increases. The effect is more pronounced for an Ar/H2 or a N2 plasma(i.e., due to better heat transfers) compared to a pure Ar plasma.

b. Heat Propagation. When heat propagation has to be taken into account,the time evolution of the temperature field within the particle is given by thefollowing conduction equation:

1

r2@

@rkpr2

@T

@r

� �¼ rpcpp

@T

@t(19)

0

rati

o of

H.F

. Q1/

Q0

plasma temperature [K]

0 5000 10000 15000

0.2

0.4

0.8

1.0

Ar/H2 (4/1)

N2

Ar

FIG.38. Effect of evaporation on heat transfer to a tungsten particle under different

plasma conditions [122].


where the index p refers to the particle, r is the radial distance from thecenter of the particle and cpp is the specific heat at constant pressure. Ofcourse when melting and vaporization take place simultaneously, the cor-responding fronts have to be determined, which renders calculations heavier[123]. Bourdin et al. [117] carried out a systematic study of the transientheating of spherical particles of different materials (Ni, Si, Al2O3, W, SiO2),of particle sizes ranging from 20 to 400 mm as they are suddenly immersed indifferent plasmas (Ar, N2, H2) at atmospheric pressure and different tem-peratures (TN ¼ 4000–10,000K). Typical results obtained for an aluminaparticles of 100mm in diameter in Ar, N2, H2 plasmas at 10,000K aredisplayed in Fig. 39. This figure illustrates temperature differences betweenthe surface (dotted line) and the center of the particle (solid line). Thesedifferences are as high as 1000K even for particles with diameters as low as0.1 mm! With its low thermal conductivity, Ar results in a very low heatpropagation. This is one of the major interests of using RF plasmas wherethe particle residence time is long enough to melt refractory particles.A contrario, d.c. plasma gas mixture need to incorporate H2 or N2 to meltsuch particles which could impact on the substrate otherwise with a moltenshell and a solid core. As expected, the difference between the temperatureof the surface of the particle and the one of its center depends on thetemperature of the plasma and the composition of the plasma gas as well as

0

500

1000

1500

2000

2500

part

icle

tem

pera

ture

[K

]

10-7 10-6 10-5 10-4 10-3 10-2 10-1

immersion time [s]

melting temperature: 2326 K

alumina – 100 µm

T∞ = 10000 K

H2

N2

Ar

FIG.39. Temperature history of 100mm diameter alumina particles immersed in different

plasmas at 10,000K [117].


on the thermal conductivity of the particle material. Nevertheless, it is in-dependent of the particle size.

c. Radiation Emitted by the Metallic Vapor. During the evaporation of me-tallic particles, energy losses by radiation from the metal vapor cloud sur-rounding the particle cannot be neglected as that of the plasma [122–126].Essoltani et al. [122] have shown that in the 3000–8000K temperature range,the radiation losses of the vapor can be several orders of magnitude higherthat those of a pure argon plasma.

This effect is observed with different metals, though its extent varies withthe nature of the vapor [125]. Of course, the self-absorption reduces the netradiation losses [122]. It is thus very important when spraying small particles(do20 mm) to adjust the plasma conditions to limit their vaporization. Andwhen vaporization occurs, the loading effect (i.e., the cooling of the jet byparticles) can start at feedstock rate as low as 1 kg h�1 against 5–6 kg h�1

when no vaporization occurs.

G. CHEMICAL REACTIONS

1. Chemical Reactions with the Vapor Surrounding a Particle

Several phenomena have to be taken into account when describing andmodeling heat and momentum transfers. They concern:

� the mass conservation which, according to the prefect gas law, can beexpressed as function of temperature;

� the conservation of the chemical species taking into account thediffusion transport of each species;

� the momentum conservation;� the energy conservation including the transport of energy due to

diffusion and taking into account, via a source term, the variation ofthe mole numbers of the different chemical species.

What renders the problem very complex is the fact that all the transportproperties (including the different diffusion coefficients) have to be deter-mined at each step of the calculation. Indeed, the presence of a reactive gasin the atmosphere surrounding the in-flight liquid particles may affect theirvaporization [121]. In the case of metallic particles sprayed in air, two typesof mechanisms may be responsible for an increased rate of vaporization[127]: A chemical process involving the formation of volatile metal com-pounds and a transport process involving the counter diffusion of oxygenand metal vapor within the boundary layer around the particles. Thesemechanisms interact together and the homogeneous oxidation reactionconsumes the metal vapor and thereby increases the rate of volatilization


from the liquid surface. Turkdoyan et al. [127] observed that the rate ofvaporization of a number of metals increased with oxygen partial pressure inthe atmosphere. Above a critical oxygen partial pressure, the flux of oxygentoward the surface is greater than the counter flux of metal vapor. Undersuch conditions, a solid or liquid oxide layer may then form on the particlesurface and change drastically the rate of vaporization.

When spraying in an inert atmosphere, the vapor molecules produced byparticle vaporization diffuse without reacting through the boundary layersurrounding the particles. Therefore, the metal vapor partial pressurearound the droplets increases and the rate of vaporization of particles de-creases. This is the case for iron particles processed in an Ar–H2 plasma[128]. The density of iron atoms is two orders of magnitude higher when thesurrounding atmosphere is air instead of a neutral atmosphere despite alower plasma flow temperature because the cooling down of the flow by themixing with the ambient air and the resulting O2 molecule dissociation.A simple calculation [121] can also determine if the oxidation is controlledeither by the diffusion or by the chemistry.

2. Chemical Reactions with the Particle

a. Diffusion-Controlled Reactions. When the partial pressure of the reactinggas in the core of the plasma surrounding the particle reaches a specificvalue, defined as the critical pressure [127], the flux of reacting gas towardthe surface of the droplet surface exceeds the counter flux of metal vapor.Under this condition, a liquid or solid layer of carbide, nitride, oxide, etc.depending on the plasma-forming gas composition and the entrapped sur-rounding atmosphere, develops on the droplet surface and vaporizationpractically ceases.

In the specific case of spraying in air (i.e., the most encountered case), twophenomena take place simultaneously:

� evaporation with the oxidation of the vapor (if a metal is evaporated);� oxidation of the particle.

This is illustrated in Fig. 40 [121] for iron particles injected in an Ar–H2

d.c. plasma jet (600A, 65V, Ar: 45 SLPM, H2: 15 SLPM, nozzle internaldiameter: 7mm) displaying the mole fraction of evaporated and oxidizediron along the torch axial distance for two particles of 40 and 80 mm indiameter, respectively, injected in the plasma jet both with the same velocityof 10m s�1. Such injection conditions signify that the trajectory of the 40 mmparticle is almost optimum whereas that of the 80 mm crosses faster theplasma jet and thus is less heated. It results in a much lower evaporation of


oxidation

evaporation

oxid

atio

n zo

ne

20

16

12

8

4

0

mol

e fr

acti

on o

f ev

apor

ated

/ox

idiz

ed ir

on [

%]

20

16

12

8

4

0

mol

e fr

acti

on o

f ev

apor

ated

/ox

idiz

ed ir

on [

%]

axial distance [mm]

0 20 40 60 80 100

axial distance [mm]

0 20 40 60 80 100

particle average diameter: 40 µminjection velocity: 10 m.s-1

oxid

atio

n zo

ne

evap

orat

ion

zone

oxidation

evaporation

particle average diameter: 80 µminjection velocity: 10 m.s-1

(a)

(b)

FIG.40. Mole fraction of evaporated and oxidized iron along particle trajectory [121].

(a) Initial particle size diameter: 40 mm, injection velocity: 10m s�1. (b) Initial particle diameter:

80 mm, injection velocity: 10m s�1.


the larger particle with a strong oxidation while the opposite is observed forthe smaller particle (higher evaporation and lower oxidation).

It is important to underline also that the oxide layer phase (solid or liquid)plays also a significant role in the mechanisms. Solid oxide is easily dis-rupted (‘‘broken’’) due to the coefficient of thermal expansion (CTE) mis-match between metal and oxide. This modifies diffusion through the layerand liquid oxide can be entrained partially, if its viscosity is low, by the gasflow toward the tail or the front of the moving particle resulting in a non-uniform oxide layer thickness [129].

The compound and its phase which can be obtained at the particle surfacedepends on the reactants present within the plasma and which can reach theparticle surface and also very strongly on the particle temperature.

b. Convection-Controlled Reactions. When collecting at 100mm down-stream of the plasma nozzle exit iron or stainless steel particles sprayed inair with an Ar–H2 plasma gas mixture and operating parameters leading tomost of the particles in an over melting temperature, two oxide facieses onparticles can be observed when examining their cross sections:

� an oxide shell resulting from the oxidation phenomenon diffusioncontrolled,

� oxide nodules inside the metallic particles corresponding to a con-vective movement induced within the particle by the gas flow. Toachieve convection within the particle by the gas flow, the followingconditions have to be met:

the ratio R of the kinematic viscosities of the plasma gas (ng)and the particle (np) must be such that:

R ¼ ngnp

455 (20)

the particle-flow relative dimensionless Reynolds number mustsatisfy:

NRe420 (21)

� the shear forces at the particle surface can result in toroidal flowwithin the particle [130–136].

In most cases under plasma-spraying conditions, Eq. (20) is satisfied assoon as the particle temperature is much higher than its melting point.Nevertheless, Eq. (21) is only satisfied in the plasma jet core [137,138].


The convective movements within the particle result in the formation of aspherical vortex sweeping fresh fluid to the particle surface and oxides, ordissolved oxygen, within the particle. Since liquid oxides have a surfaceenergy significantly different from that of liquid metal, oxides and metalseparate. This results in oxide nodules inside the particle itself.

Figure 41 (a) depicts a 30mm stainless steel particle collected at 100mmdownstream of an Ar–H2 d.c. plasma jet (see caption for the spray

FIG.41. Stainless steel particle 30mm in diameter collected at 100mm downstream of a d.c.

plasma torch nozzle exit (I: 550A, Ar–H2, 45–15 SLPM, nozzle internal diameter: 7mm, feed-

stock external injection ). (a) Particle with a cap. (b) Cross section of a particle with a cap [136].


conditions). It can be seen waves at the particle surface corresponding to theconvective movement induced within the particle. A cap can also be observedat the particle surface. The cross section in Fig. 41 (b) shows the cap andpieces of the oxide shell at the particle surface together with oxide nodules(dark areas) inside the particle. Energy dispersive spectroscopy (EDS) anal-yses of the base material, oxide cap and oxides show that, compared to thebase material, oxides contain more chromium and less iron and of coursemuch more oxygen. Phase analyses [137] by X-ray diffraction (XRD), Four-ier transform infrared spectroscopy (FTIR) and Mossbauer spectroscopyindicate that the oxides are non-stoechiometric iron-chromium oxides(Fe3�xCrxO4 where 1.954x41.56). The oxide cap results from the segrega-tion of liquid oxides to the tail of the particle when its velocity becomeslarger than that of the plasma flow, i.e., outside the plasma jet plume [136].

c. Reactions Occurring Between Condensed Phases. In the case where reac-tions occur between condensed phases, the primary reagents are in solidphases either as agglomerated or cladded particles [138–142]. The mostcommonly used cladded particle feedstock is the Ni–Al one where an Al coreis surrounded by a Ni shell. Upon melting, Al reacts with Ni creating inter-metallic species such as Ni3Al, NiAl, etc., through an exothermic reaction.The same mechanism occurs with agglomerated particles of Ti and C, forexample. The plasma heating of the particle ignites a self-propagation hightemperature synthesis (SHS). The reaction depends strongly on the size ofagglomerated particles and the possibility to heat the agglomerated particleswithout its desagglomeration by the produced gas expansion. As its meltinginterface velocity is typically between 0.1 and 15 cm s�1, the SHS reactionpropagation is not necessarily totally completed upon particle impact andmay continue after impact, inducing in such a case very dense and hardcoatings [142].

H. IN-FLIGHT PARTICLE MEASUREMENT

The purpose of in-flight particle measurements is to locally determine inthe plasma jets their surface temperature Tp (i.e., 1800–4500K), their char-acteristic size dp (i.e., ranging typically from 10 to 100 mm), their velocity up(ranging usually from 60 to 500m s�1), their average trajectory and thespray pattern distribution.

Two important points have to be outlined relatively to these measure-ments. The first one is related to the sensors limitations. For example,infrared pyrometers commonly used to diagnose in-flight particle tempera-tures exhibit a lower detection level at about 1800K and particles at lowertemperatures are not diagnose. The same detection limit is observed for laser


anemometers which are limited to particles over a few micrometers. Thesecond point is related to the plasma jet core emission: the flux emitted orscattered or reflected by the particles must be higher than that of the plasmacontinuum. The observation wavelength of the emitted or scattered or re-flected light must be carefully selected in a wavelength range where neitherline nor molecular emission exists. Thus, it is possible to implementpyrometry measurements only in the plasma plume and laser scattering inthe plasma core requires high power continuous-wave lasers (i.e., a min-imum of 2W per line) or high-power pulsed lasers. It means for examplethat the comparison of calculations and measurements in the plasma core,where most of the particle heating and acceleration occurs, is impossible.

1. Velocity, Diameter and Temperature

According to Fincke et al. [143], in-flight particle temperature, velocityand diameter measurements can be categorized as single-particle techniqueswhere each particle is observed ‘‘one at a time’’ or ensemble techniqueswhere the sensors observe simultaneously an ensemble of particles.

Single-particle technique is difficult to implement according to thenumber of particles in-flight: 105–106 part s�1 at the minimum (correspond-ing for a ceramic-based feedstock of low density to a powder mass flow rateof about 10 g h�1). Under such conditions, the particle measurement volumeneeds to be limited so that individual particles can be observed withoutoverwhelming interference from other nearby particles.

In ensemble measurement techniques, the measurement volume has not tobe small necessarily. Volumes, roughly cylindrical, of 2mm in diameter and50mm in length are very commonly used for example in pyrometry [144].Results issuing from an ensemble of particles have to be considered withcare because they can be biased. In most cases, measurements are related towarm particles and based on the radiative flux they emit, depending on theirtemperature, apparent surface and emissivity. Thus, the warmest and big-gest particles are mostly detected. In the single-particle technique, Vardelleet al. [145] implemented a measurement volume may be a cylinder of about160 mm in diameter and 200 mm in length. Of course, the optics are moresophisticated in this case and to achieve such small measurement volumes,coincidence methods have to be used where the plasma is viewed by twooptical systems arranged perpendicular to each other. Whatever the tech-nique used, the best precision on velocity is about 5%, that on temperature15–20% and that on diameter less than 50% if it is calculated from theradiated flux after particle surface temperature has been determined by two-color pyrometry and less than 10% when it has been measured by phasedoppler anemometry (PDA).


The velocity of cold and warm particles in the jet core or plume can bemeasured either by laser doppler anemometry (LDA) [146] or by PDA, thelatter also measuring the particle diameter [147,148]. For high velocities (i.e.,velocities over 400m s�1 with particle sizes as low as 3mm in diameter), a lasertwo focus points (2-F) is used, the separation of the two focus points beingadjusted to the particle velocity [149]. The advantages and drawbacks ofPDA and 2-F are discussed in [150]. The time-of-flight method, using pyro-meters as detectors in the plasma plume, developed first in 1987 by Boulosand Sakuta. [151] for RF plasmas has been adapted to d.c. plasma jets [152].

For particle diameter diagnostic, Particle Shape Imaging based on laserassisted shadow-image technique that consists in illuminating the particlesfrom two different directions has been developed at the Bundeswher Uni-versity in Munich, Germany [153,154]. Capturing digital pictures from theparticle shades, their shape is obtained directly by image processing based ona rigid particle classification, additionally to their size. Nevertheless, to proc-ess reliable statistical data, a high number of pictures has to be evaluated.

Particle surface temperature is determined by fast (i.e., about 50� 10�9 sresponse times) two-color pyrometry which signal does not depend onparticle diameter nor on emissivity. Such methodologies were developedbetween 1987 and 1991 [145,156,155].

2. Particle Fluxes and Trajectories

The cold particle trajectories can be followed from the feedstock injectorexit to impact upon substrate by using a uniform laser sheet orthogonal tothe torch centerline axis and generated by an oscillating mirror (i.e., at afrequency of about 2000Hz) with a continuous-wave argon ion laser of atleast 2W, average power. The bursts generated by the light scattered byparticles crossing the laser beam are counted by a photodiode array, asshown in Fig. 42.

The heat flux emitted by the warm particles traveling in the plasma plumeis analyzed and the collected signal is proportional to the number of warmparticles, their temperature (Plank’s law), their average emissivity and theirapparent surface. This method allows determining the warm particle tra-jectory distribution within a ‘‘slice’’ of the plasma plume on a photodiodearray or a CCD camera. This technique has been developed in laboratories[128] and its application will be illustrated later in the section about particleinjection (see Section IV.I.1).

3. Particle Vaporization

The particle evaporation rate is measured either by emission spectroscopyof metallic species [157] (based on numerous assumptions) or by absorption


spectroscopy (assuming LTE) [156,158]. Both types of measurements areonly performed in the plasma plume.

The condensation in the plasma plume of vapors issued from the vapor-ized particles is usually performed by using an electrical low pressure imp-actor [158].

The load effect of the particles (inducing a cooling of the plasma jet) iscarried out through the emission of an argon atomic line which intensitydecreases when the mass flow rate of particles increases [144].

4. Industrial Sensors

Industrial sensors are designed to work in the harsh environment of aspray booth and give the evolution of the principal characteristic parametersinfluencing the spray process [159,160]. They are either fixed and in this casethe plasma torch is positioned in front of the sensor from time to time (thisis the technique mostly used) or moved with the plasma torch.

The most popular industrial sensor is the DPV 2000 [161] developed byTECNAR (Saint Bruno, QC, Canada). It measures the average temperatureof particles by two-color pyrometry, their velocity by a time-of-flightmethod, their diameter, very approximately, through the emitted flux of aparticle knowing its temperature and assuming its emissivity and the warmparticles distribution by a CCD camera. Another sensor called ACCURA-SPRAY [162] is also commercialized by the same society. At last velocityand spatial distribution of warm particles are measured by CCD cameras

plasma

torch

plasmajet

R

particle flow pattern

data acquisition

measured light

intensity

feedstockparticle injector

diode

array

monochromator

laser radiation

lens L1

lens L2

oscillatingmirror

lasersheet

focusedbeam

"chord"

FIG.42. Schematic view of the experimental set-up to determine the cold particles radial

distribution in a d.c. plasma jet [156].


[163,164]. The velocity is deduced from the traces of particles resulting froma given exposure time (from 1 ms to tens ms). With the Spray Watch (Oseir,Tampere, Finland) commercial sensor [163] used in spray booths, a recentdevelopment allows to capture cold and/or warm and fast particles withthe help of a laser pulse which irradiation duration is between 0.1 and1.5 ms [165].

A two-color pyrometer was designed for large volume measurements (i.e.,measuring volume of 5mm in diameter and 50mm in length, approxi-mately)[152]. This system is commercialized as the in-flight particle pyro-meter (IPP) [147,148]. Similarly, Stratonics Co. (Idaho Falls, ID, USA) hasproposed an imaging pyrometer using a CCD camera [166] similar to theSpray Watch [163] and using a custom double dichromic mirror to achievespectral resolving capabilities.

At last, the spray and deposit control (SDC) [159] fixed on the torch andcontinuously monitoring the measured parameters, is based on a CCDcamera giving the distribution of warm particles in the jet plume and theirvelocity through the lengths of their traces for given CCD camera exposuretimes. Besides, an infrared pyrometer (i.e., in the 8–14 mm range) measuresthe surface temperature of substrate during the preheating and coatingstages either during spraying or upon cooling.

Such sensors allow monitoring the thermal spray process and determiningthe evolution of measured parameters. They constitute an excellent basisfor on-line process control which requires the possibility for the sensors tohave a feedback on the torch operating parameters. But many works arestill needed in this direction because correlations between coating thermo-mechanical and in-service properties and in-flight particle parameters as wellas substrate and coating temperature are still very scarce [159,160].

5. Transient Measurements

The transient behavior of d.c. jets and particles in-flight is generallystudied with the help of fast cameras, either standard digital video cameraswith very short shutter times (i.e., in the order of � 10�5 s) or motionanalyzers or digital/video cameras coupled with laser flashes. Whatever theselected device, it has of course to be synchronized with a transient signalsuch as the voltage fluctuations [7]. For examples, the spray watch sensorcoupled with a laser flash or the Laser Strobe Control Vision (LSV) systemdeveloped in 1990 [167] (which uses up to 6 pulsed nitrogen laser strobeswith a 5 ns pulse duration irradiation of 337 nm wavelength delivered viafiber optics to transport and focus to the viewing area of interest) can beused. For example, Fig. 43 shows the drastic effect of arc root fluctuationson the interaction of injected particles with the fluctuating plasma jet.


I. ENSEMBLE OF PARTICLES

1. Particle Injection

Powder particle injectors are generally of very simple geometries andcan be typified approximately [143–156] as straight (Fig. 44 (a)), curved(Fig. 44 (b)) or double flow ((Fig. 44 (c)).

The curved geometry is in fact mainly used due to specific designs of d.c.plasma torches: particles have to be injected orthogonally to the torch cen-terline axis at its nozzle exit. The injector is curved to follow the torch mainbody where all the pipes, including powder pipe, arrive at the rear of thetorch. In such configuration, the gas flow but mainly the particle flow aredisturbed by the curvature of the injector. Here, an important point is thelength L necessary to damp the perturbation [156]. Double-flow geometry isused to focus more the particle, especially the small (do20 mm) and light

FIG.43. Pictures of plasma jets and molybdenum particles injected in an Ar–H2 plasma jet

(pictures taken with a Control Vision set-up, a laser flash duration of 5 ms with no synchro-

nization with voltage fluctuations).


ones, exiting the injector [166]. Typical injector diameters used in d.c.plasma spraying range between 1 and 2mm (generally 1.6 or 1.8mm) andthe carrier gas is mostly argon (due to its viscosity) with sometimes purehelium (to increase viscosity).

The main problem in powder injection in the plasma flow is the posi-tioning of the injector relatively to the plasma jet. Fig. 45 illustrates whathappens when the injector is placed too far from the d.c. plasma jet: particlesat the periphery of the injection cone bypass the plasma jet, as shown by themeasurement of Vardelle et al. [145,156]. Those particles are then re-entrained farther downstream and generated defects within the coating sincethey are not adequately processed by the plasma. However, if the distance Dbetween the jet axis and injector exit is shortened too much, the injectorextremity may be significantly heated: clogging results and may generatealso defects within the coating structure when it detaches from the injectortip. Two strategies can be selected: either to water-cooled injectors (but thisstrategy is by far the most complex to implement) or the injection distancehas to be adjusted to find a compromise between clogging and bypassing.Water cooling is however a prerequisite for RF plasma spraying or powderprocessing when the injector must be positioned almost at the level of thesecond turn of the coil [69,70].

According to the gas pressure difference between the inlet and outlet ofthe injector, the flow inside reaches high velocities and is very often

D

hddd

a) b) c)

FIG.44. Several geometries of powder injectors. (a) Straight geometry. (b) Curved ge-

ometry. (c) Double-flow geometry.


compressible [168]. Thus, the carrier gas flow rate has to be adjusted in orderto obtain an adequate velocity. To do this, the velocity can be for examplecalculated with the compressible fluid equation of St Venant. For an argongas flow of 3–8 SLPM, the flow dimensionless Reynolds number in a1.75mm internal diameter injector ranges from 3000 to 8000 and can behence assumed as turbulent. Computations of the gas flow through variouscurved injectors showed that the streamlines are distorted toward the outerperiphery of the curvature and are re-established in the straight portion ofthe tube after the curvature. As a result [169], the carrier gas exiting from acurved injector with a straight portion higher than 35mm is not affected bythe presence of the curvature. Unfortunately it is not the case of particles(see next section).

The model developed by Vardelle et al. [156] for the pneumatic transportof powder was based on a standard k-e turbulence model with a correctionfor low Reynolds numbers (i.e., close to the injector wall). Particle trajec-tories were computed using a Lagrange scheme and their dispersion dueto turbulence was taken into account. Particle interactions with the injectorwall were considered but their collisions between themselves were neglected.This assumption, for particles following linear trajectories, is validwhen the mean distance between two particles (depending on the feedstockmass flow rate) is approximately 10 times higher than their averagediameter. However, this assumption may not be valid for curvedinjectors. Results presented in the following were obtained for fused andcrushed zirconia particles with three size distributions: 38719, 53721 and93724mm.

feedstockinjector

plasma flowparticles by-passing

the plasma flow

injection

distance

FIG.45. Schematic of particles bypassing the plasma flow when injection distance is too

high.


Figure 46 displays for example the computed velocities versus diameterfor zirconia powder considering a 1.8mm internal diameter straight injectorand argon as carrier gas with a flow rate of 4 SLPM. For particles largerthan 20 mm, the particle average velocity is not affected much by the particlesize. The zero value on the minimum curve indicates particles that wouldpreferentially segregate to the wall.

The dispersion of the particles at the injector exit can be characterized bythe diameter of the particle jet at different distances z from the injector exitand by the size distribution of particles collected in rings of different dia-meters at z. Experiments at SPCTS (University of Limoges, France) withalumina particles of different size distributions have shown that they presentabout the same distribution as their initial one for any position of the col-lecting ring. It probably means that collisions between particles are aboutthe same irrespective of their size. The particle jet diameter changes verylittle if the argon carrier gas flow rate increases from 4 to 6 SLPM (i.e., atypical range in plasma spraying) for powder of 22–45 mm particle sizedistribution. However, for finer particles (5–22 mm), the diameter of theparticle spray jet increases more drastically with the carrier gas flow rate[156]. This is due to the increase of interactions between smaller particle andthe injector walls. The internal diameter of the injector also plays a relevantrole on the particle velocity which increases, for a given carrier gas flow rate,when the injector internal diameter decreases, but also on the jet divergence

0 20 40 60


part

icle

ave

rage

vel

ocit

y [m

.s-1

]

40

30

20

10

0

maximum

average

minimum

STRAIGHT

FIG.46. Computed particle average velocity at the injector exit as a function of their size

[156].


which decreases with the injector internal diameter [156]. It is alsointeresting to note that the average velocity of small particles (for exam-ple zirconia particles of average diameter smaller than 20 mm) is higherwhen He is used as carrier gas instead of Ar (considering the same gas flowrates).

The geometry of the curved injector has a significant effect on particlebehaviors [156]. As the particles approach the bend, they decelerate and aredriven to the outer regions of the bend due to the centrifugal forces impartedby the flow. In this zone, the gas has a lower velocity, resulting in a decreasein the drag force exerted on the particle by the surrounding fluid. Theparticle distribution within the injector is no more symmetrical, 90% of theparticles being concentrated in the outer part of the curvature [156].Figure 47 shows the computed evolution of velocity profiles of particles withtheir size for several types of injectors. The curved injectors reduce dras-tically the particle velocity but, as with a straight injector, particles withdiameters over 20 mm have little influence on particle velocity.

The usefulness of the double-flow injector is important for small (averageparticle diameter lower than 20 mm) and light particles to collimate them[156,168] and make the particle distribution much more symmetrical com-pared to that without double flow.

The inclination of the injector relative to the plasma flow can also play arelevant role. When counter flow is considered, particle heating and

0 20 40 60


part

icle

ave

rage

vel

ocit

y [m

.s-1

] straight

R = 12.7 mm

R = 50.8 mm

20

15

10

5

0

FIG.47. Computed particle average velocity at the injector exit as a function of their size

for several injector geometries (R represents the curvature radius of curved geometries) [156].


acceleration are improved but clogging is enhanced. When flow direction isconsidered, particle heating and acceleration decrease.

The positioning of the injector is also very important when using high-power torches with a strong vortex injection of plasma-forming gases.Powder injection must be adjusted in such a case off the geometric axis ofthe torch and against the swirl direction to have the particle flow pattern incoincidence with the plasma plume [170].

At last for d.c. plasmas, as already underlined for single particles and asillustrated in Figs. 35 and 36, it is important to adjust the mean momentumof injected particles about the same as that imparted to them by the plasmajet to achieve their optimum trajectory and thus acceleration and heating[171]. It is clear that the particle jet divergence drastically increases with theratio of smallest to biggest particle diameters which has to be kept, if pos-sible, below 2 (already corresponding to a mass ratio of about 8!). Thus,when co-spraying particles of different characteristics (in terms of size dis-tribution and specific mass, especially), for example alumina and iron, theonly way to have a uniform melting of all of them (without over melting ironin the present case) is to adapt their size distribution and use two injectorsnot necessarily disposed at the same distance from the nozzle exit [156].

With RF plasmas the injector, positioned along the torch axis, has to bewater cooled. It is usually made of stainless steel, the coupling with the coilbeing inexistent due to the small injector size compared to that of the coil.The carrier gas flow rate has to be adjusted relatively to the recirculationvelocity, if any. However, even without recirculation, a small flow rate isnecessary for particle penetration, but it has to be kept in mind that anycarrier gas flow cools down the central part of the plasma which is heatedonly by conduction–convection. One way to achieve a good penetration is tolower the injector extremity to the level of at least the first turn of the coil(usually the second turn) where no recirculation exists any more.

2. Particle Distribution within the Plasma Jet

a. Measurements. The dispersion of the warm particles within the d.c.plasma jet is illustrated in Fig. 48 [9] for alumina particles with a narrowparticle size distribution (15–21 mm). The median trajectory represented inFig. 48 (a) corresponds to a non-uniform particle distribution in a plasma jet‘‘slice’’ as shown along axes r and y in Figs. 48 (b) and (c), respectively.It shows also that the particle flow pattern is not centered on the plasma jet,Fig. 48 (d). Of course, the longer the distance from the injection point, thewider the particle jet dispersion. In d.c. plasma spraying, the particle dis-tribution at the stand-off distance of 100mm represents for example a fewsquare centimeters around the median particle jet position.


The importance of the adjustment of the carrier gas flow rate to plasmaoperating conditions is illustrated in Fig. 49 for alumina particles for whichradiated flux was measured with a SDC. The figure clearly reveals the drasticeffect of the carrier gas on the average trajectory and intensity (i.e., cor-responding in a first approximation to the particle heating) for given op-erating conditions. It underlines also how sensitive is the particle treatmentto their injection.

Once the optimum trajectory has been determined, particle temperaturesand velocities can be measured. A typical particle evolution along theplasma jet centerline axis for two d.c. torch power levels is shown in Fig. 50.Each point is the average of a statistics on 1000 particles and the error barscorrespond to the associated standard deviation. As it could be expected,higher input power corresponds to a better heating of particles.

This is for this reason that the development of sensors able to work in theharsh environment of spray booths (see Section IV.H.4) has been so im-portant to improve the reliability and reproducibility (the rejected partshave been reduced by 70–80%) of sprayed coatings. These sensors monitorparticle in-flight parameters prior to impact (temperature, velocity, trajec-tory and heat flux radial distributions, mostly) and keep them as constant as

N

[105.mm-2.s-1]

4

2

0

-2

-4

0.5

15000 K8000 K

10000 K11000 K

z = 20 mm

Y [mm]

0

1

0.5

-4 -2 2 4

N

[105.mm-2.s-1]

radius [mm]

12000 K

10000 K

8000 K

radius

Y

powder injection

c a

db

FIG.48. Alumina particle (15–21mm) distribution within a slice of the plasma jet at

x ¼ 20mm with an external injection (injector position x ¼ 3mm, y ¼ 7mm). (a) Particle

injection. (b) Spatial distribution in a plane perpendicular to plasma torch centerline axis.

(c) Radial distribution. (d) Radial distribution [9].


2700

3000

3500

3800

0 50 100 150 200

distance from gun nozzle exit [mm]

part

icle

ave

rage

tem

pera

ture

[K

]

melting temperature

29 kW

21 kW

ZrO2-8%wt.Y2O3

FIG.50. Zirconia particle (22–45mm) surface temperatures for two different d.c. power

levels (21 and 29 kW, respectively, Ar–H2, 75–15 SLPM, nozzle internal diameter 8mm) [9].

0

5000

10000

sign

al a

mpl

itud

e [a

.u.]

jet radius [mm]

-10 0 10 20

2.5 SLPM

3 SLPM

4 SLPM

4.5 SLPM

5 SLPM

6 SLPM

7 SLPM

8 SLPM

FIG.49. Effect of carrier gas flow rate on radial distribution (at z ¼ 70mm) of alumina

particles (fused and crushed, 22–45mm) in a d.c. plasma jet: Ar–H2, 45–15 SLPM, I ¼ 600A,

V ¼ 53V, rth ¼ 50%, internal injection 2mm up-stream the nozzle exit, injector internal

diameter 1.5mm) [172].


possible by modifying correspondingly the extrinsic operating parameters(arc current, secondary plasma-forming gas flow rate, carrier gas flow rate,etc.). They have hence allowed optimizing the carrier gas flow rate, the arccurrent intensity, primary and secondary plasma-forming gases, etc., rela-tively to specific coating properties (hardness, roughness, oxidation, etc.).This is achieved by defining an appropriate working area through factorialdesign experiments for example or other experiment design strategies. How-ever, the substrate/coating temperature has also to be considered because, asit will be discussed in Section V.E, it controls the inter-lamellar contacts, thecoating adhesion/cohesion and residual stresses.

Such sensors have also allowed following the stability of the spray jet, forexamples at the beginning of the spray operation when the powder is in-jected, as a function of the working time to quantify long-term electrodeerosion, between several spray booths, etc.

To measure the influence of the plasma jet fluctuations, the DPV-2000 hasbeen modified for time-resolved diagnostics [173,174]. When the DPV-2000is used in normal operating conditions, the acquisition of the pyrometersignals is triggered when the pyrometer signal in one channel exceeds apredefined threshold. Here, the signal used to trigger the acquisition of thein-flight particle signal is no longer the particle radiation but the torchvoltage. An example of results is given in Fig. 51 displaying the fluctuationsof the average temperature and average velocity of alumina particles. Theplasma torch used is a F4-MB-type gun working under Ar–H2, 35–10 SLPMat 550A with a power level of 37 kW. For alumina particles of 45–32 mmparticle size distribution, the temperature fluctuation (Fig. 51 (a)) reaches500K for an average value of 2650K, that is to say about 20%, while thevelocity fluctuation (Fig. 51 (b)) reaches 180m s�1 for an average value of350m s�1, that is to say about 50%! Thus, these fluctuations have to belimited, because as it will be shown in Section VI, they affect the coatingproperties and the deposition efficiency.

b. Modeling. Once the plasma flow characteristic distributions (tempera-ture, velocity, composition, enthalpy, etc.) have been calculated (see SectionIV.C. or IV.D.) or measured (see Section V.B.), the plasma-particle transferscan be calculated.

Many works have been devoted to the problem of stochastic distributionsof particles. Some authors, for example Chang [175] with the LAVA code,have started with the previous works originally developed to represent liquidsprays [176,177] and some others have assumed a stochastic approach [178].Others have introduced into calculations, injection velocity and directiondistributions (often based on experimental results) as well as size distribu-tions (see the review of Pfender and Chang [179] and also [180–182]).


However, at the moment, no one really knows how representative can bethese models to depict this problem.

Once the initial distributions have been selected, particles are divided intodifferent size classes, for example for diameters classes ranging between bothextremities of the size distribution and following a log-normal law. The

2900

2700

2500

23000 200 400 600 800

time offset [µs]

part

icle

ave

rage

tem

pera

ture

[°C

]

213

174117

96

136

151

136

133

180

181

166131

0 200 400 600 800

time offset [µs]

part

icle

ave

rage

vel

ocit

y [m

.s-1

]

91

8881

61

50

32

44

21

82

77 86

450

400

350

300

250

(a)

(b)

FIG.51. Evolution of 32–45mm size distribution alumina particle characteristics on the gun

centerline axis versus plasma torch voltage fluctuations (F4-MB type plasma gun, arc current

intensity 550A, Ar–H2, 35–10 SLPM). (a) Average temperature. (b) Average velocity [173,174].


distribution of particle injection velocities is often approximated by aGaussian distribution and an approximated distribution. Then, each com-putational particle p represents a number Np of similar physical particlesto which are applied the motion and energy transfer equations defined inSection V.A.a.

An example of calculation [99], for an Ar–H2 45–15 SLPM d.c. plasma jet(I ¼ 600A, U ¼ 65V, rth ¼ 55%, nozzle internal diameter of 7mm) is dis-played in Fig. 52 for Al2O3 particles of particle size distribution rangingfrom 5 to 46 mm divided into two classes. The left part of the figure neglectsthe voltage fluctuations whereas the right part takes it into account. Particleswere injected vertically (following the z-axis) below the plasma jet centerlineaxis which was horizontal with the injector located externally at 4mmdownstream of the nozzle exit and at 8mm from the torch axis. The in-jection velocity distribution varied between 5 and 20m s�1 and the injectionvelocity vector was randomly distributed among two angles: a varying from01 to 3601 and f (defining the particle flow pattern cone angle) between 01

0.020

0.015

0.010

0.005

0

0.005

-0.015 -0.010 -0.005 0 0.005 0.010

powder injection

steady time-dependent

axia

l dis

tanc

e [m

]

radial distance [m]

FIG.52. Computation of turbulent dispersions of alumina particles of particle size distri-

bution ranging from 5 to 46mm injected with a velocity distribution ranging from 5 to 20m s�1

depending on the particle size into a plasma flow (Ar–H2 45–15 SLPM, I ¼ 600A, U ¼ 65V,

rth ¼ 55%, nozzle internal diameter of 7mm) [99]. (a) Neglecting torch voltage fluctuations.

(b) Considering torch voltage fluctuations.


and 101. Calculations were performed for 2000 particles. The obtained resultfor steady state, presented in Fig. 52 (left) shows that the effect of turbulentdispersion is very high for small particles, their cloud extending up to 1 cmfrom the torch axis in the x-direction. With larger particles which inertia arehigh (upper part of the left figure), the cloud of particles is limited to an areaof 2–3mm in width. It is also interesting to note that when voltage fluc-tuations are taken into account, the obtained distribution (Fig. 52, right) iswider than that calculated in a steady state (Fig. 52, left).

While the assumption of a dilute system has generally been accepted for thecalculation of individual particle trajectories and temperature histories underplasma conditions, the interpretation of the results obtained is greatly hin-dered by the simple fact that any application of plasma technology for the in-flight processing of powders will have to be carried out under sufficiently highloading conditions in order to make efficient use of the thermal energy avail-able in the plasma. With the local cooling of the plasma due to the presence ofthe particles, model predictions using the low-loading assumption can besubstantially in error. In an attempt to take into account the plasma–particleinteraction effects, Proulx et al. [183–186] developed a mathematical modelbased on an interactive procedure updating continuously the computedplasma temperature, velocity and concentration fields. The interactionbetween the stochastic single particle trajectory calculations and those ofthe continuum flow, temperature and concentration fields was incorporatedthrough the use of appropriate source–sink terms in the respective continuity,momentum, energy and mass transfer equations. These are estimated usingthe so-called particle-source-in-cell model (PSI-Cell) [187].

The importance of the loading effect is directly linked to thermal prop-erties of particles (Table IV [188]), alumina for example exhibiting thehighest latent heats of melting and boiling as well as specific heats of solidand liquid. The lowest values are those related to tungsten, nickel being in-between alumina and tungsten. Similar results are obtained for the plasmavelocity along its axis, the reduction due to particles being neverthelesslower than that observed for temperature.

Similar results are obtained when considering d.c. plasma jets as illustratedin Fig. 53. Calculations and measurements were performed for alumina par-ticles injected into a d.c. plasma jet (32 SLPM Ar, 12 SLPM H2, I ¼ 600A,V ¼ 58V, Z ¼ 52%, Al2O3 particles 62–18mm, nozzle internal diameter 7mm,injector internal diameter 1.8mm, external injection, r ¼ 9mm, z ¼ 6mm)[189]. The distributions of particle velocity and surface temperature weremeasured on the jet centerline axis at 120mm from the nozzle exit for differentpowder mass flow rates. Results displayed in Fig. 53 indicate that the velocityof the particles is reduced by 11% when the powder mass flow rate is increasedfrom 0.03 to 2 kgh�1 while their surface temperature is reduced by about


14%. When calculating the particle velocities, the average value is within 10%of the experimental values for a low mass flow rate such as 0.2 kgh�1. How-ever, significant differences arouse for a powder flow rate of 2 kg h�1. Thesedifferences concern both particle characteristics; i.e., velocity and temperature,but is more pronounced for this latter. This discrepancy underlines the im-portance of representing more accurately the particle injection.

At last, the losses by radiation of metal vapor have to be taken intoaccount [125] because, as already mentioned in Section V.A.d., they dras-tically increase the load effect. Moreover, the recondensation of thesevapors, either as metal or oxide sub-micron particles [158,190], are verydetrimental for the coating cohesion by generating defects between succes-sive torch passes.

V. Coating Formation

A. GENERAL REMARKS

The impact of particles accelerated and heated up by plasma jets has beenextensively studied under plasma spray conditions. In general, a successfulapplication of thermal-sprayed coatings to engineering usage dependsstrongly on the quality of the adhesion between the coating and the subst-rate and on the cohesion between deposited layers. In most cases, theadhesion/cohesion is of mechanical nature; surface anfractuosities (i.e., pitsand grooves) of a rough surface are filled with the spreading molten materialdue to the impact pressure. Subsequent solidification leads to mechanicalinterlocking (i.e., mechanical ‘‘anchoring’’). However, inter-diffusion at high

TABLE IV

STATE OF ALUMINA, NICKEL AND TUNGSTEN PARTICLES OF 60mM IN DIAMETER AFTER THEIR

TREATMENT IN A 5KW AR RF PLASMA [188]

Material State Feed rate (g min�1)

1 10 20 30 50

Alumina Solid 0 0.02 0.43 0.84 1

Liquid 0.74 0.98 0.57 0.16 0

Vapor 0.26 0 0 0 0

Nickel Solid 0 0 0 0.02 0.19

Liquid 0.27 0.69 0.88 0.94 0.81

Vapor 0.73 0.31 0.12 0.04 0

Tungsten Solid 0 0 0 0.05 0.7

Liquid 0.9 1 1 0.95 0.3

Vapor 0.1 0 0 0 0


230

240

250

260

270

part

icle

ave

rage

vel

ocit

y [m

.s-1

]

powder mass flow rate [g.h-1]

powder mass flow rate [g.h-1]

0 400 800 1200 1600 2000

3000

3200

3400

3600

3800

0 400 800 1200 1600 2000

part

icle

tem

pera

ture

[K

]

(a)

(b)

FIG.53. Evolution of alumina in-flight particle computed characteristics at 120mm down-

stream the spray torch nozzle exit on the jet centerline axis as a function of the powder mass

flow rate. (a) Particle average velocity. (b) Particle average surface temperature. (d.c. plasma jet,

Ar–H2, 35–12 SLPM, I ¼ 600A, V ¼ 58V, Z ¼ 52%, Al2O3 particles 62–18mm, nozzle internal

diameter 7mm, injector internal diameter 1.8mm, external injection, r ¼ 9mm, z ¼ 6mm)

[189].


substrate temperatures under soft vacuum (VPS) and possibly chemical re-actions in APS across the substrate or previously deposited layers may occurif the heat transfer from the impinging molten particles causes a local meltingof the layer underlying the flattened particle. The latter is called a lamella or‘‘splat’’.

Indeed, the adhesion/cohesion of coatings, as well as many other prop-erties (thermal, electrical, mechanical, etc.), is strongly linked to the qualityof the contact between the piled-up splats. At impact, depending on itsdiameter, morphology, temperature, velocity and chemistry, each particleflattens and the high pressure inside it forces melted material to flow lat-erally and ductile material to deform. The kinetic energy of the particle ishence transformed into work of viscous deformation and surface energy[35,191]. Indeed, the flattening is controlled by mechanical and thermalconstraints. The former are linked to the underlying surface roughness andits relative inclination toward the particle trajectory (i.e., impact angle). Thelatter induce material solidification that depends on splat thickness, thermaldiffusivities of both sprayed material and underlying solid layer and thequality of contact between the latter and the flattening particle (often char-acterized by a thermal contact resistance).

The quality of the contact at the interface is a function of the particleimpact pressure and varies drastically and non-uniformly along the contactsurface during impact. The contact quality is also dependent on the dropletwetting on the substrate and the desorption of adsorbates and condensatesat the surface of the underlying layer. In addition, the contact between thepiled-up splats is controlled by the relief of the quenching stress induced bythe thermal contraction of splats upon cooling. The stored elastic strainenergy can be released by various mechanisms: micro-cracking, plasticyielding, creep, etc. [193,194].

B. CHARACTERISTIC TIMES

In thermal spraying, coatings are generally deposited layer-by-layer.Therefore, the deposition process presents two characteristics stages. Thefirst stage is related to the formation of a single splat and the second stage tothe building-up of a layer resulting from the motion of the plasma gun infront of the coated part. Both stages exhibit typical time constants [191,192],Table V:

� the characteristic durations required for a particle to flatten and tostart solidifying on the substrate (or on already solidified splats) andthen to solidify completely. These times are related both to the par-ticle parameters at impact (i.e., velocity, temperature, oxidation stage)


and those of the substrate (i.e., surface roughness, oxidation stage,contamination, temperature);

� the latencies between two successive impacts at the same location fora layer formation and then between two successive passages of thetorch. These times depend on the powder mass flow rate and on thedeposition efficiency as well as the torch/substrate relative velocityand the part dimensions. They will also condition (of course, togetherwith the cooling systems implemented) the time averaged temperatureof the substrate and then coating during deposition.

C. DIAGNOSTICS

1. Splat Collection

To our knowledge, two experimental set-ups have been developed to col-lect individual splats without overlapping and isolate the substrate from theplasma thermal flux: the line-scan test of Roberts and Clyne [195] and thatof Bianchi et al. [196,197]. The observation of the collected splats by opticalmicroscopy or scanning electron microscopy, together with the use of imageanalysis [196], give statistical information on the splat shape factor, (SF), itsequivalent diameter, D, and the location in the spray cone. SF is defined as:

SF ¼ 4pS

p2r(22)

where Pr is the splat perimeter and S its surface area.The evolutions in splat morphology with respect to substrate temperature

and roughness can be obtained from the size and shape factor distributions,especially on smooth substrates [198].

2. Impacting Particles

Diagnosing impacting particle characteristics is very complex because, fora single-particle impact, the events to be followed occur in a few

TABLE V

CHARACTERISTICS TIMES IN PLASMA SPRAYING

Mechanisms Characteristic time

Particle flattening and solidification starting A few msEnd of lamella solidification 3–10msLatency between two impacts at the same location 10–100msLayer or pass formation A few ms

Latency between to passages of the gun at the same location

(linked to the sprayed part size)

A few seconds to a few

hours


microseconds and concern particles in the tens of micrometer range. Theobjective is to measure the particle parameters prior to its impact (Tp, vp anddp), follow its temperature and size evolution during its flattening and cool-ing, and determine its impact and flattening splashing. These measurementsare twofold: on millimeter-sized particles or on micrometer-sized particles.

a. Diagnostics on Millimeter-Sized Particles. Millimeter-sized particles im-pact at a few meters per second resulting in characteristic times in the milli-seconds instead of microseconds but with the same Reynolds and Pecletnumbers as those of sprayed particles [199,200]. Under these conditions, theflattening is much easier to follow with a fast camera (i.e., less than 5000images per second are required) than with particles in the micrometer range.A typical example is given in Fig. 54 from Fukumoto. However, if conditionscan be found where two dimensionless parameters related for one to theliquid flattening and for the other to the solidification are the same as thosefor micrometric particles, it is experimentally impossible to fix operatingconditions to have all of them identical. Thus, the results of these exper-iments have to be continuously extended to micrometric particle flattening.

b. Diagnostics on Micrometer-Sized Particles. Diagnostics on micrometer-sized particles under plasma spray conditions implement either a fast

high-speed

camera

thermometer

vacuumpump

N2 gas moltendroplet

radio-frequencyheating system

heater

substrate

FIG.54. Experimental Set-up of Fukumoto et al. [199] to fallow with a fast camera

(5000 images/s) the impact and flattering of a millimeter-sized particle produced by inductively

melting a metal wire. The atmosphere is partially controlled.


pyrometer (50 ns) and laser shadowgraph [201] or a fast pyrometer and aPhase Doppler anemometer [202] which signals can trigger one [203] or two[204,205] fast cameras (with exposure delay time ranging from 100 ns to1ms). The difficulties of such investigations lie in the fact that the impact ofa single droplet in plasma conditions is not a reproducible event (i.e., inconventional spray condition between 106 and 108 particle per second, de-pending on their sizes, impact on the substrate within the sprayed spot). Achange in the particle mass causes a change in the temperature and velocityof the droplet and can modify the morphology of the resulting splat. This isthe reason why a significant number of experiments has to be carried out todetermine general tendencies. For example, splats are collected on a subst-rate at a distance of 85mm. Only particles following the trajectory close tothe plasma jet axis are collected thanks to a moving water-cooled shieldpositioned at 70mm downstream of the torch nozzle exit and a fixed onepositioned 11mm upstream of the substrate Leger et al. [202]. Shields aredrilled with 1.5mm in diameter holes.

The experimental set-up for a single particle is twofold (Fig. 55): in-flightcharacterization by an optical sensor head and a fast (50 ns) two-colorpyrometer and flattening characterization by a two-color pyrometer and twoimaging systems; i.e., fast CCD cameras triggered by the velocity signal.Particle velocity is measured using time of flight.

The signal is real time (about few hundreds of ns) handled thanks to acontroller program and this procedure allows both obtaining the particle

insulatingshields

plasma

torch

impact area

PDA analyzer

oscilloscopecomputer

beamsplitter

PDA laser

avalanche

diodes (2)pyrometer

FIG.55. Experimental set-up to follow the temperature and velocity of a single particle

prior to its impact as well as its temperature and radiated flux time evolutions [202].


velocity (with an accuracy of about 10%) and triggering cameras. The tem-perature of the particle prior to its impact and the time-evolution of theresulting splat temperature are determined from the thermal radiation emit-ted by the particle in flight and at impact (with an accuracy of about 10%).This radiation is collected by a two-color pyrometer head focused on thesubstrate with a response time of 50 ns. The temperature of a particle justprior to its impact and that of the resulting splat, are derived, after cal-ibration, from the ratio of the pyrometer photo-detector outputs, by as-suming that the diagnosed material behaves as a grey body. The main CR ofthe splat is estimated from the time–temperature evolution of the lamella. Insuch an experiment the particle fattening is characterized by the rise of theradiated flux due to its surface increase, which precision is not very high[201]. This precision is improved with the laser shadowgraphy set-up ofGougeon and Moreau [201], which unfortunately works with glass subst-rate. That is why in the last experiments of first Escure et al. [203] and thenCedelle et al. [204,205], besides the measurements described by Leger et al.[202], two imaging systems, have been added.

The experimental observation of the single-droplet impact on a substrateis carried out by an imaging technique composed of two rapid CCD cameras(which are triggered by the velocity signal) and two long distance micro-scopes. Fig. 56 describes the experimental set-up of the imaging technique.

insulating shields

plasma torch

impact area

camera #2

camera #1 pyrometer

PDA analyzer

oscilloscopecomputer

beam splitter

PDA laser

avalanchediodes (2)

x

y

FIG.56. Experimental device designed for imaging a single particle at impact along two

directions (perpendicular or orthogonal to the substrate) and determining its temperature,

velocity and diameter prior to its impact (with a fast pyrometer and a PDA) [204,205].


One imaging system is aimed parallel to the substrate surface in order tovisualize the impact splashing in the x-direction orthogonal to the substrate.Having the camera parallel to the substrate axis (y-axis) also allows visualizingimpacts on inclined substrates. The second camera is installed with a 151 angle(relative to x-axis) to the substrate surface in order to follow the flatteningsplashing occurring generally when the flattening process is almost completed;i.e., in the ms time range. Each splat corresponding to these measurementsis then characterized by atomic force microscopy (AFM), scanning electronmicroscopy (SEM) and transmission electron microscopy (TEM).

Indeed, in such measurements, smooth substrates have to be used becauseof peak sizes of a rough (i.e., grit-blasted for example) surface can be as highas 40 mm for an average roughness value (Ra) of 5mm: these peaks totallydisturb flattening mechanisms on the one hand and do not permit adequateoptical microscopic observations on the other hand.

D. MODELS AND RESULTS ON SMOOTH SUBSTRATES NORMAL TO IMPACT

DIRECTION

The particle flattening and lamella solidification depend upon the fol-lowing parameters, Fig. 57:

� in-flight particle characteristics: Tp, vp, dp, surface chemistry, impact angle;� substrate characteristics: temperature, oxide layer thickness and com-

position, roughness values both at micrometer and nanometer scales,thermal properties especially transient ones (effusivity and diffusivity).

Based on previous works on the liquid-droplet flattening without solid-ification (see for example the review of Armster et al. [206]), similarityanalyses have been implemented with the particle Reynolds and Weber di-mensionless numbers to which have been added, to cope with the thermaleffects, the Nusselt number at the liquid–solid interface, the Biot number forthe heat flux at the interface considering a thermal resistance, the Eckertnumber for viscous energy dissipation and the Stefan number for the latentheat of fusion release.

1. Flattening (Analytical Models)

In practical situations, particles impact on rough surfaces, which are moreor less oxidized for metals or alloys. However, most measurements[191,201–205] deal with smooth surfaces, while models, besides the smoothsurface, assume there is no intermediate oxide layer between the substrate andthe first splat. The first analytical models were related to droplets impactingnormally onto a smooth surface. They express the ratio x of the splat diameter


Dp, assumed to be cylindrical, to the spherical impacting droplet diameter dpas a function of dimensionless groups, characteristics of the impact and thespreading process: the Reynolds number of the impacting particle, Re, whichquantifies the viscous dissipation of the inertia forces; the Weber number,We,which expresses the conversion of the kinetic energy into surface energy; aheat transfer parameter; and the Peclet number, Pe, used to characterize thesolidification rate. The most popular analytical model is of the one proposedby Madjeski [207] who has attempted to include viscous force, surface tensionand crystallization kinetics. Simplifying the calculation by assuming spreadingis completed before solidification becomes significant and the surface-tensioneffects are negligible (We 4 100 which is true at least at the beginning of theflattening process where We can reach 10,000 at impact), it comes:

z ¼ 1:2941 Reð Þ0:2 (23)

where Re ¼ ðrpvpdp=mpÞThis expression highlights the importance of the particle velocity and

viscosity at impact.However, it is valid only for splats with disk shapes which are observed

only for substrates preheated over a certain temperature, called transitiontemperature [192]. Otherwise, splats are extensively fingered and other ex-pressions of Eq. (23) have been proposed [191], where the constant is smaller,

α

surfacechemistry

Tp

oxide layer

Vp

substrate

FIG.57. Major parameters controlling splat formation.


but most of them keeping the 0.2 exponent of Re. In this case, the splatdiameter Dp is a mean equivalent diameter of the fingered splat, very oftenfingers being neglected because they represent a very small quantity of matter.

2. Solidification (Analytical Models)

Here again, calculations and measurements were made for particle im-pacting normally to smooth substrates. As soon as solidification starts be-fore flattening is completed, the flattening process is drastically modified.

a. Cooling Rate. The cooling of the flattening droplet is mainly due to theheat conduction to the substrate or the previously deposited layers. The CRhas been predicted using analytical or 1-D heat transfer models (which arejustified for typical splat dimensions of about 100 mm in diameter against1 mm in thickness). The CR depends on the quality of the contact betweenthe splat and the underlying material and on latent heat release [208–212].

Firstly, a very simple model [213,214] gives the cooling velocity as follows:

vs ¼hTp

DHmr(24)

where DHm is the latent heat of solidification, Tp the particle temperature,r the specific mass of the material and h the heat transfer coefficient at theinterface. This expression shows that h has a drastic effect on the solidi-fication rate at the interface. Solidification generally starts at the end of theflattening process [213–217]; i.e., when the surface energy becomes impor-tant. If the contact is uniform with the underlying substrate, h can beexpressed in terms of the wetting angle as follows:

h ¼ 0:5 hcð1þ cosyÞ (25)

where hc is the heat transfer coefficient for perfect wetting (y ¼ 0). Instead ofconsidering h, the thermal constant resistance Rth ¼ 1/h is often used. Rth

makes it possible to quantify the quality of contact between the splat and theunderlying layer. A perfect contact corresponds to Rth � 10�8 m2KW�1

while a poor contact corresponds to Rth � 10�6 m2KW�1 or more.Secondly, the latent heat of fusion is released during phase transition. This

provides a heat source that needs to be compared with other sources. TheStephan number is a measure of the solidification time. It is defined as the ratioof the sensible to the latent heatNSte

s ¼ cps (Tm – Ts)/DHm where cps is the heatcapacitance of the solid phase, DHm the latent heat of fusion, Tm the meltingtemperature and Ts the temperature of the substrate. It is also sometimesdefined for the liquid phase as NSte

l ¼ cpl (Tp – Tm)/DHm where cpl is the heatcapacitance of the liquid phase, and Tp the impacting droplet temperature.


Thirdly, the ratio of splat to substrate thermal diffusivities characterizesthe CR, especially for a perfect contact.

Lastly, a great effect is linked to splat thickness. The CR decreases dras-tically when the splat thickness increases. Therefore, CR will be much lowerwith subsonic RF plasma-deposited splats than with d.c. plasma-depositedsplats. Also, CR should be higher at the periphery of the flattening droplet,provided that the contact is perfect. At the splat rim, where the contactpressure is very low and the surface tension is at its maximum, splat curlingoccurs and the contact of the flattening particle with the substrate is verypoor, thereby inducing a slower liquid cooling through the already solidifiedpart of the splat and a rounded rim due to the surface tension [191]. Outsidethe rim area within the splat, the contact splat–substrate is good and splatthickness is lower. Therefore, in principle, solidification would start there.However, in this area [206] the contact pressure may not be sufficient toovercome the pressure resulting from flash evaporation of condensates oradsorbates at the surface and the disturbance of the spreading process byasperities and surface defects, resulting in a high local thermal contact re-sistance. Thus, solidification will start in an area where the flattening dropletis thinner but also where the impact pressure is not too low.

b. Solidification Process. According to the high CRs achieved in plasmaspraying (up to 109K s�1 at the very beginning of the cooling process), theflattening droplet undergoes hyper-cooling, generally resulting in heteroge-neous nucleation starting at contact with the underlying material[212,218–220]. The rate of nucleation and crystallization can be calculatedfrom the classic theory of nucleation assuming a steady-state process. Thecritical free-energy change required to reach the critical size of nuclei islinked to the contact angle y that affects the lowering of the activationenergy required for nucleation. Reciprocally, the experimentally observedsize of the columns within splats, allows the determination of the values ofy and CRs.

Many works were devoted to the impact of millimeter-sized and microm-eter-sized droplets. These works have demonstrated the existence of a tran-sition temperature (Tt) below which splats are extremely finger-like shapedand over which they are disk-like shaped. This transition temperature de-pends on numerous factors but is related to the natures of the substrate andthe splat. Whatever the considered substrate–droplet pair, the transitiontemperatures is always low compared to the material melting temperatures.Thus, several explanations (see the review of Fauchais et al. [192] and papersof Fukumoto et al. [221,222]) have been proposed to explain such values ofTt, among which: (i) the modification of the substrate surface wettability,(ii) the desorption of adsorbates and condensates and (iii) the solidification


mechanisms. Splat CR measurements under plasma spray conditions, to ourknowledge, have been performed at the University of Limoges, France[212,223–230] for zirconia particles, and at IMI, Boucherville, Canada[231,232] for Mo particles. For example, for zirconia particles (22–45 mm),impacting on polished (Rao0.05 mm) 304L stainless steel substrate, the CRswere between 4 and 10 times higher when the substrate was preheated at573K compared to 348K below the transition temperature, as shown inFig. 58. The disk-shaped morphology obtained when Ts 4Tl exhibited ex-cellent contact with the substrate (more than 80% of this surface) except inthe splat rim. All over the sprayed spot, the about 5000 collected splatsexhibited a distribution close to disk shape as indicated by shape factormeasurement (Fig. 59).

50 100 150 200 250 300

particle velocity [m.s-1]

cool

ing

rate

1000

800

600

400

200

0

Ts > Tt

Ts < Tt

2000 2500 3000 3500 4000 4500 5000

particle temperature [K]

cool

ing

rate

1000

800

600

400

200

0

Ts > Tt

Ts < Tt

FIG.58. Evolution of the cooling rate of zirconia particles (20–50mm) impacting on

a stainless steel (304L) substrate preheated either at 573K (Ts 4 Tt) or at 348K (TsoTt) with

(a) Particle velocity and (b) Particle temperature [230].


The corresponding columnar structure exhibited regular column sizes inthe 100 nm range. A contrario, splats collected on substrates with TsoTl

presented only a small contact area, in the 10–20% range, with much biggergrain sizes in the area of poor contact [196]. Similar results, at least for the sizeof the columnar structure, were obtained recently [233] for zirconia splats.

The CRs of zirconia droplets were also studied when sprayed onto a par-tially stabilized zirconia substrate, the roughness of which being slightly higherthan that of a stainless steel substrate (Ra ¼ 0.2mm against 0.05mm). The CR,for a particle impacting with about the same velocity, temperature and di-ameter on stainless steel and zirconia substrates preheated at 600K (that is,over Tt for both substrates) was 113� 106K s�1 considering the partiallystabilized zirconia (PSZ) substrate instead of 643� 106K s�1 considering thestainless steel substrate. In both cases, splats exhibited perfect disk shapes.When performing the calculation of the CR of a splat on both substrates,assuming a perfect thermal contact resistance (Rt ¼ 10�8m2KW�1), thedifference in CRs was explained by the thermal diffusivity values, a, of bothsubstrates (aPSZ ¼ 0.7� 10�6m2 s�1 against aSS ¼ 5.2� 10�6m2 s�1) [212].

0 0.2 0.4 0.6 0.8 1

60

40

20

0

shape factor [-]

perc

enta

ge [

%]

average = 0.93

standard deviation = 0.10

TS = 300 °Cd = 92 ±28 µm

(a)

(b)

100 µm

FIG.59. (a) Observation by optical microscopy of zirconia splats collected on a smooth

Rao0.05mm warm (Ts� 3001C) stainless steel substrate. (b) Shape factor distribution of 5000

splats from image analysis [196].


3. Flattening and Solidification (Numerical Models)

As already underlined, the substrate–droplet couple plays a key role inthese phenomena. Different studies [218,234–238] assume a 2-D geometry anda perfect contact between splat and substrate (Rth ¼ 10�8m2KW�1). Nev-ertheless, the simultaneous heat interaction of the droplet with the substrate isnot taken into account. The most advanced models solve the flow equationsby considering convective, viscous and surface tension processes. They allowthe prediction of the effect of particle parameters on splat formation. Theprojected trends agree well with the analytical models. However, they cannotpredict the breakup or splashing of the flattening particle onto the surface.

In addition, these models enable the calculation of the contact pressuretime-evolution for different flattening particle radii [239,240]. The predic-tions of the analytical models are also confirmed. The low contact pressureat the interface for a reduced radius Z ¼ 2r/dp 4 2 is not necessarily suffi-cient to overcome the gas and capillary pressures resulting in a poor contact,especially at the splat periphery.

The most sophisticated models involving 3-D flow, cooling of the flat-tening particle with a thermal contact resistance at the splat–substrate in-terface, flattening splashing based on the Rayleigh–Taylor instability theory,and impact of a molten droplet on a previously deposited splat, have beendeveloped by Mostaghimi and his co-workers [220,241–247]. Such calcula-tions show the drastic influence of the beginning of solidification relative tothe droplet flattening stage on the flattening splashing phenomenon as wellas the effect of the substrate roughness, represented by the already depositsplats. The solidification process is controlled by the thermal contact re-sistance. Figure 60 represents the simulation carried out by Pasandideh –Faret al. [220] of the impact of a nickel droplet (60 mm in diameter) impacting at48m s�1 and a uniform temperature 600K higher than its melting temper-ature onto a polished stainless steel substrate preheated at 563K (over thetransition temperature). The thermal contact resistance between the splatand substrate was assumed to be Rth ¼ 10�8m2KW�1. The droplet defor-mation is already started 0.15 ms after impact (Fig. 60 (a)); after 0.8 ms theparticle has started to deform in its periphery and solidification is starting atits bottom after 0.7 ms (Fig. 60 (b)). Solidification, which propagationvelocity is about 1m s�1 cannot start before the flow velocity close to thesubstrate is drastically reduced (for a particle impacting at 200m s�1, theflow velocity parallel to the substrate can reach 100m s�1 at the beginning ofthe flattening stage). When considering the configuration depicted in theimages corresponding to 1.1 and 1.4 ms (Fig. 60 (b)) the liquid materialsplashing occurs because at the top of the flattening particle the liquid flowvelocity is still a few meters per second and then spread on the top of the


solid layer and jetted out from its periphery. As the surface of the solidifiedlayer was not smooth, the particle break-up was not symmetric. When in-creasing the thermal contact resistance, solidification was delayed and lessparticle break-up and splashing occurred. According to the assumptions ofPasandideh-Fard et al. [220], splashing is mainly observed when the thermalcontact resistance Rth is close to zero (� 10�8m2KW�1). A slower solid-ification rate, when Rth is on the order of 10�6m2KW�1, results in muchless breaking or flattening splashing. However, these results are at variancewith experiments. Calculation of the thermal contact resistance Rth startingfrom the measured CR of a zirconia splat on a stainless substrate [230] haveshown that on a substrate preheated over the transition temperature,Rth ¼ 10�8m2KW�1 whereas for a preheating below the transition tem-perature, Rth ¼ 10�6m2KW�1. Similar calculations concerning the zirconiasplat cooling on a stainless steel substrate preheated over Tt showed that alldisk-shaped splats corresponded to Rt � 10�8m2KW�1, while all fingeredsplats (TsoTt) corresponded to Rt� 10�6m2KW�1. Such results are incontradiction with the calculations performed by Mostaghimi et al.

FIG.60. Simulation of a nickel particle impacting onto a stainless steel substrate at 563K.

(a) Flattening and splashing phenomena. (b) Cross section of the flattening particle and its

solidification [220].


[220,246,247]. In a recent paper [220], where they have studied both nu-merically and experimentally the impact of Ni particles on stainless steel,they found, from modeling, that splashing occurred if Rt ¼ 10�8m2KW�1

while disk-shaped splats were obtained for Rt � 10�6m2KW�1. In thelatter case, solidification only occurs when flattening is completed. However,they recognized [220] that when spraying alumina on stainless steel, splash-ing that occurs for TsoTt is not predicted by their model.

E. TRANSITION TEMPERATURE WHEN PREHEATING THE SUBSTRATE

As already underlined, below a given substrate temperature depending onsubstrate and impacting droplet materials, splats are extensively fingeredwhile above this temperature, they are almost disk shaped. The most in-teresting feature lies in the drastic change from fingered-splat pattern tothe almost disk-shaped one at a certain narrow temperature range when thesubstrate temperature increases. The transition temperature Tt at which thesplat shape changes was defined and introduced by Fukumoto et al. [248].The fact that the splat pattern varies with the substrate temperature hasbeen recognized by many investigators such as Houben [249] for example.However, this transition temperature has not been well understood until therecent years where the change in the splat pattern near the transition tem-perature has become a great concern.

Many authors have shown that, when disk-shaped splats were obtainedon a smooth substrate (Ra� 0.05 mm) preheated at temperature Ts higherthan the transition temperature Tt, the adhesion of coatings of the samematerial sprayed on the same rough substrate also preheated at Ts was 2–5times higher than that sprayed on a substrate preheated at TsoTt

[205,250–253]. Figure 61 shows the effect of substrate temperature on thecoating adhesion. The adhesion strength changes progressively with subst-rate temperature. Its dependence on substrate temperature correspondsquite well to that of the splat shape on a smooth substrate. Thus, inves-tigation of the flattening mechanism of the sprayed particles is significantlymeaningful for the practical use of thermal spray coatings.

Preheating a metallic substrate over the transition temperature Tt mayresult in the formation of an oxide layer at the substrate surface. Dependingon the oxide formed (especially when it grows fast as iron oxides), it canresult in the formation of jagged splats and, correlatively, a decrease incoating adhesion [196]. Similar results were obtained when spraying anoxide onto an oxide substrate [252]. Fukumoto [254] has gathered the tran-sition temperature values of different materials sprayed by APS or HVOFon 304L stainless steel substrate, Table VI. It can be remarked that oxidesexhibit the lowest transition temperatures.


100

80

60

40

20

0

100

80

60

40

20

0300 400 500 600 700 800

substrate temperature [K]

frac

tion

of

disk

spl

at [

%]

adhe

sion

str

engt

h [M

Pa]

150 µm

250 µm

FIG.61. Variation of the adhesive strength of the coating and of the fraction of disk-

shaped splats with substrate temperature (sprayed Ni particles with a size distribution of

10–44mm; stainless steel AISI304 substrate) [250].

TABLE VI

TRANSITION TEMPERATURES FOR DIFFERENT POWDER MATERIALS SPRAYED BY APS OR HVOF ON

304L STAINLESS SUBSTRATE [254]

Powder material Spraying technique Transition temperature (K)

Ni APS 610

Mo – 474

Cu – 394

Cr – 387

Cu–30Zn – 505

Cu–30Zn HVOF 455

Ni – 560

Ni–5Al – 440

Ni–10Cr – 400

Ni–20Cr – 360

Cr – 345

Al2O3 APS 318

TiO2 – 350

YSZ – 345


A question which is nevertheless still pending is related to the mechanismscontrolling the transition temperature. The answer is not at all simple be-cause it depends on the surface of the substrate, in particular in terms ofoxide layer composition, thickness, roughness, skewness. Up to now, thefollowing phenomena have been considered:

� the desorption of adsorbates and condensates,� the specific properties of the substrate,� the wetting,� the surface roughness,� the surface crystalline structure.

1. Desorption of Adsorbates and Condensates

One probable explanation concerning the transition temperature dealswith the desorption of adsorbates and condensates at the substrate surface,wetting of the substrate by the liquid material, and solidification effects[202,226,250–253,256–271].

The flattening behavior and the grain or column sizes of the resultingsplat have been observed systematically for many particle/substrate materialcombinations [270,272–286]. Evaporable substances (xylene, glycol, andglycerol) with different boiling points (417, 471, and 573K, respectively)were brushed on a polished (Rao0.05 m) stainless steel substrate [275,276],and the preheating of the substrate was used to control the presenceof organic substances on the substrate surface. The plasma-sprayedmaterials were aluminum (Al), nickel (Ni), copper (Cu), alumina andmolybdenum (Mo).

The results show that, except for Mo which effusivity is significantlygreater than those of substrates, the presence of an evaporable substance onthe surface affects significantly the flattening process. As soon as the subst-rate is preheated 50K over the boiling point temperature of the organic film,which also corresponds for the studied system to a substrate temperatureover Tt, disk-shaped splats are obtained. Splats are extensively fingeredbelow the evaporation temperature.

With Mo, the substrate preheating has little influence and disk-shapedsplats are never obtained, as already mentioned [277]. It is thus believed thatthe evaporation of the organic layer upon impact of the molten dropletinduces the flattening splashing, probably by changing the flow directions inthe periphery of the flattening droplet [275,276].

The transition temperature over which splats are disk shaped was alsoobserved in low-pressure falling droplet experiments [263,264,278]. For ex-ample, Fukumoto et al. have shown that with Cu [263] or Ni [264] dropletsof 2mm in diameter impacting onto a 304L stainless steel substrate, the


transition temperature depends also on a critical chamber pressure pt. Belowpt, the transition does not depend anymore on substrate temperature asillustrated in Fig. 62. At atmospheric pressure over 500K, as already men-tioned, the transition to disk-shaped splats takes place and over 600K, thecolumn sizes are rather small. Once the substrate has been preheated eitherin air or soft vacuum, the column sizes are rather small (point 3 and 4 inFig. 62). When the substrate is left at room temperature at a pressure of10 Pa, the column size is small even at 300K and decreases a little when thesubstrate temperature increases. Thus, it can be assumed that desorption ofadsorbates and condensates promotes the occurrence of disk-shaped splats[263,264,278]. This assumption was also made by Pershin et al. [253] whenconsidering the impact of alumina particles plasma sprayed on stainless steelor glass substrates where temperatures were varied in the range 20–5001C.

2. Specific Properties of the Substrate

The transition temperature can also be modified by additives to thesubstrate material, modifying the oxide composition at its surface. This hasbeen illustrated for a nickel substrate doped with Al or Cr [230] onto whichstainless steel was sprayed by HVOF. On the alumina PECVD-coated

30

20

10

0300 400 500 600 700

substrate temperature [K]

grai

n si

ze [

µm]

(1)

(2)

(3)

(4)

disk-splat

splash-splat

(1): room temperature @ atmospheric pressure

(2): room temperature under low pressure (10 Pa)

(3): 673 K (preheated in air)

(4): 673 K (preheated in soft vacuum)

FIG.62. Grain size of a nickel splat under several conditions [264].


substrate, the plasma sprayed alumina coating adhesion is excellent even ifsplats exhibit lace or ring structure. Such a structure might be due to theevaporation of gases entrapped in the PECVD film and escaping throughthe flattening alumina droplet [254]. A possible explanation may also lie inthe wetting properties, but they cannot be measured. To check the influenceof the substrate thermal conductivity, Ni particles in the millimeter sizerange were sprayed on different substrates covered with the same PVD filmof thickness lower than 1 mm. Results of Fukumoto and Huang [259]showed that there is a tendency for the transition temperature to be higherwhen the thermal conductivity of the substrate increases.

3. Droplet– Substrate Surface Wetting

The flattening behavior of Ni particles thermally sprayed (in the size rangeof 10–44 mm) was investigated on AISI304 steel substrate coated with PVDthin films of various metals to assess the effect of the wetting at particle/substrate interface. The transition temperature of metals not very sensitiveto oxidation (such as gold and Ni) is low compared with that of morereactive metals such as aluminum (Al) and titanium (Ti). It can be pointedout that the wetting of a liquid metal relative to a solid oxide depends on thethermodynamics of the oxide material, that is, the more thermodynamicallyunstable the oxide, the easier the wetting [273,274].

The flattening behavior of plasma-sprayed oxide particles was also in-vestigated together with the effect of PVD film material on splat morphol-ogy. It is well known that the standard free energy of formation of the oxidelayer from the metal can be closely related to the static wetting of the moltenmetal on the oxide substrate [279]. Tanaka and Fukumoto [256] have as-sumed that such a relation was applicable to dynamic wetting. For thermallysprayed alumina particles, the smaller standard free energy of the metalcorresponds to the lower transition temperature. The fact that the tendencyis less than that obtained with Ni particles is obviously due to the differencein materials. Anyhow, it is confirmed that a better wettability promotes theoccurrence of disk-shaped splats.

The morphology of the resulting splat was observed for d.c. plasma-sprayed alumina particles impinging (below the transition temperature ofgold and close to that of stainless steel) onto the boundary between a gold-coated and a stainless steel substrate surface. The substrate temperature was400K. A half-splashed splat was observed on the gold-coated substrate,while it was half disk shaped on the substrate [269]. Furthermore, on thenon-coated surface, the disk splat was probably formed without any initialsolidification of the splat, as shown by the corresponding central part on thecoated substrate [269]. This fact clearly indicates that initial solidification is


not always a necessary condition for flattening splashing, and the wettingaffects flattening at least as much as solidification.

A linear relationship between the thermal conductivity and transitiontemperature can be noted on PVD-coated and non-coated substrates madeof AISI304 stainless steel (Fig. 63). The transition temperature decreaseswith the increase in particle thermal conductivity. Moreover, the slope of thecurve is steeper when the transition temperature is higher. Since the interfacewettability, temperature and viscosity of particles were different for all ma-terial couples, the linear relationship between Tt and particle thermal con-ductivity could be observed for each material. This linear relationshipindicates that the flattening of oxide particles could be linked to the particlethermal conductivity. In addition, the gold-coated substrate exhibits theworst wetting with respect to ceramic particles; thus, the higher transitiontemperature corresponds to the worst wetting at the splat/substrate inter-face. Therefore, an initial solidified layer at the bottom surface of the par-ticle can exist even for ceramic particles. Thus, this solidified layer mustaffect the spreading of the liquid material on the surface. The roughness ofthe surface (in the nm range) modifies the surface tension and thus thewetting which can be expressed as follows:

cosy ¼ n cosy0 (26)

600

550

500

450

400

350

3001.5 2.5 3.5 4.5 5.5

particle thermal conductivity [W.m-1.K-1]

tran

siti

on t

empe

ratu

re [

K]

Au-coated substrate

Al-coated substrate

uncoated substrate

FIG.63. Variation of the transition temperature with the themal conductivity of impacting

particle [268].


where y0 is the wetting angle on a perfect smooth surface and n a quantityhigher than unity.

On good wetting, cosy0 40 and y is smaller than y0. However, the questionwhich rises is how to control the substrate roughness? Of course, to reach thetransition temperature preheating is mandatory and then the surface rough-ness of the substrate is modified. Table VII presents different average surfaceroughness obtained after a polishing followed or not by a heat treatment.

The interesting work of Fukumoto et al. [248] studying Cr and Ni splatsd.c. plasma sprayed onto a 304L stainless steel substrate has brought a newinsight on that point. They have shown that the composition of the oxide atthe substrate surface was the same after polishing and heat treatment. Onlythe oxide thickness increases with the heating (from 2 to 12 nm, about). Thesplats were disk-shaped on the preheated substrates and extensively fingeredon the non-preheated substrate. Even when letting the preheated substratecool down and spraying immediately after, splats were still disk-shapedwhich means that the adsorption/desorption of adsorbates and condensatesis not always the dominant phenomenon for the disk-shaped splats or thatthe absorption of condensates and adsorbates is much longer than thesubstrate cooling time. The substrate average surface roughness Ra in-creased from 0.7 to 2.7 nm (and the Rt from 5.73 to 21.2 nm, correspond-ingly) while the oxide composition was unchanged. But the most significantparameter that evolved was the skewness Sk defined as follows:

Sk ¼ 1

s3

Z þ1

�1ðz�mÞ3fðzÞdz (27)

where f(z) is the distribution of the surface heights [280], z the surfaceheight, m the average value of the surface height l and the sampling length.

TABLE VII

AVERAGE SURFACE ROUGHNESS OF SUBSTRATES AFTER DIFFERENT MECHANICAL AND/OR HEAT

TREATMENTS

Substrate Surfacing Heating Ra (nm) Reference

Aluminum Polished None 5 [264]

Polished In air at 673K 13

Polished In vacuum at 673K 13

Stainless steel (304L) Polished None 0.9 [264]

Polished In air at 673K 3.2

Polished In vacuum at 673K 5.5

Grounded In air at 673K 50 [212]

Electropolished In air at 673K 400 [212]


The skewness was – 0.256 for the as-polished substrate against +0.652 forthe preheated one (i.e., shifting from more undercuts, negative Sk, to morepeaks, positive Sk). This work shows that the flattening behavior, probablythrough the better wetting, is significantly affected by the surface roughnesschange at the nanometer scale through the skewness. Upon impact, it is im-portant of course that the molten material penetrates within the surface un-dercuts or pores. A rough estimation of the condition of the molten materialpenetration within the surface undercuts or pores can be established. It consistsof comparing the stagnation pressure in an impacting droplet, which drivesliquid into the substrate undercuts or pores, and the surface tension force thatrestrains the liquid. Assuming that the pores radius r is equivalent to theroughness r � Ra, the condition for a pore to be filled with liquid is as follows:

Ra44srV2

p

(28)

For example, with alumina particles impacting at 2800K and 200ms�1,Ra425nm, which is the case with FeOx oxide.

4. Wetting or Desorption?

More recently, Cedelle [205,281] has performed a systematic study of theimpact of micrometer-sized zirconia particles on smooth stainless steel andzirconia substrates at room temperature or preheated over the transitiontemperature. The same study was carried out also considering the impact ofmillimeter-sized particles on smooth stainless steel substrates. When pre-heating stainless steel substrates in ambient atmosphere, an oxide layer at itssurface develops and changes its morphology (Fig. 64). The surface rough-ness quantified via the SA parameter increases hence with the preheatingtemperature and surface skewness Sk increases also from 0 (i.e., normalpeak-to-valley distribution) to 0.9 (i.e., more peaks than valleys).

After studying the impact of Cu, Ni and Cr millimeter-sized particles onpreheated at 673K mirror polished AISI 304 stainless steel plates, Fuku-moto et al. [282] have attributed the improvement of the flattening time to abetter wettability with the positive Sk resulting from the preheating. The netresults are shown in Table VIII displaying the evolution of the flatteningvelocity and the CR for millimeter-sized nickel particles and micrometer-sized zirconia particles. In both cases, both the flattening time and CR areincreased as soon as the surface skewness changes. Since no modificationoccurs when polishing stainless steel with a SA value four times higher but aSk value close to zero, the change in CR and flattening time can be attrib-uted to the Sk positive value. Such a result was confirmed implementing


static wettability experiments, the wettability of copper for example on astainless steel substrate increasing when Sk becomes positive (i.e., morepeaks) [281]. This better wettability increases the liquid contact with thepeaks, as schematically depicted in Fig. 65.

However, the problem of adsorbate/condensate desorption during par-ticle flattening cannot be excluded from the mechanisms analysis. To em-phasize its role, two experiments were achieved as follows: one consisting inspraying zirconia particles on a zirconia substrate for which preheating doesnot modify the surface topology in a first approximation (i.e., Sk close tozero with or without preheating) and another one consisting in sprayingzirconia on preheated stainless steel but which was cooled down to roomtemperature (i.e., positive Sk value but substrate proved to have adsorbatesand condensates at its surface). Results are summarized in Table IX.

The lower values of CRs with zirconia substrate against stainless steel aredue to the lower diffusivity of the substrate.

TABLE VIII

CHARACTERISTIC FLATTENING TIMES AND COOLING RATES ON STAINLESS STEEL SUBSTRATES AT

ROOM TEMPERATURE OR PREHEATED AT 673K [281]

Substrate temperature (K) Room temperature Preheated 673K

ZrO2, 30mm, Tf � 3000K Flattening time (ms) 2–5 1–2

Cooling rate (K s�1) o40� 106 480� 106

Ni–� 1mm, Tf � 1850K Flattening time (ms) 3.5 1.5

Cooling rate (K s�1) o20� 103 460� 103

Tf, splat temperature at the end of flattening.

FIG.64. Stainless steel substrate surface morphology measured by AFM. (a) At room

temperature: SA ¼ 0.6 nm, Sk ¼ 0–0.1. (b) Preheated at 673K in ambient atmosphere:

SA ¼ 3.5 nm, Sk ¼ 0.9 [281].


These results clearly demonstrate that with the zirconia substrate, theimprovement of the CR with preheating is due to desorption of adsorbatesand condensates. Desorption also plays a role when considering stainlesssteel substrate for which the CR is between those obtained at room tem-perature and 673K. The positive Sk increases of course the wettability asshown by the flattening time evolution but adsorbates and condensates re-duce the thermal contact. Nevertheless, more experiments are still necessaryto further clarify these results.

F. MODELS AND MEASUREMENTS ON ROUGH ORTHOGONAL SUBSTRATES

1. Models

Approximate equations describing the time evolution of the splat thick-ness and radius during the flattening process and taking into account thesurface roughness have been proposed in the literature [283]. It is assumedthat roughness increases the shear stress due to friction between the flat-tening droplet and rough surface. A mathematical model including differentgeometrical asperities has been developed by Fukanuma [284] and recently

FIG.65. Schematic of the contact between the lamella and the surface asperities at a

nanoscale. (a) Poor wettability. (b) Good wettability [281].

TABLE IX

CHARACTERISTIC FLATTENING TIMES AND COOLING RATES OF ZIRCONIA PARTICLES (30mM IN

DIAMETER, TF � 3000K) ON ZIRCONIA AND STAINLESS STEEL SUBSTRATES [281]

Substrate ZrO2 Stainless steel

Room temperature 673K Room temperature 673K

Sk � 0 � 0 � 0 � 1

Flattening time (ms) 6–8 3–5 2–5 1–2

Cooling rate (K s�1) 10–20� 106 40� 106 o40� 106 50� 106oRo70� 106

RT, Room temperature.


improved [285]. The main problem here is the estimation of the roughnessrelative to the splat thickness. A fractal dimension indicator has been pro-posed [286]. These models show that the surface roughness promotessplashing at impact and during flattening. Splats are extensively distorted.As they are thicker (up to three times) than those obtained on smoothsubstrates, their CR is decreased. Recently, Raessi et al. [287] have adaptedthe numerical models developed for the impact of droplets on smoothsubstrates [242,288] to rough ones. The surface is patterned by cubes whichare regularly spaced at an interval twice their size. The splat shape changeswith the increasing roughness which modifies solidification.

2. Measurements

In most cases, the roughness is achieved by grit blasting resulting in av-erage surface roughness Ra values between 0.5 and about 10 mm. It has to bekept in mind that Rt (distance between the highest peak and the deepestundercut) is about eight times Ra and that this is Rt which has be comparedwith the splat diameter. When comparing to a smooth substrate, the be-havior will be completely different. The spreading of the droplet is limitedby surface irregularities, resulting in smaller and thicker splats, as well as animportant flattening splashing behavior and a poorer contact than onsmooth substrates. It is also impossible to analyze the oxide layer formed atthe rough substrate surface.

Studies of splats collected on roughened surfaces are rather scarce. Theyare devoted to Mo splats sprayed onto glass or Mo substrates [232], alumina[225] and zirconia splats on stainless steel substrates [212,205,228,230]. Splatmorphologies (flattening degree and shape factor) have been determinedby SEM. Splat CRs have been measured by fast pyrometry and the ori-entation of the columnar growth has been determined by TEM. All theresults are in good agreement. For example, compared with results obtainedon smooth substrates, splats are more extensively fingered when formedon warm substrates (Ts 4Tt) and are completely exploded on cold ones[212,230]. Another feature is that the splat flattening degree decreaseswith an increase in substrate roughness as depicted in Fig. 66 (a) and (b)obtained with zirconia splats on stainless steel and Mo on glass, respectively.

Finally, the splat CR decreases when roughness increases (Fig. 67). This isin good agreement with the theory, i.e., the CR increases when the splatthickness decreases and, thus, it varies with the inverse of the flatteningdegree. It is worth noting that, if on a smooth stainless steel substrate (Ra �50 nm) at 573K, the CR reaches 643� 106K s�1, it drops to 133� 106K s�1

when Ra � 640 nm, but it is still 123� 106K s�1 when Ra � 9 mm. Asimilar result is observed on a zirconia substrate: CR equals 113� 106K s�1


for Ra ¼ 0.2 mm whereas is equal 86� 106K s�1 for Ra ¼ 4 mm. Since thethickness of splats increases with Ra, these results, which would be worthyof confirmation, seem to indicate a better local contact on rough warmsubstrates. The observation of zirconia splats on a grooved stainless steelsubstrate [233] have indeed shown that curved columnar grains are shapedby the local direction of heat flow. As well the interfacial cracks developed atthe relatively smooth part of the splat surface/interface do not develop in therough part where interlocking strengthens the interface. At the oppositeend of behavior, roughness can generate shrinkage-induced failure of theceramic/metal interface.

G. IMPACTS ON INCLINED SUBSTRATES

1. Models

Models for off-normal impacts have been developed for smooth surfaces.They generally neglect solidification that is assumed to start when flattening

5.1

4.7

4.3

3.9

3.50 500 1000 1500

particle dimensionless Reynold number [-]

flat

teni

ng d

egre

e [-

] Ra = 0.05

Ra = 0.4

Ra = 9

0 2 4 10

flattening degree [-]

surf

ace

roug

hnes

s

smooth

grit-blasted (fine)

grit-blasted (coarse)

coating surface

6 8

FIG.66. Flattening degree of (a) Zirconia splats on stainless steel substrates for different

roughnesses [230] and (b) Mo splats on Mo from smooth to coating surface with two grit-

blasted substrates (fine and coarse) in between [232].


is completed [206,289–294]. Expressions of the elongation factor (EF; ratioof the long length to the short one of the splat assumed to be elliptical) havebeen established. This ratio is independent of the splat size and depends onlyon the spray angle j [290–292].

Other theories relate the average splat thickness to a dimensionlessReynolds number, NRe, in which the considered velocity is the normalcomponent of np (nN ¼ np� cos j, where j is the angle between the normalto the substrate and particle trajectory: nN ¼ np when the substrate is or-thogonal to np:j ¼ 0). As a matter of fact, the splat thickness varies alongthe longer axis of the ellipse and is thicker in the liquid material flow di-rection. Thus, the onset of solidification occurs most likely in the thinnerpart of the splat. It will promote horizontal splashing in the liquid flowdirection, especially when j increases. Experimentally, it has been shown

0

flattening degree [-]

cool

ing

rate

[K

.µs-1

]

0 4 8 10

cooling rate [K.µs-1]

surf

ace

roug

hnes

s smooth

grit-blasted (fine)

grit-blasted (coarse)

coating surface

2 10

200

150

100

50

ZrO2/metal; Ra = 0.4 µm

ZrO2/ZrO2; Ra = 0.2 µm

ZrO2/ZrO2; Ra = 4.0 µm

12 142 6

4 6 8

FIG.67. (a) Evolution of the cooling rate with flattening degree for a stainless steel

substrate and two zirconia substrates, which temperature is over the transition temperature

and roughness are different [230]. (b) Evolution of cooling time with surface roughness for Mo

particles onto Mo substrates [232].


that the effect of the spray angle on coating properties is weak as long asj4451. Above that value coating porosity and roughness increase whilemechanical properties decrease [291,295].

2. Measurements

On stainless steel polished (Rao0.1 mm) substrates preheated over thetransition temperature, when the spray angle increases from 01 to 751, splatshave an elliptical shape, the ratio of the long to the short axes increasingwhen the spray angle increases [223,294,295]. For different materials (alu-mina, zirconia, titania, Al, Ni and Cu), the relationship between the longand short axes shows a strong linearity over a wide range of splat sizes. Thisobservation implies that the EF does not depend on particle diameter andimpact velocity but only on spray angle [294]. The splat thickness increasesslightly along the inclined surface. The elliptical shape can only be under-stood if the beginning of solidification occurs before flattening is completed.As soon as the spray angle is higher than 301, flattening splashing along thesubstrate occurs in the direction of the molten material flow; i.e., where thesplat is thicker [223], and its importance increases with the spray angle. Atan impact angle of 301, the contact area of a zirconia splat over a stainlesssteel substrate exhibits no defects with 100% contact except in the rim.Under the same conditions, an alumina splat exhibits elongated crystals2� 4 mm2 in the direction of the molten flow, corresponding to an area ofpoor contact where heat flow must go through the already solidified area.For the whole splat, the good contact surface area represents less than 80%of the surface, excluding the rim. Compared with the same alumina splatscollected on a substrate normal to the impact direction, the column sizes aremore irregular [255]. The elliptical shape and the poor contact area areprobably related to the droplet wetting.

As soon as the substrate exhibits a Ra40.2–0.4 mm, the flattening splash-ing phenomenon becomes severe even with impact angles as low as of 301.

H. SPLASHING

Two types of splashing may occur: one just at the beginning of the impactcalled ‘‘impact splashing’’ and another one at the end of the flatteningprocess called ‘‘flattening splashing’’ [296].

1. Impact Splashing

Upon impact, the liquid droplet can rebound, deposit, or splash, at leastpartially. This splashing corresponds to the ejection of tiny droplets mostly


in the impact direction. In the following, it will be depicted as ‘‘impactsplashing’’. These phenomena are related, at least for a water or an ethanoldroplet [206,297,298], to critical values of the Sommerfeld parameter K ofthe particle at impact defined as follows:

K ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiWe

ffiffiffiffiffiffiRe

pq(29)

where We and Re are the dimensionless Weber and Reynolds numbers,respectively.

Ko3 corresponds to rebound. 3oKo58 results in deposition and K 458induces splashing.

Under plasma spray conditions, the limit between deposition and splash-ing is not so precise, but the trend is identical [203]. The measurements ofEscure et al. [203] have shown that splashing could occur at K values as lowas 20, while no splashing could occur up to K ¼ 70. This is probably linkedto an insufficient control of the surface on which particles are impacting andwhich becomes rough after the deposition of a few ten splats. Moreover,with alumina particles d.c. plasma sprayed, calculated values of K varybetween 50 and 1800 [203], which means that impact splashing is more therule than the exception.

Allen [208] has suggested that splashing may be the result of Rayleigh–Taylor instabilities that occur when a fluid accelerates into a less dense one.However, recent measurements [257,258] with fast cameras synchronizedwith the particle impact, through the measurement of its velocity, diameterand temperature prior to its impact, have shown that impact splashing oc-curs a few tens of nanoseconds after impact. This time seems to correspondwell to the wave propagation [206] at sound velocity as illustrated in Fig. 68.It has been confirmed by the measurements of Cedelle et al. [257,258] whichhave shown that the ejection of tiny droplets occurs in an angle between 451and 901 relatively to the substrate, as shown in Fig. 68. Exposure shots, 5 mseach, were taken separated by a delay of 5 ms in order to determine thevelocity of the ejected droplets (below 1 mm in diameter). For a given particleimpacting at 200m s�1 the ejected droplet velocity is between 15 and20m s�1 (Fig. 69). The droplets reach distances from the substrate (at leasttheir emitting track) up to 3mm. It means that they are out of the boundarylayer between the plasma plume and the substrate and most of them areprobably entrained by the plasma flow. This impact splashing phenomenonoccurs whatever may be the substrate temperature (below or over the tran-sition temperature) and can be observed whatever the shape of the resultingsplat: disk shape or extensively fingered.


2. Flattening Splashing

Flattening splashing occurs at the end of the flattening process and, asshown by the measurements of Cedelle et al. [257,258], corresponds todroplet ejections parallel to the substrate. If authors agree on the fact that,on smooth substrates (Rao0.05 mm) normal to the particle trajectory at atemperature below the transition temperature, Tt, splats are extensively fin-gered and disk-shaped when the substrate is over Tt, they give different

Vparticle

substrate

impact – high pressurewave front

propagation

wave expansion rupture of liquid

FIG.68. Schematic of the wave propagation at impact with the resulting impact splashing [257].

FIG.69. Impact splashing of a zirconia particle measured with a fast camera, triggered at

the moment of the particle impact and with 10 shots exposure: 5ms each and separated by a

delay of 5ms [258].


explanations about the parameters controlling this phenomenon. The ex-periments of Cedelle [258] with plasma-sprayed zirconia and millimeter-sized nickel drops (see Section VI.E.c.) have shown that Tt depends on bothsurface skewness and desorption of adsorbates and condensates. For ex-ample, Fukumoto et al. [254,282,299] have experimentally shown with ce-ramic and nickel particles plasma sprayed that the bottom surfaces ofextensively fingered splats exhibit numerous pores and rapidly solidifiedstructures for a nickel particle. It seems that the splat solidification starts atpoints unevenly distributed at the bottom of the flattening particle and theresultant solidified part affects drastically the flowing behavior of the moltenpart. On the contrary for disk-shaped splats, at substrate temperatureshigher than Tt, almost no pores can be observed with a solidification struc-ture looking quite flat and dense over more than 50–60% of the bottomsurface of splats. In the latter case, solidification occurs very likely whenflattening is almost completed. Similar observations of rapidly solidifiedmicrostructures in the bottom part of splats have been made by Safai [260],Sampath [261], Inada and Yang [262] and Bianchi et al. [196,223]. Thus, itcould be assumed that flattening splashing occurs where the splat contactwith substrate is poor (low-surface contact) which should correspond to ahigh Rth (� 10�6m2KW�1), while the disk-shaped case corresponds to arather good contact except in the rim of the splat and a low Rth

(o10�7m2KW�1). These results, as already underlined in Section 16.5.3care at variance with the model of Bussmann et al. [241].

To get a better insight of the phenomena occurring during particle flatten-ing, free-falling experiments with millimeter-sized particles, having the samePeclet and Reynolds numbers than micro-sized particles processed underplasma spray conditions, have been conducted [263,265]. Here again, thecross section of a Ni splat collected on a stainless steel substrate at roomtemperature exhibits an isotropic coarse grain structure, whereas on a high-temperature substrate, it has a fine columnar structure. The mean grain size ofthe splat obtained on a substrate at room temperature is obviously larger thanthat obtained on a high-temperature substrate. This result indicates that thesplat solidification rate on a substrate kept at room temperature is consid-erably lower than on a high-temperature substrate. Similar results wereobtained with splats of alumina or zirconia deposited onto stainless steelsubstrates [196]. The splat CR is affected by the thermal contact resistance atthe splat/substrate interface [196]. The latter controls the interface microstruc-ture of the splat. For free-falling experiments similar to that of Fukumoto,measurements of the heat transfer coefficient at the droplet/substrate interfacehave been reported by Liu [300], Hofmeister [301] and Bennett [302].

Experiments were also performed with molybdenum particles on steelsubstrate. In this case, the effusivity of Mo being higher than that of steel,


the impacting particle can melt the substrate and modify the flattening par-ticle behavior. The melting is effectively observed in the crater formed belowthe particle impact [289]. As underlined by the theory [206], the formation ofa crater modifies splat formation. However, with the increase in substratetemperature, the splat changes from highly splashed, flowerlike to relativelycontiguous morphology. This underlines, again, the importance of the tran-sition temperature. Similar results were obtained by Li et al. [303]. However,spraying Mo on a glass lamella and following the shadow of the flatteningparticle illuminated by a laser, allows understanding the fingers formation[208]. Results show that the particle initially flattens in about 2 ms afterimpact to reach a 250–300 mm equivalent diameter. At that moment, thethickness of the liquid metal sheet is less than 1 mm. Once the particle hasreached its maximum size, its surface area decreases by a factor 4 in 2–3 ms.The decrease of the particle surface after the initial flattening indicates thatthe decrease of the particle surface area corresponds to a segmentation ofthe thin metal film in different parts, followed by a contraction of the sur-face of each segment. However, to our knowledge, this type of finger for-mation has only been observed for molybdenum particles.

Another phenomenon can also promote flattening splashing. It occurs forexample when spraying oxides at stand-off distances up to 150mm, leavinga sufficient time for the particle to cool down and form a solid crust aroundthe molten core. Such a crust can also be obtained when using an air barrier,to reduce the heat flux from the plasma jet, which cools down the particlesurface and promotes the crust formation. Upon impact on a smoothsubstrate preheated over the transition temperature, the crust explosionpromotes splashing [304].

I. PARAMETERS CONTROLLING THE PARTICLE FLATTENING

1. Particle Temperature

In plasma spraying of fully or partially molten particles, contrarily towater or fuel droplets which have been extensively studied, the parameterscontrolling the particle flattening vary drastically with temperature. If theevolutions of the surface tension s as well as the specific mass r are almostlinear with T (s ¼ s0 – aT and r ¼ r0 – bT), the viscosity m varies drasti-cally (m ¼ m0exp(E/kT)). Thus, its importance in the flattening degree x(see Eq. (23) will be drastic as well in the liquid flow ability after impact.Some authors have assumed that a too high temperature of the impactingparticle promotes splashing even over the transition temperature. However,it has not been observed for zirconia particles impacting at 4300K andforming disk-shaped splats on substrates over Tt [196,223].


Temperatures close to or over the melting temperature will promote the in-flight particle reactions with its surrounding atmosphere. In air atmosphere,for example metals and alloys are oxidized while nitrides and carbides aredecomposed or partially decomposed. Spraying them under controlled at-mosphere can limit their decomposition without meanwhile totally avoidingthem. As explained in Section V.A.c., the oxide formation is controlled bydiffusion below the melting temperature and since, in most cases, the meltingtemperature of oxides is slightly higher than that of the metal, an oxide crust(often broken into multiple fragments by the mismatch in CTE) will form atthe particle surface [136]. Correspondingly, it will modify the particle flatten-ing. When the oxide formed at the surface of the particle is fully molten, therelative velocity between the particle and the plasma flow drives the moltenoxide as a cap either at the trailing or the forward edge, depending on therelative velocities. From impact result two superimposed splats: that of themetal and that of the oxide. Moreover, for fully molten particles, a convectivemovement induced by the plasma flow entrains the oxide formed at the surfacewithin the particle and modify its wettability [129], and thus its flattening [263].

With nitrides and carbides formed at the surface of metals sprayed in con-trolled atmosphere with plasma containing methane or nitrogen, the problemis even more complex with the possibility of formation of nitride crusts ornitrides within the particle [139] modifying also the particle flattening.

2. Velocity

In plasma spraying, usual particle velocities upon impact vary between 20and 400m s�1 (up to 700m s�1 when considering supersonic RF plasmaspraying). When compared to the sound velocity in the liquid metal or ce-ramic (ranging between 2000 and 4000m s�1, approximately), the Machnumber of the particle is generally below 0.2 and in principle (but not at theright beginning of the impact) compressibility effects are negligible. The effectof the viscous dissipation to the energy balance for the heat transfer betweenthe particle and the substrate or the previously deposited splats is describedby the dimensionless Eckert number. The Eckert number is the ratio of twicethe kinetic energy to the sensible heat. The latter is defined as follows:

Ec ¼ V2p

Cpp ðT � TmÞ(30)

where the difference between the droplet temperature (T) and the meltingtemperature (Tm) has been taken as the characteristic temperature difference.In plasma spraying, the Eckert number is very small and need not to beconsidered. The compressibility of the colliding material is very important as


well as its impact pressure (‘‘hammer’’-type pressure). The latter is defined asfollows:

phrp � ap �Up (31)

where ap is the sound velocity in the particle.For example, considering a plasma-sprayed iron particle (ap ¼ 3000m s�1

and rp ¼ 6000 kgm�3) with an impact velocity of 200m s�1, the hammerpressure is ‘‘only’’ 36,000 atm (� 3600MPa)! Upon impact, the velocity ofthe liquid is suddenly changed and the liquid is compressed by the wavepropagating into the drop (see Section VI.H.a.). However, this pressurestarts to be released after a time tc � dp.Up/4ap

2 [206]. Still considering theabove example and a droplet radius of 20 mm, tc ¼ 2� 10�10 s, which is veryshort compared to the flattening time of about 10�6 s. This value is in goodcorrelation with the formation time of droplets at impact as measured byCedelle et al. [257,258]. After this impact time, the liquid starts flowingparallel to the substrate (Fig. 69).

3. Substrate

The substrate can be characterized by its tilting relative to the particleimpact direction (Fig. 57), its surface topology and the nature of the oxidelayer at its surface (most substrates are metals or alloys).

a. Tilting. The effects of titling can be important. They are generally two-fold: at the splat level and at the microscopic level. The liquid flow resultingfrom the particle flattening on a smooth substrate preheated over the tran-sition temperature creates splats with an elliptical shape independent of theimpacting particle diameter and the impact velocity but only on the sprayangle [272,293]. The splat thickness increases slightly along the inclinedsurface. When the spray angle j is over 301, the splat adhesion decreaseswith a flattening splashing phenomenon [223,305].

At the macroscopic level, the deposited bead intercepts part of the im-pacting particle flux resulting, for an angle j over 451, in a large amount ofsplashed material re-depositing over large areas on the target surface. The re-deposited overspray, composed of isolated poorly adherent particles withlarge spaces between them, exhibits a poor contact with the substrate. There-fore, the next bead deposited on this material has a poor adhesion [290,291].

b. Surface Topology. The substrate surface topology is a very important pa-rameter in flattening mechanisms but unfortunately not clearly defined.Fukanuma [284] used a regular array of simple, smooth Euclidean geometric


features to model the flattening process. If his work provides insight to flat-tening, real surfaces such as those formed by grit blasting or oxide layergrowth on the smooth surface of a metallic substrate are chaotic and moretypically fractal, i.e., collection of smaller features and larger features con-tinuing over a large range of scale [286]. However, in 100% of the casesconsidered (see for example the review paper of Fauchais et al. [35]), thesurface topology is described either by the average roughness Ra or Rt (i.e.,distance from the highest peak to the deepest undercut). Furthermore, theanalysis parameters and data acquisition parameters, such as tracing length,which can affect the calculated value of the average roughness [306], are notgenerally reported. As studied by Guessasma et al. [286], the use of suchdescriptors is not complete when the surface ruggedness (e.g., ‘‘complexity’’)becomes important: for example when the roughness of the deposit is high(i.e., high differences in levels), when the scale of the roughness becomes muchlower than the size of the sensor or when the ‘‘anchor’’ effect is emphasized.In such cases, the bias resulting from the measurements becomes importantand the average roughness (Ra) ceases to be representative of the surfacetopology. To circumvent such a difficulty, the surface fractal dimension canappear as a complementary index to the commonly used roughness param-eters. However, this concept has not been used very often to characterize therelationship between grit-blasted surfaces and adhesion/cohesion of coatings[306–308], the quantification of the thermally sprayed coatings roughness[286], and the microstructure evaluation of plasma-sprayed coatings [309].The integration of the fractal dimension in the surface topology character-ization for the impacting particles flattening and cooling seems to be man-datory to achieve a better understanding of the involved phenomena, but yetnothing has been done. Recently, Fukumoto et al. [310] have demonstrated,when considering smooth surfaces, the effect of the surface roughness definedat the nanometer scale using, for example, the skewness Sk (Section VI.E.c.):when Sk is positive (more peaks than undercuts), the splat adhesion is pro-moted as confirmed by the recent measurements of Cedelle et al. [257,258].

c. Substrate Surface Oxidation. Most substrates (more than 90% verylikely) are metals or alloys and the composition, roughness and thickness ofthe oxide layer at their surface play also a very relevant role on the splatformation and its CR, controlling its final shape and thickness [311–319].The oxide layer composition, roughness and thickness vary for the samemetal or alloy with the preheating temperature, the preheating kinetic andthe time during which the substrate is preheated. The preheating temper-ature plays a very important role in the oxide layer development because itfollows a kinetic law of Arrhenius type (i.e., depending on temperaturethrough an expression proportional to exp(�E/kT)). However, for a given


preheating temperature, the increase of the preheating time results in athicker oxide layer but with no change in its composition [264].

When the oxide layer is thin (a few tens nanometers), as with titaniumalloys or stainless steels, under certain conditions the oxide layer can bemelted and an intermediate oxide formed enhancing the adhesion of thesplat. This is the case with titanium substrates where the TiO2 oxide layer ismelted by the impact of liquid alumina particles forming a TiAl2O5-typeoxide. It allows achieving a very good coating adhesion (450MPa) onsmooth substrate (Rao0.05) [319]. A contrario, with stainless steel, thespinel layer at the surface even when melted cannot react with liquid alu-mina (no existing oxide) and the adhesion is fairly low.

When the oxide layer is thick, as with low carbon steel where the hematite(Fe2O3) layer can reach a few micrometers, no melting can occur and theadhesion is again purely mechanical.

J. ADHESION OF COATINGS

1. General Remarks

It is currently admitted [320,3] that adhesion depends on several types ofmechanisms, including chemical reaction, diffusion and mechanical interlocking.

a. Chemical Reaction. Chemical reaction occurs only if the impacting par-ticle melts locally the substrate and, when diffusion or mixing occurs be-tween both liquids, a new compound can be formed.

For substrates at room temperature, it can occur only if the particleeffusivity, ep ðep ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirpcppkp

p Þ, where rp, cpp and kp represent the specificmass, the specific heat at constant pressure and the thermal conductivity ofthe particle, respectively), is higher than that of the substrate esðes ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffirscpsks

p Þ. It occurs for example with Mo or Nb on iron (or steel)or aluminum. With iron, a compound MoFe2 is formed and adhesion ispromoted even on a smooth substrate.

For substrates preheated at higher temperatures (up to 700–1000K forstainless steel), it can occur with high temperature particles (for exampleZrO2 at about 3500–4000K impacting on high temperature stainless steel).It has to be kept in mind that the highest the preheating temperature, thethickest the oxide layer. Its composition will also drastically change. Forexample, partially stabilized zirconia is strongly bonded to the 20–30 nmthick thermally grown oxide layer formed at the surface of a 316L stainlesssteel substrate preheated at 773K. TEM measurements showed that theinterface splat–oxide layer was composed of elements coming both from theceramic splat (Zr) and substrate (Cr, Fe) [196]. Similar results were obtainedwith alumina coatings [321] sprayed onto polished Ti-6Al-4V alloy, the


adhesion of the alumina coating being 3675MPa for an initial Ra� 10 nmdue to the oxide layer against 1875MPa for an initial Ra� 50 nm. On apolished 316L substrate with an oxide layer 20 nm thick, an alumina coatingpeeled off during spraying; when the substrate was covered with a 3 mmthick PECVD alumina coating (Ra� 6 nm), the adhesion reached6675MPa. The good adhesion on polished Ti-6Al-4V is probably due tothe melting of the TiO2 layer resulting in the formation of Al2TiO5, while noFexAlyCrzOw oxide can be formed with the spinel at the surface of the 316Lsubstrate.

b. Diffusion. Diffusion can be achieved for metals and alloys only if thesubstrate temperatures are over 1100–1200K. It happens only if spraying isperformed under soft vacuum and if the oxide layer at the substrate surfaceis previously withdrawn. It can be achieved for example by using a reversepolarity transferred arc between the substrate and the anode of the plasmatorch, with the plasma torch controlling the arc current of the transferredarc at low levels (a few tens of amperes).

c. Mechanical Interlocking. Mechanical interlocking is the most encoun-tered mechanism for coating adhesion. The heights of the peaks (Rt) must beadapted to the splat diameter (2–3�Rt ¼ D). However, the transition tem-perature plays here again a crucial role and the adhesion can be increased bya factor 2–4 when the substrate is preheated over the transition temperature.

2. Substrate Oxidation

Of course, as preheating promotes oxidation, it is of primary importanceto know what happens with the development of the oxide layer. The char-acteristics of this oxide layer are linked to the substrate material, to thesurrounding atmosphere for preheating and the way the substrate is pre-heated (flame, plasma jet or furnace, heating kinetic Vm, preheating tem-perature Tps and preheating time tps [196,223,229,304,311–316,322,323]).For example, considering 304L stainless steel substrates [196,223,322], twotypes of oxide layers are observed at 573K: a Fe3�xCrxO4 spinel and a purehematite, of 30–50 nm thickness depending on the preheating time. At773K, dual oxide layers with sesquioxide Fe2�xCrxO3 (x � 0.1) and a Nichromite spinel, of 50–100 nm thickness, develop.

With low-carbon steel substrates (1040 steel), and depending on the pre-heating parameters Vm, Tps and tps, the relative thickness of both oxidelayers formed (hematite at the top and magnetite at the bottom) can bevaried [313]. The adhesion of alumina coating on a rough substrate reaches3474MPa when the hematite content is high and 4078 when it is low [313].In fact, on smooth substrates, the hematite layer is very brittle and adhesion


defects occur within it as soon as the thickness is higher than 150 nm, withsplats detaching from the substrate and leaving a hole in such layers [313].The importance of the preheating temperature and time is illustrated inTable X. It is observed that cast iron is very sensitive to the preheating timewith a fast development in oxide layers; the adhesion/cohesion is almostdivided by a factor of 3 as soon as the preheating time is multiplied by 3. Thestainless steel oxidation is not so drastic and when the preheating time ismultiplied by 5, the adhesion/cohesion is only reduced by 30%. In goodconnection with the preceding remarks about oxide layers, it might also bepossible that roughness promotes the substrate or oxide layer melting, es-pecially for the peaks under splats.

3. Crystalline Structures Adaptation

Alumina particles were sprayed onto polished (Ra � 0.4 mm) plasma-sprayed coatings [255]. The latter were either as-sprayed (with more than 99wt% of g phase) or preheated at 1373K at a kinetic of 5Kmin�1, annealedfor 6 h and cooled at a kinetic of 5Kmin�1 resulting in a 100% a-columnarstructure. Some were also preheated to 1873K at a kinetic of 5Kmin�1,annealed for 3 h and cooled at a kinetic of 5Kmin�1 resulting in aa-granular structure with grains between 3 and 5mm. A plasma-enhancedchemical vapor deposition (PECVD) coating (� 3 mm thick) was also de-posited on a stainless steel 304L substrate at 573K. It presented a columnarstructure with column diameters in the range of 100–150 nm and a Ra of6 nm. The results obtained with splats and corresponding coatings are sum-marized in Table XI.

Such results have been recently confirmed by Valette et al. [312,314,322].When preheating a low-carbon steel substrate under a CO2 atmosphere, aFe1�xO develops at its surface. After plasma preheating of the substratesurface over the transition temperature, the Fe1�xO layer is transformedinto Fe3O4. The resulting oxidized surface is composed of flat grains 1–2 mmthick and 3–7 mm wide. The alumina coating adhesion in this surface reaches60MPa and seems mainly due to a good progressive crystalline structuresaccommodation with five interfacial zones:

� a transition zone between the initial 1040 steel and C-impoverishedsteel resulting from the pre-oxidation treatment;

� a transition zone between steel, very poor in carbon and pure iron atthe top of the C-diffusion area;

� an interface between pure iron and iron monoxide (wustite), these twophases being linked by a well-known epitaxial relationship; it alsopossibly plays the role of a compliance zone because it is sometimeconsidered as the most plastic iron oxide;


TABLE X

EFFECT OF THE PREHEATING TEMPERATURE AND TIME ON SPLAT MORPHOLOGY AND ADHESION/COHESION OF ALUMINA OR ZIRCONIA COAINGS DEPOSITED

ON STAINLESS STEEL SUBSTRATES [212,305]

Substrate

material

Roughness

Ra (mm)

Preheating

time (s)

Preheating

temperature (K)

Sprayed

material�Adhesion/

cohesion��

(MPa)

Splat shape on

smooth substrate

Column size

(nm)

Cast iron 6 90 500 Alumina 6075 Disk 100–150

6 300 500 Alumina 2274 Fingered Irregular

SS 304L 12 60 573 Zirconia 5072 Disk 125–250

12 120 773 Zirconia 6574 Disk 125–250

12 600 773 Zirconia 4572 Lace 125–250

�Particle size distribution ranging from 22 to 45mm; fused and crushed particles.��Ten data points for each value.

318

P.FAUCHAIS

AND

G.MONTAVON

TABLE XI

CHARACTERISTICS OF SPLATS AND RESULTING COATING ADHESION WHEN SPRAYING ALUMINA ON DIFFERENT ALUMINA SUBSTRATES [255]

Alumina substrate manufacturing process Substrate phase Ra (nm) Splat morphology Adhesion/cohesion� (MPa)

Plasma spraying g-alumina�� 400 Columnar: regular � 100–150 nm 3573

PECVD a-columnar�� 400 Columnar: irregular � 150–300 nm 371

a-granular 400 Columnar: very irregular � 100–400 nm Detached

a-columnar�� 6 ‘‘Lace’’ or ‘‘ring’’ splat 6075

�Ten measurements were performed for each condition.��For the polished plasma-sprayed substrates, the substrate columns are oriented in almost all directions.��For the PECVD substrate, columns are all parallel to the particle impact dimension.

319

FROM

PLASMA

GENERATIO

NTO

COATIN

GSTRUCTURE

� a transition zone between Fe1�xO and Fe3O4 keeping memory of theinitial iron monoxide structure (clusters observed in TEM pictures);

� an interface between Fe3O4 and g alumina with possible crystallo-graphic relationship.

These interfaces correspond to a zone where the physical propertiesevolve gradually without any gap which is an essential condition for a goodresistance to mechanical or thermal stresses [323].

K. SPLAT LAYERING AND COATING CONSTRUCTION

The models of coating formation are generally based on simple analyticalcorrelations to predict the final size of the splats after impact and a set ofphysically based rules for combining the impact events to manufacture thecoating (see the review in [215]). The results depend strongly on the rulesand assumptions used. Moreover, phenomena such as cracking in ceramics,creeping, plastic yielding, interfacial sliding in metals and impact angle fa-voring shadow effect and splashing are neglected. A simple 1-D thermalmodel related to splat layering [324] makes it possible to calculate thetemperature history during coating formation and relate it to stress devel-opment.

Indeed, all models use simplifying assumptions and most of them neglectthe effects of residual stresses induced by quenching, expansion mismatchtemperature gradients and phase change [325]. Stresses can be relaxed bymicro-cracking, macro-cracking, creeping and yielding and these relaxationsmodify significantly coating properties [200,326].

Up to now, no experiments have been developed to follow the layering ofsplats with, for example, the measurement of the CR of a splat on thepreviously deposited ones.

If numerous studies describe the properties of many coatings according totheir macroscopic spray conditions, it is only a few years ago that a fewattempts have been made to link the particle parameters at impact, thecoating temperature and the coating properties [159,327–330]. As the da-tabase is very limited, it is still necessary to collect data relative to the sprayparameters and ‘‘in-flight’’ parameters correlated to coating in-serviceproperties in order to create an expert system. This can be achieved forexample by using factorial designs permitting to establish regression equa-tions relating the coating properties to particle parameters at impact andcoating formation temperature. However, the link between coating thermo-mechanical properties and in-service ones is not yet straight forward. This isstill a challenge because nobody, according to the present knowledge, has aclear idea of these relationships.


Of course, if the results of experiments are very scarce, models are evenpoorer. They all define complex rules of deposition [99,180,331,332]. Themost recent ones are based on 3-D stochastic models simulating the dropletimpact and coating formation on a solid surface [333,334]. They are basedon the same strategy:

� first particles upon impact must be described with the detail of eachparticle flattening to produce a splat which is allowed to curl upduring cooling. Porosity is produced if the gap between the curledsplats is not filled by the next flattening particle,

� second a set of physically based rules for combining the flatteningevents and splats layering has to be described,

� third, as already underlined in Section V.C., distributions of particlesize, injection velocity and direction at the injector exit have to bedefined in a stochastic approach.

Even if the pore distribution and inter-lamellar contacts are poorly de-scribed, such models start to give static distributions at impact which areclose to experimental ones. It is illustrated for example in Fig. 70 [99] whereit can be seen that the predicted value with a time-dependent plasma jet is ingood agreement with the experiment. It has to be noted also that the heightof the coating is much higher with the experiment relative to a 3 s spray timewhile the model corresponds to 7ms.

L. COATING ARCHITECTURE

The comparison between calculations and measurements is not necessar-ily simple because the latters are not straightforward and can be biased whenpreparing coating cross section or according to the method limitation asillustrated in the following for the pore network and splat characterizationwithin the coating.

1. Pore Network

As already mentioned, plasma spraying is a random deposition processduring which molten particles impact upon a substrate or previously de-posited layers at high velocity, spread and solidify to form thin lamellae. Thecoating resulting from the stacking of those lamellae is characterized by ahighly anisotropic lamellar structure. Moreover, stacking defects generatespecific inter-lamellar features within the structure, mainly cavities (i.e.,globular pores), which can be, or not, connected to the upper surface of thecoating (i.e., open pores). Finally, vapors and gases stagnating in the vicinityof the surface to be coated and peripheral decohesions around lamellae


induce, as for them, delaminations between the lamellae (i.e., inter-lamellarcracks). In other respects, intra-lamellar microscopic cracks appear consec-utively to the particle rapid solidification process after spreading. Such aphenomenon is especially emphasized for ceramic materials, which do notcomply so much the shrinkage at the solidification.

The combination of these features generates an interconnected pore net-work, from which derives the permeability of most of the thermal-spray coatings [335]. This network can dramatically limit the coating inservice performances, especially when the coated component is exposed to areactive environment. In such a case, the substrate material reacts withthe medium which percolates through the pore network: corrosion occursat the substrate/coating interface and eventually leads to the coating spa-llation.

Coating structure, especially porosity, depends on the particle properties(momentum and viscosity) at impact. These properties are strongly relatedto the spray gun operating parameters.

The influence of the porosity on the coating properties involves a finedescription of the porosity level and its nature.

FIG.70. Comparison between experimentally measured and numerically computed static

spray beads [99].


Several experimental protocols can be implemented to address the porenetwork characteristics; Table XII lists the most common of them easilyavialable. None of them allow nevertheless an exhaustive characterization ofthese characteristics. Moreover, each of them exhibits some major disad-vantages that can jeopardize the result revelancy.

a. Physical Methods. These methods are based on the intrusion of a sub-stance into the pore network. It can be water or mercury (the non-wettingliquid volume of mercury is measured as a function of the applied impreg-nation pressure; this technique permits to measure the size of the openpores: smaller the open pores, higher the required impregnation pressure[336,337]) or gas (generally helium; the pressure increase of an unvaryinggas volume; measured implementing a cell which is successively empty andincludes then the sample [338]). These techniques permit to quantify thepores connected to the coating surface (i.e., open pores). The main draw-backs are the fact that porosity measurement is not direct and that theimpregnation of the whole open porosity is not certified. Archimedean po-rosimetry permits to quantify the non-connected porosity level by measur-ing the ‘‘dry’’ weight and the ‘‘wet’’ weight (immersion into water) of thesample.

b. Metallographic Observations and Image Analysis. The observation of thecoating cross section (implementing SEM) coupled with appropriate imagetreatments and statistical analyses permits to quantify pores and cracks(porosity level, crack orientation and linear density) [338–340]. This methodpermits to measure the overall porosity level with no discrimination betweenopen and closed porosity. An appropriate magnification must be determinedto reproduce the as finer as possible details (i.e., microcracks) using anadequate image resolution without cutting many large objects (i.e., pores).Experience indicates that images should be between 10 and 15 times largerthan the objects of interest to be analyzed. Whatever the selected magni-fication, it is almost impossible to extensively analyze the very thin cracksdeveloping within the lamellae consecutive to stress relaxation or the de-cohesions developing at the periphery of the lamellae after solidificationconsecutive to surface tension effects (molten stage) and residual stresses(solid stage). Consequently, image analysis and stereological protocols donot extensively address the pore network architecture. This may in certaincases leads to some misinterpretation of results, especially when consideringthe coating mechanical properties, its compliance in particular. Moreover,such protocols require a metallographic preparation of the samples, that isto say cutting, pre-polishing and polishing. All of these steps, especially


TABLE XII

COMMON TECHNIQUES QUANTIFYING PORES IN A POROUS MEDIUM SUCH AS A THERMAL SPRAY COATINGS

Technique Type Pore connectivity Pore overall level Pore morphology

Connected Non-connected Globular pores Cracks Delaminations

AP Physical |MIP |P |IA Metallo-graphic | | | |EIS Electro-chemical |

AP, Archimedean porosimetry; MIP, mercury intrusion porosimetry; P, picnometry; IA, image analysis; EIS, electrochemical impedance

spectroscopy.

324

P.FAUCHAIS

AND

G.MONTAVON

when carried out on brittle materials such as ceramics, may induce artifacts(i.e., scratches, pull-outs, etc.) when not fully managed and controlled. Fromthese artifacts results variability in analyses, to such extends that misinter-pretations can be made.

c. Electrochemical Method (Electrochemical Impedance Spectroscopy). Thepercolation of an electrolyte inside the interconnected porosity permits toquantify the open porosity level by analyzing the corrosion reaction at thesubstrate/electrolyte interface. Hence the electrochemical impedance spec-troscopy technique is used to measure the impedance of the electrochemicalcell. The immersed coating surface behaves as the working electrode[341,342]. This technique appears as particularly well-adapted to quantify toconnectivity to the substrate. Nevertheless, this technique requires the se-lection of an electric model simulating the system; the electric characteristicsare extrapolated in order to fit the electrochemical behavior of the system.The model has to remain coherent from a physical point of view and somebehaviors may be sometimes very difficult to be described. Moreover, as theelectrochemical reaction takes place in confined spaces (into the pores, at theelectrolyte/substrate interface), it can be expected that the local acidificationof the electrolyte evolves as the reaction takes place, modifying the systemresponse. At this stage of the development, it is almost impossible, or verydifficult, to address this point.

2. Phase (lamella) Size and Spatial Distributions

The size and spatial distributions of lamellae within the coating playrelevant roles in the coating characteristics and functional properties.

When considering single-phase coatings, the lamella size and spatial dis-tributions can be easily extrapolated from the pore size and spatial distri-butions.

When considering multi-phased coatings, specific stereological analyseshave to be carried out for each phase. The protocols are identical to thoseapplied for the pore network architecture quantification. The same limita-tions fully apply also.

VI. Concluding Remarks

Since the very first ignition of a d.c. plasma torch in 1939 in Germany(Reinecke), plasma torches have found multiple applications in numeroustechnological fields, from raw material processing to waste treatments.


This is in the 1950s that the very first trials were made in the USA and inFrance to produce thick ceramic coatings by plasma spraying with dedicatedplasma torches. Since, these torches are used in numerous industrial fields,such as for example:

� in aeronautics and aerospace where more than 30 different coatingsare required to protect engine component surfaces. The unique per-formances of today’s engines result in a large extend in the massiveintroduction of high-performance plasma-sprayed coatings. Alongthe years, the development of plasma spray techniques has been mostof the time driven by the requirements of this industrial field (such as,for example, the introduction of automated mass flow plasma gascontrollers). These solutions provide for example protection againstfretting wear of titanium fans at the engine air intake, thermal in-sulation of the combustion chamber or clearance control at the com-pressor or turbine blade tips;

� in the automotive industry for more and more engine components areprotected by plasma spray coatings, the latest developments broughtto service having being sprayed coatings in cylinder bores of engineblocks. The specific requirements of this industrial field, ‘‘zero de-fault’’ culture, mass production, low costs and ‘‘green’’ technologies,among others, stimulate, as did the aeronautic industry, of more re-liable spray systems and on-line diagnostic devices;

� the petrochemical industry where coatings increase the lifetime ofequipments. In this case, the coatings operate in particularly harshand severe environments and specific composition have to be devel-oped;

� the steel industry, the endoprosthesis industry, etc.

The development of these applications has been possible along the pastfifty years thanks to:

� the continuous development of plasma torches (d.c. and RF) andtheir associated electric sources and controllers towards more stabil-ity, more automation, more robustness and more reliability. This de-velopment was rendered possible by a better understanding of theoperating modes of such torches and the thermodynamical and trans-port properties of the plasma flows;

� the disruptive development of on-line industrial diagnostic devices inthe 1990s permitting to quantify in-flight particle characteristics, suchas their temperature and velocity;

� the better understanding of the physicochemical mechanisms leadingto the formation of coating lamellae from the spreading and the


solidification of impinging particles. In particular, the identification inthe mid-1990s of the transition temperature and the understanding ofthe involved mechanisms permitted to better manage the spray op-erating conditions.

Of course, all of these developments have beneficed largely from theprogresses in computational simulations.

Thanks to these progresses, both from the industrial/technological andthe scientific sides, each one taking advantage of progresses made by theother, plasma spraying knew almost continuous growth of annual sales.Figures for the coming years are rather optimistic, especially due to theappearance of new potential applications of plasma spraying such as:

� applications related to the production of energy following alternativeways, such as solar and solid oxy-fuel cells;

� applications related to environmental concerns, such as catalytic andphotocatalytic layers;

� applications in extreme environments, in terms of heat flux and cor-rosive species.

Beside these new potential applications, conventional applications willbecome more and more challenging also since, in most cases, the coatingswill become prime reliant for the considered system.

To reach such ambitious objectives, some progresses still have to be made,both from the technological and fundamental points of view. Theseprogresses would have in particular to be directed towards:

� a larger development and use of plasma spray torches exhibiting ahigher stability in term of flow in order to manufacture more homo-geneous coatings. Cascade-type plasma torches could constitute asolution on a short-term basis. To reach this goal, a better under-standing of the plasma gun operating modes and of the arc rootfluctuations will be required. Non-stationary 3-D numerical simula-tions should bring a very significant contribution to such progresses;

� the generalization of on-line diagnostic tools in order to reach a bettercontrol of the intrinsic operating parameters such as, of course, theparticle characteristics upon impact, but also of some coating char-acteristics such as the deposited yield;

� the development of on-line closed-loop controllers permitting hencean adjustment in real time of the extrinsic operating parameters(i.e., plasma torch power parameters, feedstock injection parameters,kinematics parameters, etc.) in order to keep constant the intrinsicoperating parameters (i.e., particle temperature and velocity uponimpact, particle trajectory distribution, coating temperature, etc.).


Nomenclature

GREEK SYMBOLS

e total emissivity of the plasma

(Wm3 ster�1)

g isentropic coefficient g ¼ cp/cv(dimensionless)

k thermal conductivity (Wm�1K�1)

m viscosity (kgm�1 s�1 or Pa s)

ni cold gas velocity (m s�1)

ri cold gas volumetric mass

(kgm�3)

rw water volumetric mass (kgm�3)

se electrical conductivity (AV�1m�1

or mhom�1)

s0 electrical conductivity at tempera-

ture T0 (corresponding to 1% of

electrons)

j heat potential: j� jref ¼R TT ref

KðTÞDT (Wm�1)

SYMBOLS

a sound velocity (m�1 s�1)

aj coefficient relating the heat poten-

tial to the enthalpy (kgm�1 s�1)

a0 slope of the transient voltage signal

(V s�1)

CD drag coefficient (dimensionless)

cv specific heat at constant volume

(J kgK�1)

cxp specific heat of species x at con-

stant pressure (J kg�1K�1)

d electrode diameter (internal dia-

meter for anode or cold well-type

cathode, external diameter for

stick- or button-type cathode) (m)

D internal diameter of the vortex

chamber (m)

dAK anode–cathode distance (m)

Ed0 open circuit voltage of the power

source (V)

Fag azimuthal component of gas drag

force (N)

Fag axial component of drag force (N)

G mass flow rate (kg s�1)

h heat transfer coefficient

(Wm�2K�1)

h0 enthalpy (J/kg�1 or sometimes

kWhkg�1:

1 kWhkg�1 ¼ 3.611 J kg�1))�h plasma mean specific enthalpy:

�h ¼ P�Pth

m0gðJ kg�1Þ

Id maximum arc current achievable

in a torch (A)

j current density (Am�2)

k Boltzman constant

(1.38� 10�23 JK�1)

Kn ‘e/d, Knudsen number (dimen-

sionless)

mog plasma-forming gas mass flow rate

(kg s�1)

Ma Mach number Ma ¼ v/a (dimen-

sionless)

n0 flow rate of the air entrained by the

plasma jet (kg s�1)

P power (kW or MW)

pa surrounding atmosphere pressure

(Pa)

Pth power losses in the cooling circuit

(W)

Pr Prandtl number Pr ¼ mcp/k(dimensionless)

qa heat flux received by the anode

(Wm�2)

R negative resistance of the arc

(dV/dI) (O)Ra average roughness [m]

Rt peak-to-valley height [m]

Re Reynolds number (dimensionless)

for cold gas Re ¼ rnd/mfor plasmas Re ¼ G/m0d (index 0

corresponds to the temperature T0

at which the electron molar frac-

tion is 1%)

S swirl number (dimensionless)

T0 temperature at which the electrons

molar fraction is 1% or 3% (K)

tanY va/vztr response time of a control unit (s)

U plasma gas velocity (m s�1)

Va anode voltage drop (V)

VK cathode voltage drop (V)

va azimuthal component of the gas

velocity (m s�1)


vw water flow velocity (m s�1)

vz axial component of the gas velocity

V torch voltage (V)

z axial distance along the plasma jet

axis (m)

‘ distance between torch nozzle exit

and substrate or stand-off distance

in spraying (m)

‘e mean-free path (m)

ACRONYMS

AJD anode jet dominated

APS atmospheric plasma spraying

BTC button-type cathode

CCD coupled charge device

CJD cathode jet dominated

d.c. direct current

LDA laser Doppler anemometry

LPPS low pressure plasma spraying

OFHP oxygen-free high purity

OMA optical multi-channel analyzer

PDA phase Doppler anemometry

PSI particle shape imaging

Ra average roughness [m]

RF radio-frequency

Rt peat-to-valley height [m]

SDC spray deposit control

SLPM standard liters per minute

VPS vacuum plasma spraying

2F 2 focus point measurement

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310. Fukumoto, M., Ohgitani, I., and Yasni, T. (2004). Mater. Trans. 45(6), 1869.

311. Maıtre, A., Denoirjean, A., Fauchais, P., and Lefort, P. (2002). Phys. Chem. Chem. Phys.

15(4), 3887.

312. Valette, S., Denoirjean, A., Lefort, P., and Fauchais, P. (2003). J. High Temp. Mater.

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313. Pech, J., Hannoyer, B., Lagnoux, O., Denoirjean, A., and Fauchais, P. (1999). In

‘‘Progress in Plasma Processing of Materials’’ (P. Fauchais and J. Amouroux, eds.), p. 543.

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314. Valette, S., Denoirjean, A., Soulestin, B., Trolliard, G., Hannoyer, B., Lefort, P., and

Fauchais, P. (2004). Alumina coatings on preoxidized low carbon steel. Interfacial phe-

nomena between alumina and iron oxide layer. In ‘‘Proceedings of the International

Thermal Spray Conference,’’ Osaka, DVS Dusseldorf, Germany (electronic version).

315. Haure, T. (2003). Multifunctional layers by PACVD and Plasma Spraying, Ph.D. Thesis,

University of Limoges, France, 14 November.

316. Espie, G., Fauchais, P., Hannoyer, B., Labbe, J. C., and Vardelle, A. (1999). In ‘‘Heat and

Mass Transfer under Plasma Conditions during the APS on the Wettability’’ (P. Fauchais,

et al., eds.), Vol. 891, p. 143. N.Y. Academy of Sciences, NY, USA.

317. Seyed, A. A., Denoirjean, P., Denoirjean, A., Hannoyer, B., Labbe, J. C., and Fauchais, P.

(2000). In ‘‘Progress in Plasma Processing of Materials’’ (P. Fauchais, ed.), p. 465. Begell

House, NY, USA.

318. Pech, J., Hannoyer, B., Denoirjean, A., Bianchi, L., and Fauchais, P. (1999). Influence of

substrate preheating monitoring on alumina splat formation in d.c. plasma processes.


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319. Pech., J., Hannoyer, B., Lagnoux, O., Denoirjean, A., and Fauchais, P. (1999). Influence

of preheating parameters on the plasma jet oxidation of a low-carbon steel. Progress in

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Begell House, NY, USA.

320. Thermal spraying: Practice, theory and application, prepared by AWS Committee on

Thermal Spray (1999). American Welding Society, Miami, FL, USA, pp. 2–15.

321. Haure, T., Denoirjean, A., Tristant, P., Hidalgo, H., Leniniven, C., Desmaison, J.,

and Fauchais, P. (2001). In ‘‘Thermal Spray 2001: New Surfaces for a New Millenium’’

(C.C. Berndt, K.A. Khor and E. Lugscheider, eds.), p. 613. ASM International, Materials

Park, OH, USA.

322. Valette, S. (2004). Influence of the Preoxidation of a Steel Substrate on the Adhesion of an

Alumina Coating d.c. Plasma Sprayed, Ph.D. Thesis, University of Limoges, 30 November.

323. Zanchetta, A., Lefort, P., and Gabbay, E. (1995). J. Eur. Ceram. Soc. 15, 238.

324. Haddadi, A., Grimaud, A., Denoirjean, A., Nardou, F., and Fauchais, P. (1996). In

‘‘Thermal Spray: Practical Solutions for Engineering Problems’’ (C.C. Berndt, ed.), p. 615.


325. Ghafouri-Azar, R., Mostaghimi, J., and Chandra, S. (2001). Deposition model of thermal

spray coatings. In ‘‘Thermal Spray: New Surfaces for a New Millenium’’ (C.C. Berndt,

K.A. Khor and E. Lugscheider, eds.), pp. 951–958. ASM International, Materials Park,

OH, USA.

326. Kuroda, S., Dendo, T., and Kitahara, S. (1995). Quenching stress in plasma sprayed

coatings and its correlation with the deposit microstructure. J. Therm. Spray Technol. 4(1),

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(C. Coddet, ed.), pp. 1681–1696. ASM International, Materials Park, OH, USA.

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advanced materials processing by plasma spraying. Pure App.Chem. 77(2), 443–462.

330. Leblanc, L. and Moreau, C. (2001). Optimization and process control for high perform-

ance thermal spray coatings. J. Therm. Spray Technol. 11(3), 27–57.

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332. Remesh, K., Ng, H. W., and Yu, S. C. M. (2003). J. Therm. Spray Technol. 12(3), 377–392.

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Spray Technol. 12(2), 53–69.

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Japan, DVS Dusseldorf, Germany (electronic version).

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336. Kuroda, S., Dendo, T., and Kitahara, S. (1995). J. Therm. Spray Technol. 4(1), 75–84.

337. Ilavsky, J., Berndt, C. C., and Karthikeyan, J. (1997). J. Mater. Sci. 32, 3925–3932.

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341. Zhang, J. and Desai, V. (2005). Surf. Coat. Technol. 190(1), 98–109.

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aluminide. Mater. Sci. Eng. A372(1-2), 278–286.


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Heat Transfer Processes and Modeling of Arc

Discharges

E. PFENDER and J. HEBERLEIN

High Temperature and Plasma Laboratory, Department of Mechanical Engineering, University of

Minnesota, 111 Church Street SE, Minneapolis, MN 55455, USA

Abstract

Energy transfer from an arc is of crucial importance in numerous appli-cations, and its control will frequently determine the viability of a process or adevice. Heat transfer from an arc plasma is characterized by several distinctfeatures, such as transport of dissociation and ionization energy and of elec-trical charges in addition to mass transport. Any model of an arc thereforemust contain not only the conservation of mass, momentum and energy, butalso Maxwell’s equation and current conservation. Furthermore, usually anarc is at least partially in a non-equilibrium state, and the model has to beadjusted to the specific non-equilibrium conditions. The thermodynamic andtransport properties required for the model description of the arc represent oneof the most important input, and a significant part of this contributionis devoted to a review of these properties for equilibrium and for kineticnon-equilibrium conditions. The arc models are introduced with a very simpleone-dimensional example, but then equations and results are presented fortwo-dimensional and three-dimensional cases. The heat transfer is discussedwith emphasis on heat transfer to the electrodes, and results of models withdifferent assumptions are presented. The advantages and shortcomings of thepresent approaches are briefly summarized in the conclusions.

I. Introduction

Heat transfer processes associated with arc plasmas are important fornumerous applications. In many applications the arc heat is used directly forthe process (transferred arc process). Examples are plasma cutting whereheat fluxes of several times 109W/m2 are encountered, arc welding, and arcfurnaces for metallurgical processes, where the total heat transfer from the




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arc can reach 105W. In these applications an electric arc is used becauseit offers a combination of high heat fluxes/high energy densities and a con-trolled environment or process medium. A plasma model of such processescan optimize energy utilization and product quality. In other applications,arc heated gases are used for processing, i.e. for melting or evaporatingdispersed particulate matter, or providing supplementary heat and reac-tants. Examples are plasma waste treatment, plasma synthesis of chemicalsor particles, or plasma spraying, and plasma models are used to optimize thewanted reaction, to obtain the best product quality and the highest yield.However, in this latter group of applications, the arc is usually confined to aplasma torch, and the performance and operational reliability of this torchare dependent on the control of the arc inside the torch, in particular on theheat transfer to the electrodes. Control of torch electrode erosion effectsdetermine in many cases the viability of a process, and understanding of thearc–electrode interaction is crucially important. Two of the most importantapplications of electric arcs are circuit breakers and discharge lamps, and inboth applications, prediction of the arc behavior will allow optimization ofthe operational effectiveness of the device, and control of electrode erosionwill determine its reliability.

While the number of important applications would warrant extensiveefforts in arc plasma modeling, the difficulties associated with the formu-lation of such models have limited their usefulness. Heat transfer underplasma conditions requires consideration of several special effects:

1. Plasmas are reacting gases, with dissociation, ionization, and recom-bination reactions influencing the energy transport, and the presence ofmultiple species determining the values of the transport coefficients.

2. Arc plasmas have very high temperatures and energy densities, and areconsequently surrounded by very steep gradients of temperatures anddensities. Kinetic and composition non-equilibrium are usually theconsequence, and description of the energy transport requires consid-eration of these effects. In particular in the electrode regions, the gra-dients can be so steep (in the order of 108K/m or several hundreddegrees per mean free path (mfp)) that the continuum concept maybreak down and discontinuities in properties may be encountered.

3. Heat transfer to the electrodes is intimately tied to the current transferand the heat generation, and change of either one will affect the other.

4. Arc plasmas display instabilities, and for many applications, transientdescriptions of the plasma have to be offered.

These factors lead to some situations, which are unique for arc plasmasand make it difficult to transfer solution techniques derived for other

346 E. PFENDER AND J. HEBERLEIN

ARTICLE IN PRESS

situations, e.g. flames. For example, since for arc plasmas the arc current isthe independent variable, some apparently paradoxical observations can bedescribed: (a) cooling of the arc fringes can increase its temperature becausethe cooling results in a constriction of the arc, higher electric fields for thesame current, and therefore higher energy dissipation; (b) strong convectiveenergy transport to the anode surface can reduce the specific heat flux to theanode by allowing the current transfer to be distributed over a wider area(diffuse attachment).

Early models of the arc considered the arc mostly as a component in anelectrical circuit and treated the arc properties empirically. This includes inparticular arcs in circuit interruption devices. A more physical model basedon energy conservation was derived by Elenbaas [1], and by Heller [2], forthe case of a one-dimensional steady state situation, i.e. heat generationbalanced by radial energy losses. Because the strong non-linearity of thedifferential equations require numerical solutions, more sophisticated mod-els were only pursued after the advent of digital computers, and everyincrease in computing power available to the scientific community hasimmediately led to increased sophistication and realism of the arc models.These early models led to the development of a framework for transportcoefficients, allowing the modeling results to become more realistic. Theexplosive growth of arc plasma applications since the 1970s resulted in thedevelopment of modeling approaches of increasing sophistication. The de-mands for describing actual arcing devices led to developments of usableradiation transport models, to determination of properties for gas mixtures,and to three-dimensional descriptions of the plasmas. Descriptions of non-equilibrium regions have been formulated so far only for relatively simplesituations, and a significant effort is still required to realistically describe thenon-equilibrium regions of complex multi-component arcs.

In the following section, a general overview of the essential featuresof electric arcs is given. The subsequent section describes the determinationof thermodynamic and transport properties of arc plasmas. This section isfollowed by a description of arc models, including description of laminarand turbulent arc models and recent developments in time-dependent sim-ulations. The section on heat transfer processes associated with arcs isdivided into energy transfer to electrodes, and to walls without currenttransfer. The review ends with a conclusion section.

II. General Features of Thermal Arcs

By definition, in a thermal arc the thermodynamic state of the plasmaapproaches local thermodynamic equilibrium (LTE), which includes kinetic

347HEAT TRANSFER PROCESSES AND MODELING OF ARC DISCHARGES

ARTICLE IN PRESS

as well as chemical equilibrium. Such arcs, known as high-intensity arcs,typically require currents above 100A and pressures in excess of 10 kPa.At lower-pressures electron and heavy-particle temperatures are signifi-cantly different due to the lack of collisional coupling between these twospecies. A large number of references related to thermal arcs are listed in asurvey on ‘‘Electric Arcs and Thermal Plasmas’’ [3] and in a more recentreview on ‘‘Electric Arcs and Arc Gas Heaters’’ [4].

There are three principal features, which distinguish an arc from otherdischarge modes. For the sake of simplicity the following discussion will berestricted to steady-state (DC) arcs.

A. RELATIVELY HIGH CURRENT DENSITIES

The current density in the arc column of a typical high-intensity arc mayreach values in excess of 106A/m2 which is considerably higher than thecorresponding values of 10–100A/m2 which are characteristic for the pos-itive column of a glow discharge. The situation is even more pronounced atthe electrodes. Arcs may attach to the electrodes, and in particular to thecathode, in the form of tiny spots in which current densities can be as high as1010A/m2.

B. LOW CATHODE FALL

The potential distribution in an electric arc changes rapidly in front of theelectrodes forming the so-called cathode and anode fall. The cathode fall isof particular interest; it assumes values of around 10V in contrast to thetypical cathode falls in glow discharges which usually exceed 100V. Thisrelatively low cathode fall is a consequence of the more efficient electronemission mechanisms at the cathode compared with those prevailing in glowdischarges.

Although the overall arc voltage in a given discharge vessel is lower thanthat of a glow discharge in the same vessel and at the same pressure, theoverall voltage drop over the discharge does not provide a useful criterionfor distinguishing an arc from other types of discharges. Depending on thearc length, and the energy balance for the arc column, the overall voltagedrop of an arc may be very high.

C. HIGH LUMINOSITY OF THE COLUMN

This criterion provides a useful distinction between an arc and otherdischarge modes, provided the pressure is sufficiently high (pZ10 kPa). Theextremely high luminosity of the column of high pressure (pZ100 kPa)thermal arcs finds many applications in the illumination field.


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1. The Arc Column

Since cathode and anode regions may be considered as thin ‘‘boundarylayers’’ overlying the electrodes, the column with its comparatively smallpotential gradient represents the main body of the arc. In contrast to theregions immediately in front of the electrodes in which space charges exist,the arc column represents a true plasma in which quasi-neutrality prevails. Thepressure in the arc column is uniform and equal to the pressure in the sur-rounding fluid with the exception of arcs operated at extremely high currentlevels (I45000A). In such arcs the interaction of the current with the self-induced magnetic field produces a pressure gradient in radial direction (pincheffect) so that the pressure becomes elevated in the axis of the arc column.

For a given arc current the conditions in the column (temperature dis-tribution and associated distribution of thermodynamic and transportproperties) adjust themselves in such a way that the field strength requiredfor driving this current is minimized (Steenbeck’s minimum principle) [5].

The relatively small field strength prevailing in the arc column may also beinterpreted as a consequence of the favorable energy balance which is, to alarge degree, determined by the charge carrier balance.

The dominating process responsible for ionization in the arc column is dueto electron impact. The field strength in the arc column in the case of highpressure arcs (p410kPa) is by far insufficient for an electron to accumulateenough kinetic energy over an mfp to make an ionizing collision, i.e.

e � le � E � EI (1)

where, E, represents the field strength, le the mfp length, e the elementarycharge, and EI the ionization energy. In this inequality it is assumed that theelectron travels in field direction, accumulating the maximum possibleenergy from the electric field. Charge carrier production in this situation mustbe accomplished by thermal ionization rather than field ionization. Electronsin the tail of the Maxwellian distribution possess sufficient energy for makingionizing collisions.

2. The Cathode Region

Phenomenologically, the current attachment at the cathode of arcs maybe divided into two broad categories:

‘‘Diffuse attachment’’ without evidence of single or multiple cathodespots, and attachment in the form of one or several distinct spots.

The term ‘‘diffuse attachment’’ characterizing the first mode requiresfurther explanation because this mode is frequently referred to in the lit-erature as ‘‘spot attachment’’. The arc may indeed reveal in this mode an


ARTICLE IN PRESS

appreciable constriction in front of the cathode so that the actual currenttransition zone appears as a ‘‘spot’’ with current densities in the range from107 to 108A/m2 which are at least one order of magnitude higher than inthe arc column. This mode, however, may be clearly distinguished from thesecond mode for which the constriction is much more severe, with currentdensities in the range from 1010 to 1012A/m2. In addition to the entirelydifferent cathode electron emission mechanisms for the two modes, thecathode attachment in the first mode is stationary or slowly moving incontrast to the second mode which frequently shows one or several spotsmoving randomly with high velocities over the cathode surface.

In the first mode thermionic emission of electrons is the governing mech-anism for liberation of electrons from the cathode. This mode will be furtherdiscussed in Section V.

Arcs attaching to the cathode in the form of a single or multiple, rapidlymoving, extremely small spots are of great practical importance for appli-cations in arc gas heaters and plasma torches. Since the current density inthe case of thermionic emission depends critically on the cathode surfacetemperature, electron emission on cold cathodes can no longer be ascribedto thermionic emission, because the size of the attachment and the therm-ionically feasible current densities do not match with the observed currents.In this case a more complicated mechanism for electron liberation from thecathode must be postulated, which is described in Section V. Cathodes forwhich the electron emission is ascribed to this mechanism are referred to asnon-thermionic or cold cathodes, because the overall temperature of thecathode is substantially below that required for thermionic emission. Sec-ondary effects, such as vapor and plasma jets originating in the cathoderegion or on the cathode surface itself may exert a strong influence on thecathode region and sometimes on the entire arc.

Cathode jets have been observed with thermionic as well as non-thermioniccathodes, particularly at high current levels. These cathode jets may beattributed to four different sources.

(i) Electromagnetically induced jets.(ii) Vaporization of cathode material and/or surface impurities.(iii) Ablation and explosive release of cathode material.(iv) Chemical reactions on the cathode surface producing gases.

The interaction of the arc current with its self-induced magnetic field leadsin arc sections of variable cross-section to the phenomena of induced plasmajets. These phenomena are not restricted to the cathode or anode region ofan arc; they may also occur in other parts of the arc column where theconditions of variable column cross-section are met. If an arc, for example,is forced through a diaphragm which reduces its cross-section, plasma jets


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are induced with the flow directed away from the location of the most severeconstriction of the arc column (Maecker effect) [6]. Such an arrangementacts as pump; gas is continuously moving toward the opening of thediaphragm by suction and the gas ingested, and heated by the arc, is thenaccelerated away from the orifice in the diaphragm.

For an analytical description of this phenomenon, momentum and con-tinuity equation are required which, in vector notation, may be written fora steady arc neglecting viscous effects as

rd~v

dtþrp ¼ ~j � ~B (2)

divðr~vÞ ¼ 0 (3)

where r is the plasma density, ~v the plasma velocity vector, p the pressure,and ~B the self-induced magnetic field vector. The ~j � ~B force which,in general, is responsible for the pinch effect in current-carrying plasmacolumns, may build up a pressure gradient and/or accelerate the plasma.Equation (3) determines which fraction of the magnetic body force is usedfor plasma acceleration. For a rotationally symmetric arc, the radial pres-sure gradient and the resulting over-pressure in the arc may be expressed by

DpðrÞ ¼Z R

r

jðsÞBðsÞ ds (4)

where R is the arc periphery often called arc radius beyond which the elec-trical conductivity is negligible (To7000K for most plasma gases).

With

r � ~B ¼ m0~j (5)

one obtains

BðrÞ ¼ m0r

Z r

0

j � s � ds (6)

where, m0 ¼ 1:26� 10�6 Hy=m, is the permeability of vacuum.If the current density distribution j(r) is known Dp(r) can be calculated.

Assuming a uniform current density distribution (one step model) over thecross-section of the arc,

�j ¼ I

pR2(7)


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where, I, represents the total arc current, Dp(r) can be determined. Com-bining Eqs. (4), (6), and (7) one finds

DpðrÞ ¼ m0ðI � �jÞ4p

1� r2

R2

� �(8)

According to this model (Eq. (8)), the over-pressure on the arc axis at thepoint of constriction is proportional to the product of total arc current, I,and current density.

With the increase of the constriction of the arc channel in the cathoderegion, the current density as well as the self-induced magnetic field willincrease which, according to Eq. (8), will also increase the over-pressure onthe arc axis. The axial pressure gradient pointing toward the cathode willinduce a flow in the opposite direction away from the cathode with a max-imum velocity, vmax, given by

vmax ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffim0 � I � �j2p �r

s(9)

where �r is the average plasma density. For a free-burning 200A carbon arc,maximum velocities of the order of 100m/s have been found [3]. The max-imum velocity depends critically on the arc constriction in the cathode re-gion which may be influenced by the cathode shape in the case ofthermionically emitting cathodes.

The cathode jets listed under (ii), (iii), and (iv) in this section originate atthe cathode surface. These jets contain cathode material and/or impuritieseither in vapor form or as particulate matter, including gases stemming fromchemical reactions on the cathode surface. Oxidation of carbon steel, forexample, will produce CO and CO2.

The cathode jets may also enhance the ‘‘stiffness’’ of the cathode regionand the adjacent arc column. In fact, the electromagnetically induced cath-ode jet may serve as a stabilizing mechanism for a free-burning arc pro-ducing the well-known bell shape of such an arc.

3. The Anode Region

The anode region, as any other part of an electrical discharge, is governedby the conservation equations including the current equation. Unfortu-nately, any attempt to solve these equations for the anode region faces threemajor problems. First of all, the conventional conservation equations applyonly as long as the continuum approach is valid. Since the anode fall spacing


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(sheath) is in the order of one mfp length of the electrons, the continuumapproach is no longer valid for that part of the anode region. Secondly, theapplication of the conservation equations requires that the plasma is in LTEor at least that its thermodynamic state is known. There is no doubt thatLTE does not exist for the entire anode region. In the anode boundary layerdeviations from LTE occur due to differences in electron and heavy-particletemperatures and due to deviations from chemical composition equilibrium.Finally, the specification of realistic boundary condition faces similar prob-lems as in the cathode region.

Charge carrier generation in the anode region may occur by two basicallydifferent ionization mechanisms, namely field ionization (F-ionization) andthermal ionization (T-ionization).

Field ionization seems to play an important role in low intensity arcswhere anode falls in the order of the ionization potential of the workingfluid have been observed. For high-intensity arcs which are of interest in thecontext of this chapter, the anode falls are substantially lower (a few volts oreven negative). For such arcs thermal ionization is the governing ionizationmechanism. Electrons in the high energy tail of the Maxwellian distributionare responsible for ionization.

The attachment of the arc at the anode surface may occur diffusely as wellas severely constricted (spot). This fact will be further discussed in Section V.

Similar as in the case of a constricted attachment at the cathode, con-striction of the arc in front of the anode will give rise to the formation of ananode jet as illustrated in Fig. 1 [4]. In this configuration the axis of thecathode is parallel to the surface of a plane anode so that the cathode jetdoes not impinge on the anode. The deflected cathode jet provides evidencethat there must be an appreciable constriction of the anode attachment. Anyconstriction of the current path leads to the previously described pumpingaction which results in this case in an anode jet which causes the observeddeflection of the cathode jet from the anode surface. The relative strength ofthe two jets determines the angle of deflection.

In a free-burning arc configuration the cathode jet is able to providea continuous flow of hot plasma into the anode region reducing in this waythe necessity of heat generation by the arc itself. The influence on the anodicarc attachment has been studied by Sanders et al. [7] using a transferred arcstabilized by a water-cooled segmented tube. For an atmospheric pressureargon arc, with an i.d. of the stabilized channel of 10mm, and an arc currentof approximately 300A, a diffuse arc attachment was obtained as shown inFig. 2b. Under such conditions, known as the cathode jet dominated (CJD)anode region, the current densities at the anode were in the range of106–107A/m2 [8].


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The mechanism of constricted anode arc attachment called anode jetdominated mode (AJD) (see Fig. 2a) is related to the cooling of the anoderegion. It is well known that the arc column constricts more and more as theradial heat losses increase. Simultaneously, the heat dissipation in the arccolumn increases or, at a given arc current, the field strength in the arccolumn rises. The described effect in the anode region occurs if the influenceof the cathode jet on this region is strongly reduced or entirely eliminated.The relatively low temperature in the vicinity of the anode induces, asa primary effect, a certain constriction which, however, is always accom-panied by the already mentioned pumping effect. The cold gas adjacent tothe anode surface is accelerated toward the center of the arc and to a certaindegree ingested into the arc, reducing its diameter further, according to this

FIG.2. Anode jet dominated (AJD) and cathode jet dominated (CJD) mode of anode arc

attachment [7].

FIG.1. Interaction of cathode and anode jet in a high-intensity arc [4].


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additional heat removal mechanism. A stronger constriction leads to highervelocities of the cold gas which, in turn, constricts the arc even more. Whilethere seems to be no bound for this process which may be termed a ‘‘flowinduced thermal pinch’’, the increase of heat dissipation in conjunction withheat conduction in radial direction counterbalances the constriction due tothe induced gas flow, establishing a steady state situation. Owing to the arcconstriction in front of the anode, the current densities, at the anode endof the transition region (constriction region) are substantially higher than inthe arc column. This is accompanied by a corresponding increase of the fieldstrength and the plasma temperature in the constriction region. There isevidence that the steep gradients of the plasma parameters in the constric-tion zone are responsible for strong deviations from LTE. Since the arcattachment at the anode may be sharply constricted, the correspondingcurrent densities may be as high as 107–109A/m2.

When the heat fluxes imposed on the anode result in anode evaporation,the behavior of the arc may markedly change, depending on the type ofattachment. In the case of CJD attachment, the anode vapor (in most casescopper) does not readily mix with the plasma gas and close to the anodesurface an almost pure copper plasma has been found [9] with temperatureswhich may be quite different from those of the argon plasma column [10].In the case of AJD attachment the copper vapor from the anode mixesreadily with the plasma forming gas [11], resulting in a modification of thearc voltage. The increase of the electrical conductivity of the plasma bythe metal vapor results in a voltage decrease across the arc, which, however,is partially compensated by the increase of the electric field resulting fromthe added cooling of the arc imposed by radiation from the metal vapor.

III. Thermodynamic and Transport Properties Relevant to Thermal Arcs

A prerequisite for any modeling of plasma and plasma systems is theavailability of a database, containing both thermodynamic and transportproperties.

In this section, a brief overview of such properties will be presented forboth equilibrium and non-equilibrium plasmas with reference to more de-tailed treatments of this subject.

A. EQUILIBRIUM PROPERTIES

In contrast to non-equilibrium plasmas, calculations of plasma propertiesunder LTE conditions are rather straightforward, because both electronsand heavy particles have the same temperature and this temperature


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determines the plasma composition. Plasma composition for a given plasmagas or gas mixture is a prerequisite for calculating plasma properties,because these properties depend on the plasma composition.

1. Plasma Composition

Considering the simple case of a monatomic plasma gas (such as argon)heated to temperatures which preclude second or higher ionization stages,the plasma is composed of electrons, singly ionized atoms, and neutralatoms. Both ions and neutral atoms may be in the ground state or in excitedstates. In this case the plasma composition is described by a set of threeequations: the Eggert-Saha equation, Dalton’s law, and the condition forquasineutrality of the plasma, i.e.

neni

n¼ 2Qi

Q

2pmekT

h2

� �3=2

exp � Ei

kT

� �(10)

p ¼ ðne þ ni þ nÞkT (11)

ne ¼ ni (12)

In the Eggert-Saha equation (10), ne is the electron number density, and niand n represent ion and neutral number densities, respectively. Qi and Q arethe partition functions (p.f.) of the ions and neutrals, respectively, h isPlanck’s constant, and Ei represents the ionization energy. The p.f.s (or sumover all states) are given by

Qi ¼Xs

gi;s expð�Ei;s=kT Þ

Q ¼Xs

gs expð�Es=kTÞ ð13Þ

where gi,s and gs are the statistical weights of the energy levels of the ionsand neutrals, respectively, and Ei,s and Es are the corresponding energylevels of their excited states. The equations for the p.f.s imply that thepopulations of the excited states follow a Boltzmann distribution, which isone of the requirements for LTE.

The Eggert-Saha equation can be derived from thermodynamic principles(minimization of Gibbs free energy), and therefore it can be considered asa ‘‘mass action law’’ for the ionization process. It should be pointed out thatthe ionization energy Ei requires a correction term,�dEi, which accounts forthe lowering of the ionization energy due to the electric microfields in


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a plasma. These microfields are primarily a function of the charged particledensities.

For a given pressure, Eqs. (10)–(12) permit the calculation of the plasmacomposition as a function of temperature. Since the previously mentionedionization energy correction term is primarily a function of the electron(or ion) density, a few iterations are necessary to calculate ne(T) ¼ ni(T) andn(T). Figure 3 [12] shows, as an example, the composition of a thermalargon plasma at a pressure of 100 kPa. Since the pressure is kept constant,the total particle number density nt ¼ ne+ni+n decreases with increasingtemperature.

If a plasma is generated from a molecular gas (e.g. nitrogen), the numberof possible species comprising the plasma will be increased due to the pres-ence of molecular species. The chemical processes that may occur in theplasma will include dissociation of molecules into atoms and ionizationof some atoms. The formation of molecular ions will be neglected. The

FIG.3. Composition of an argon plasma at p ¼ 100kPa [4].


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dissociation process in a nitrogen plasma

N22NþN

can be described by an equation similar to the Eggert-Saha equation, i.e. themass action law for the dissociation process. Taking dissociation, ionization,and the presence of additional species into account, the composition of thenitrogen plasma can be calculated. The results for a nitrogen plasmaat p ¼ 100 kPa are shown in Fig. 4 [12]. For T4104K, nitrogen moleculesare no longer present due to dissociation, and ionization of nitrogen atomsreaches a peak around T ¼ 1.5� 104K. For temperatures T42� 104K, theplasma is, in practical terms, fully ionized, i.e. the number density of atomsbecomes negligible.

Similar calculations are feasible for plasmas generated from more com-plex molecules and from gas mixtures. As an example Fig. 5 [12] shows thecomposition of an air plasma at 100 kPa and for temperatures up to14,000K. Although there are only a few species present at room temperature(N2, O2, Ar), the complexity of the plasma composition increases withincreasing temperature, due to the formation of new species by chemicalreactions.

FIG.4. Composition of a nitrogen plasma at p ¼ 100kPa [12].


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2. Thermodynamic Properties

The thermodynamic properties of plasmas include the mass density, theinternal energy, the enthalpy, the specific heat, and the entropy. In addition,there are derived thermodynamic functions: the Helmholtz function (freeenergy) and the Gibbs function (free enthalpy or chemical potential).

The mass density r follows directly from the plasma composition as

r ¼Xr

nrmr (14)

where nr refers to the number density of the various species present in theplasma and mr represents the corresponding mass.

As an example, Fig. 6 [12] shows the mass density of a nitrogen plasmaat p ¼ 100 kPa. Similar calculations can be performed for more complexplasmas, including plasmas produced from gas mixtures.

The other thermodynamic functions, including the derived functions, canbe calculated from the p.f.s, which play a crucial role in the evaluationof thermodynamic functions. For this reason, the evaluation of p.f.s will bebriefly discussed, along with the underlying basic assumptions for theirderivation.

a. Partition Functions. The partition functions establish the link betweenthe coordinates of microscopic systems and macroscopic thermodynamicproperties.

FIG.5. Composition of an air plasma at p ¼ 20 kPa [12].


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In general, the p.f. of a particle can be expressed as

Q ¼Xs

gs expð�Es=kTÞ (15)

where Es represents all forms of energy that a particle can assume and gsaccounts for the degeneracy or statistical weight of each energy level.

It is customary to divide the energy of a particle into translational energy(Es, tr) and internal energy (Es, int), i.e.

Es ¼ Es;tr þ Es; int (16)

These energies are associated with the corresponding translational andinternal degrees of freedom of a molecule. The latter include electronicexcitation, rotation, vibration, nuclear spins, and chemical reactions. In theBorn-Oppenheimer approximation that is valid for gases and plasmas,the total internal energy of a molecule can be expressed as the sum of all thepreviously mentioned energies. Thus the total partition function Qt of a

FIG.6. Mass density of a nitrogen plasma at p ¼ 100 kPa [12].


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molecule can be expressed by a simple product

Qt ¼ Qtr �Qrot �Qvib �Qel �Qnucl �Qch (17)

where the individual p.f.s represent translational, rotational, vibrational,electronic, nuclear, and chemical contributions, respectively.

The translational p.f. can be obtained by integration over all spatial andmomentum coordinates of a molecule resulting in

Qtr ¼V

h3ð2pmkTÞ3=2 (18)

where V is the volume of the system and m the mass of the molecule.The evaluation of the internal p.f. for atoms is rather straightforward,

because atoms do not have rotational and vibrational degrees of freedomand the chemical contribution is the ionization process with a single energylevel Ei–DEi. Therefore, the p.f. of an atom can be expressed as

Qt ¼V

h3ð2pmkTÞ3=2 �Qel �Qnucl � exp½�ðEi � DEiÞ=kT � (19)

where

Qel ¼Xs

gs expð�Es=kTÞ (20)

accounts for electronic excitation. Qnucl is associated with the spin of theatomic nucleus. Even at the highest arc temperatures, atomic nuclei are notexcited, i.e. only those nuclei which have a spin, is, in the ground state needto be considered. With the unit of spin is ¼ h/2p, the nuclear p.f. can beexpressed by

Qnucl ¼ 2is þ 1 (21)

for the nuclei of H, is ¼ 1/2, for He, is ¼ 1/2, for 0, is ¼ 0, for Al, is ¼ 5/2,etc. [13]. As an example, Fig. 7 shows the internal p.f.s of nitrogen atomsand ions [12].

According to Eq. (17), there are additional contributions to the total p.f.in the case of molecules, i.e. Qrot, Qvib, and Qch.

The classical rotational p.f. for diatomic molecules may be written as[12,13]

Qrot ¼8p2IkT

kh2(22)


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where I is the moment of inertia of the molecule and k is the symmetrynumber. For non-symmetric molecules (NO, HCl, etc.) k ¼ 1 and for sym-metric molecules (N2, O2, etc.) k ¼ 2. For polyatomic molecules, thesituation is more complex [13].

The vibrational contribution to the total p.f. of a diatomic molecule maybe written as

Qvib ¼ expð�hn=2kTÞ1� expð�hn=kTÞ (23)

provided that the vibration may be treated as a harmonic vibration (lowamplitude). The frequency, n, refers to the fundamental vibration frequency.

For the more complex situation of large vibrational amplitudes (as themolecule approaches dissociation) and for polyatomic molecules, the readeris referred to the literature [12,13].

Finally, the contribution of Qch can be written as

Qch ¼ expð�Ech=kT Þ (24)

where Ech is the dissociation energy in the case of dissociation and theionization energy for ionization.

FIG.7. Partition functions of nitrogen atoms and ions [12].


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In general, the translational contribution to the total p.f. of a moleculeor atom is by far the largest contribution. Among the contributions to theinternal p.f. of a molecule, the rotational and vibrational contributionsdominate.

As previously mentioned, the internal energy, enthalpy, specific heat,entropy, Helmholtz function, and Gibbs function of a plasma can be cal-culated from the corresponding p.f.s and the previously discussed plasmacomposition. The derivation of these expressions will not be reiterated here.These derivations can be found in text books as, for example, in Refs.[12–14].

In the following, some typical examples of some thermodynamic prop-erties will be shown and discussed. Extensive tables of such properties maybe found in Ref. [12].

b. Internal Energy and Specific Heat for Constant Volume. Based on the p.f.,the internal energy per mole may be expressed by

U ¼ RT2 @ lnQt

@T

� �V

(25)

where R is the universal gas constant (R ¼ 8.315 kJ/molK). As an exampleFig. 8 shows the internal energy of a nitrogen plasma at p ¼ 100 kPa. Dis-sociation and ionization lead to ‘‘humps’’ of the internal energy whichis even more pronounced for the specific heat at constant volume, whichfollows from the internal energy as

Cv ¼ @U

@T

� �V

(26)

Figure 9 shows a graph of the behavior of Cv for a nitrogen plasma ata pressure of 100 kPa. Pronounced maxima around 7000K and around15,000K account for dissociation and ionization, respectively.

c. Enthalpy and Specific Heat at Constant Pressure. By definition the enthalpyis

h ¼ U þ pV (27)

where p may be expressed by

p ¼ RT@ lnQt

@V

� �T

(28)


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Therefore the enthalpy per mole is

h ¼ RT@ lnQt

@ lnT

� �V

þ V@ lnQt

@V

� �T

� �(29)

Figure 10 [12] shows the enthalpies of two monatomic plasma gases as wellas those for plasmas generated from diatomic molecular gases. In contrast tomonatomic plasma gases, molecular gases show a pronounced ‘‘shoulder’’around the dissociation temperature: The fact is even more pronounced for cpwhich is given by

cp ¼@h

@T

� �p

(30)

Figure 11 [12] which shows cp for nitrogen at 100 kPa with and without(‘‘frozen’’) chemical reactions. The first maximum around 7000K corre-sponds to dissociation, the second maximum close to 15,000K indicatesfirst ionization of the nitrogen atoms, and the third maximum accounts forsecond ionization. These peaks indicate that the capacity of the plasmafor storing energy (dissociation and ionization energy) is substantially

FIG.8. Internal energy of a nitrogen plasma at p ¼ 100kPa [12].


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FIG.9. Specific heat at constant volume for a nitrogen plasma at p ¼ 100 kPa [12].

FIG.10. Enthalpy of various gases at p ¼ 100 kPa [12].


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enhanced. Because of the strong contributions of chemical reaction to thespecific heat, it is customary to separate these contributions from all othercomponents of the specific heat (‘‘frozen’’ chemistry) so that the total specificheat can be expressed by

cp ¼ cpf þ cpr (31)

where cpf is the ‘‘frozen’’ part and cpr the reactive contribution to the specificheat. For the previously shown enthalpies of various plasma gases (Fig. 10),the corresponding specific heats are shown in Fig. 12. Again, the moreor less pronounced peaks are an indication of chemical reactions in theplasma. Examples of enthalpies of gas mixtures which are frequently used inapplications (e.g. in plasma spraying) are shown in Figs. 13 and 14 forp ¼ 100 kPa [12]. It is obvious that the addition of H2 or He to argon leads toenhanced enthalpies.

The behavior of the enthalpies and of the specific heats at different pres-sures are illustrated for the case of dry air in Figs. 15 and 16 [12], respec-tively. As the pressure increases, the enthalpies decrease at highertemperatures due to chemical reactions (Fig. 15). These reactions requiremore energy at higher pressures. Figure 16 shows that the peaks of thespecific heat shift to higher temperatures as the pressure increases and, at thesame time, the amplitude of the peaks decreases.

FIG.11. Specific heat at constant pressure for a nitrogen plasma at p ¼ 100 kPa [12].


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d. Entropy, Helmholtz Function, and Gibbs Function. The entropy of aplasma is directly related to its specific heat by

S ¼Z T

T0

cpðTÞT

dT (32)

where T0 is a reference temperature. As an example, Fig. 17 shows theentropy of dry air for three different pressures [12]. Similar as in the case ofthe enthalpy (Fig. 15), the entropy decreases with increasing pressure andthe slope of the curves changes due to chemical reactions. After internalenergy and entropy are known for a plasma, the Helmholtz function (or freeenergy) and the Gibbs function (or chemical potential) which are both

FIG.12. Specific heat at constant pressure of various gases at p ¼ 100 kPa [12].


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FIG.13. Enthalpy of argon/hydrogen (vol.%) mixtures at p ¼ 100kPa [12].

FIG.14. Enthalpy of argon/helium (vol.%) mixtures at p ¼ 100kPa [12].


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FIG.15. Enthalpy of dry air for different pressures [12].

FIG.16. Specific heat at constant pressure for dry air at different pressures [12].


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derived functions, can be easily established based on the definitions:

Helmholtz function : F ¼ U � TS (33)

Gibbs Function : G ¼ U � TS þ pV

¼ F þ pV ð34Þ3. Transport Properties

Many theoretical considerations in plasma physics are based on the as-sumption of uniform plasmas. It is, however, very difficult – if not impos-sible – to produce such uniform plasmas. Actual plasmas will revealgradients in such characteristics as, for example, particle number densities(n), applied electrical potentials (V), temperatures (T), and velocity compo-nents (vx). These gradients can be considered ‘‘driving forces’’ that give riseto fluxes. If the magnitude of these gradients remains within certain limits,there will be linear relationships between the driving forces and the fluxes.

Examples of such relationships are

Fick’s law ~G ¼ �D grad n (35)

FIG.17. Entropy of dry air for different pressures [12].


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Ohm’s law ~j ¼ �se grad V (36)

Fourier’s law ~q ¼ �k grad T (37)

and

~f x ¼ �m grad vx (38)

where ~G; ~j; and ~q refer to fluxes due to diffusion, electrical conduction, andthermal conduction, respectively. The term ~f x represents the frictional forcein x-direction. These linear relationships between fluxes and driving forcesincorporate the so-called transport coefficients, D, se, k, and m which areknown as the diffusion coefficient, the electrical conductivity, the thermalconductivity, and the viscosity, respectively.

Energy and momentum, for example, are transferred between particles bycollisions. Thus sufficient details of the collision processes between particlesmust be known in order to determine transport coefficients, because thesecoefficients depend on the interaction potentials or collision cross-sectionsbetween particles. Since molecules and atoms have complex electronicstructures, a theoretical description of the collisional interaction betweenparticles becomes a formidable task. In many cases, highly simplified models(considering, for example, a molecule or atom as a classic sphere) have beendeveloped for determining collision cross-sections. Unfortunately, measure-ments of such cross-sections at high temperatures are very difficult. There-fore, the experimental database is still rather limited. For this reason,transport coefficients, especially in more complex mixtures, are frequentlyunknown or suffer from a high degree of uncertainty. The problem is furtherexacerbated by deviations from LTE, which are frequently experiencedin actual plasmas. This situation will be further discussed in Section III.B.At this point it seems that the establishment of a reliable database to covera wide spectrum of gas mixtures including deviations from LTE will stillrequire many years.

Since a thermal plasma is a highly luminous body, radiative transportmust be considered. To determine radiative transport coefficients, the var-ious mechanisms responsible for the emission and absorption of radiation insuch plasmas must be taken into account. The spectrum from a typicalthermal plasma generated from a monatomic gas reveals continuous as wellas line radiation. Electronic transitions of excited atoms or ions from higherto lower energy states cause the emission of spectral lines. Since the electroninvolved in the radiation process remains in a bound state, radiation of thistype is also referred to as bound– bound radiation. The energy transport


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depends on the number and wavelength of the emitted lines, which in turndepend on the nature of the plasma fluid, in particular, on the number ofpossible species at a given temperature. The plasma of a given gas may bea ‘‘strong’’ or ‘‘weak’’ line radiator, depending on the plasma density andcomposition, which are functions of pressure and temperature.

Continuous radiation in a plasma under the previously specified condi-tions results from recombination of ions with electrons (free– bound radi-ation) and from bremsstrahlung (free– free radiation). In the processof radiative recombination, a free electron is captured by a positive ioninto a certain bound energy state and the excess energy is converted intoradiation. Recombination may occur into all possible energy levels of anion; thus the number of continuous spectra for a particular species coincideswith the number of electronic energy states of this ion. The entirefree–bound continuum consists, therefore, of a superposition of all contin-uous spectra emitted by the different species that exist in the plasma.

One type of bremsstrahlung has its origin in the interaction of free elec-trons with other charged particles, i.e. a free electron may lose kinetic energyin the Coulomb field of an ion, and this energy is readily converted intoradiation. Since both the initial and the final state of the electrons are freestates in which the electrons may assume arbitrary energies within theMaxwellian distribution, the emitted radiation is of the continuum type.The same holds for the interaction of neutral particles which also contributeto bremsstrahlung. Depending on the spectral range, the total radiationcontinuum, consisting of free–free and free–bound radiation, may dominatethe radiative balance or it may be negligible in thermal plasmas(pZ100 kPa). As an example, Fig. 18 shows the spectral emission coeffi-cient for an argon plasma at p ¼ 100 kPa and T ¼ 12,000K for wavelengthsfrom 0.03 to 25 mm [15]. In some wavelength intervals, continuum radiationdominates, in others line radiation makes a major contribution to the totalemission coefficient. If molecular species are present in the plasma,the spectrum will also contain radiation bands due to the excitation ofvibrational and rotational energy modes of molecules.

The total radiation originating from the various emission mechanisms justdescribed leaves the plasma without appreciable attenuation as long as theplasma can be considered optically thin. This assumption may fail for lineand band radiation, as well as for continuum radiation. Very strongabsorption occurs, for example, for resonance lines. In general, absorptioneffects become more pronounced as the pressure increases. Plasmas at veryhigh pressures become optically thick and may approach the radiationintensity of a blackbody radiator if the temperature is sufficiently high. Anargon arc, for example, will behave as a blackbody radiator in a certainwavelength range for pressures pZ104 kPa and temperatures T42� 104K.


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a. Diffusion Coefficients. Imposing a density gradient on a gas consisting ofidentical molecules or atoms, there will be diffusion of particles from high-density to low-density regions, until equilibrium is established. This processis known as self-diffusion and the corresponding diffusion coefficient can beexpressed by [13]

D ¼ �vl3

(39)

where �v is the average thermal velocity of the particles and l is their mfplength. Besides ordinary diffusion (due to particle density gradients), diffu-sion coefficients have been defined due to pressure, temperature, and electricpotential gradients.

Ambipolar diffusion is another diffusion process which plays an impor-tant role in plasmas. Charged particle density gradients are particularlysteep close to plasma confining walls. Considering a one-dimensionalsituation in which a plasma borders a wall, the gradients of electron and iondensity in the vicinity of the wall drive electron and ion fluxes toward the

FIG.18. Spectrum of a pure argon plasma at 1 atm and 12,000K for the wavelength range

0.03–25mm in terms of the spectral emission coefficient [15].


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wall, but the electron flux initially exceeds the ion flux because of the higherelectron mobility. Since the wall is assumed to be isolated (no net currentflow), it will acquire a negative potential, producing an electric field, Ex, thatpoints toward the wall. This field subsequently balances electron and ionfluxes (electrons are retarded and ions are accelerated) and in a steady statesituation, electrons and ions reach the wall at the same rate and recombineon impact with the wall. In this case the wall serves as the third collisionpartner for three-body recombination.

Assuming that the plasma contains singly ionized species only (ne ¼ ni),the ambipolar diffusion coefficient can be expressed by [12]

Da ¼Demi þDime

mi þ me(40)

where Da is the ambipolar diffusion coefficient, De and Di are the diffusioncoefficients of electrons and ions and me and mi are the mobilities of electronsand ions, respectively.

With mi � me, the ambipolar diffusion coefficient reduces to

Da ¼ Di þmime

De (41)

And for kinetic equilibrium this equation reduces further to [12]

Da ¼ 2Di (42)

This relation indicates that in a plasma in which kinetic equilibriumprevails, the ions diffuse at twice the rate they would in the absence ofelectrons. This finding has important consequences for situations in whichheat transfer by diffusion of charged particles becomes significant. For themuch more complex situation of ambipolar diffusion in multi-componentthermal plasmas of arbitrary composition the reader is referred to theliterature [16].

The previously mentioned various diffusion processes are of particularinterest for mixtures of plasma gases. In the following, some examples willbe shown for binary mixtures of Ar with He [17]. Figures 19 and 20 showcalculated coefficients of the combined (Ar+He) ordinary diffusion, pres-sure diffusion, and temperature diffusion for five different plasma compo-sitions ranging from 1%He (99% Ar) to 99% He (1% Ar) [17]. As shown in[18,19], the magnitude of the diffusion coefficients for an Ar–He mixture ismuch larger than that of mixtures of argon with nitrogen, oxygen, and air,because the light helium diffuses much faster than nitrogen and oxygen(Fig. 21).


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b. Electrical Conductivity. The existence of charge carriers in plasmas leadsto substantial values of the electrical conductivities which are one of the keytransport coefficients for modeling of electric arcs.

Figure 22 shows the electrical conductivities for argon, nitrogen, hydro-gen, and helium plasmas for 100 kPa [12]. Since the electrical conductivity,se, depends primarily on the electron density which, in turn, depends on the

FIG.19. Combined ordinary diffusion coefficient of mixtures of argon and helium: –– 99%

argon, 1% helium; – – –75% argon, 25% helium; – � – 50% argon, 50% helium; –– - –– 25%

argon, 75% helium; y 1% argon, 99% helium. Percentages refer to mole fractions [17].

FIG.20. Combined pressure diffusion coefficient of mixtures of argon and helium. Symbols

are as in Fig. 19 [17].


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ionization potential of the various species for a given temperature, it is notsurprising that helium with the highest ionization potential (24.5V), requirestemperatures in excess of 10,000K to reach significant values of se.

Figure 23 shows se for Ar–He mixtures at p ¼ 100 kPa [12]. Since sepne,ionization of argon (15.8V) dominates se, even for larger fractions of He inthe mixture. Only for 100% He, se drops substantially, because of the highionization potential of He.

Small amounts of metallic contaminants from the electrodes of arcplasma devices may exert a strong influence on the electrical conductivityof such plasmas as shown in Fig. 24 for the case of an Ar plasma con-taminated by Cu [12]. Because of the low ionization potential of metalatoms, the electrical conductivity of such plasmas is shifted to lowertemperatures.

c. Thermal Conductivity. If qx is the heat flux due to a temperature gradientin x-direction, the thermal conductivity k may be defined as

qx ¼ �k@T

@x(43)

In general, k may be expressed as the sum of three terms:

the translational contribution, ktr,the reactional contribution due to chemical reactions, kR,

FIG.21. Combined temperature diffusion coefficient of mixtures of argon and helium.

Symbols are as in Fig. 19 [17].


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FIG.22. Electrical conductivity of various gases at p ¼ 100 kPa [12].

FIG.23. Electrical conductivity of Ar/He mixtures (vol.%) at p ¼ 100 kPa [12].


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and the contribution from internal degrees of freedom, kint, i.e.

k ¼ ktr þ kR þ kint (44)

The translational contribution includes both electrons and heavy parti-cles. As an example Fig. 25 shows the total thermal conductivity of argon atatmospheric pressure with its individual contributions [18] and Fig. 26compares the results of [18] with those of other authors [20–24]. With ex-ception of the data from Kulik [21,24], there is excellent agreement betweenthese data.

Using molecular gases as plasma gases, the behavior of the thermalconductivity becomes more complex due to additional chemical reactions(dissociation). As an example, Fig. 27 shows the total and the individualcontributions to the thermal conductivity of nitrogen at p ¼ 100 kPa [12].

FIG.24. Electrical conductivity of an argon plasma containing small amounts of Cu

(mol.%) at p ¼ 100kPa [12].


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FIG.25. Components of the thermal conductivity of argon: –– total; – – – heavy particle;

–– –– electron; – � – internal; y reactional thermal conductivity [18].

FIG.26. Thermal conductivity of argon [18];WAubreton et al. [20];}Collins and Menard

[22]; � Devoto [23]; J Kulik [21,24].


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Both, Figs. 25 and 27 show that chemical reactions lead to pronouncedpeaks in the thermal conductivity and heavy particles make only minorcontributions, whereas electrons will dominate at higher temperatures(beyond 2� 104K). In the case of molecular gases, the contribution due tointernal degrees of freedom is negligible.

The calculation of thermal conductivities and of other transport coeffi-cients depends very sensitively on the interaction potentials or collisioncross-sections. Depending on the choice of interaction potentials, the trans-port properties may show a large variation as illustrated, for example,in Fig. 28 [12,25,26] such variations will have a strong impact on modelingof electric arcs to be described in Section IV.

There is a wealth of data in the form of tables and in graphical formavailable for all transport properties, not only for thermal conductivities.This will be discussed in more detail at the end of Section III.A.

d. Viscosity. The transport of momentum in a gaseous medium is governedby the viscosity, m. Simple kinetic theory predicts the viscosity of an

FIG.27. Individual contributions and total thermal conductivity of a nitrogen plasma at

p ¼ 100kPa [12]; kint: contributions due to internal degrees of freedom of nitrogen molecules;

khtr, translational contributions of heavy particles; ketr, contributions of electrons; kR, contri-butions due to chemical reactions; and ktotal, total thermal conductivity.


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ordinary gas consisting of identical molecules of mass, m, as

m ¼ 1

3

m �v

s(45)

where �v is the average velocity of the molecules and s is the collision cross-section. For plasmas, the situation is more complex due to the presenceof charged particles. In the following, the general behavior of the coefficientof viscosity will be discussed for an arc operated with a molecular gasat p ¼ 100 kPa. In the arc fringes where temperatures are below the disso-ciation temperature, the viscosity will be governed by collisions betweenmolecules and it will increase with increasing temperature, because �v � T1=2.In arc regions where the temperature exceeds the dissociation temperature,collisions among atoms determine the viscosity which, again, increases withincreasing temperature. As the arc temperature surpasses the ionization

FIG.28. Thermal conductivity of a hydrogen plasma at p ¼ 100kPa for two different val-

ues of the H–H interaction potentials [12].


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temperature (for hydrogen, nitrogen, and argon typically around 10,000K),ions will be produced and the long range Coulomb forces lead to a drasticincrease of the collision cross-section, leading to a rapid decrease of theviscosity as shown in Fig. 29 [12]. Figure 30 shows the behavior ofthe viscosity in a binary mixture (Ar/H2) [12]. Since the ionization potentialsof the argon and hydrogen atom are rather close, the peak of the curves forvarious compositions remains close to 10,000K. Another example in Fig. 31[12] shows the behavior of the viscosity for different pressures in dry air.Since ionization requires higher temperatures as the pressure increases, theviscosity shows a corresponding shift of the maxima.

Figure 32 compares the results of various authors [12,27–33] for the vis-cosity of hydrogen. In general, there is reasonable agreement among thevarious authors with exception of the values around the maximum. Thisdeviation is primarily due to the use of different collision cross-sections bydifferent authors. Over the years, more accurate values of these cross-sectionsbecame available and it seems that the data from [27] are most up-to-date.

e. Radiative Transport. Radiation emitted by plasmas has been extensivelyused for diagnostic purposes. Over the past 40 years plasma spectroscopyhas become a highly sophisticated and powerful diagnostic tool that playsan extremely important role in plasma physics and technology [34–39]. Asa simplification for modeling, thermal plasmas have been frequently treatedas optically thin, even at higher pressures. However, the significance of

FIG.29. Viscosity of various gases at p ¼ 100 kPa [12].


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reabsorption of radiation in the plasma must be recognized as an importantmechanism that may affect other plasma transport properties, particularlythe thermal conductivity. Figure 33, which shows a schematic diagram ofthe radiative balance in high-pressure argon arcs [12], illustrates theseeffects. At low pressure and/or temperatures, the contribution of radiationto the energy balance is negligible (region I). Since only ohmic heating and

FIG.30. Viscosity of an Ar/H2 mixture at p ¼ 100kPa [12].

FIG.31. Viscosity of dry air for different pressures [12].


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0 10000 20000 30000temperature (K)

0.00000

0.00002

0.00004

0.00006

0.00008

0.00010

visc

osity

(kg

m–1

s–1)

FIG.32. Viscosity of hydrogen. –– Murphy [27]; y Boulos et al. [12]; –– –– Aubreton and

Fauchais [28]; – – – Baronnet et al. [29]; – � – � – Capitelli et al. [30]; � Devoto [31]; & Kovitya

[32]; J Belov [33].

FIG.33. Radiative properties of high-pressure argon arcs [12].


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heat conduction are involved, the resulting temperature profiles are rela-tively narrow. As the temperature increases, radiation can no longerbe neglected, particularly at higher pressures. In general, radiation forwavelengths l42000 A can be considered optically thin, whereas radiationfor lo2000 A (UV) will be partially or totally absorbed in the plasma,depending on the mfp length of the photons (lph). For UV radiation, lph isinversely proportional to the absorption coefficient, which, in turn, is pro-portional to the number density of the atoms. Therefore, lph decreases withincreasing pressure for a given temperature. At pressures p4300 kPa andtemperatures To15,000K, lph � R (arc radius), i.e. UV radiation is im-mediately reabsorbed without contributing to the energy transport in the arc(region II in Fig. 33). In this situation the energy balance of the arc isdetermined by ohmic heating, heat conduction, and optically thin radiation.

At higher temperatures (T415,000K) in the same pressure region(pZ300 kPa) and lphoR, the transport of UV radiation can be describedby ordinary diffusion of radiation (region III). In this region, the energybalance is governed by ohmic heating, optically thin radiation, and a mod-ified heat conduction term that includes radiative transport (emission andreabsorption of UV radiation).

As the temperature further increases (or at relatively low pressures)lph�R and radiative transport can no longer be described by local prop-erties in the arc. An integral expression is needed that depends not only onlocal temperature and pressure in the arc but also on the field strength. Theresulting radiation term is denoted as ‘‘far-reaching diffusion of radiation’’(region IV), in contrast to the ordinary diffusion of radiation. Optically thinradiation as well as the previously described far-reaching radiation exerta strong influence on the temperature profile of arcs. Radiative energytransport toward the arc fringes enlarges the arc diameter, and in the caseof confined (wall-stabilized) arcs, this energy transport leads to almost rec-tangular shapes for the temperature profiles.

It is interesting to note that for a given pressure, energy transport byradiation increases sharply with temperature. At axis temperatures of26,000K, for example, approximately 95% of the energy input to the arccore of an atmospheric pressure nitrogen arc is dissipated by radiation [40].For temperatures above 13,000K, the emission and reabsorption of radi-ation play a governing role in the energy transport within atmosphericpressure nitrogen arcs [41]. A similar situation is to be expected for otherworking gases or gas mixtures, especially at higher pressure levels [42].

Few measurements of radiation properties at high temperatures have beenpublished. We present here results for three gases, nitrogen, oxygen, andargon, of the total intensity (integrated over the wavelength range from 200to 6000 nm) as a function of temperature, measured using a wall constricted


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arc [43]. Figures 34–36 show the experimental results as well as some com-parison with theoretical results. The higher predicted values for nitrogenand oxygen are attributed to partial absorption which has not beenconsidered in the model.

In general, the prediction of radiative properties of thermal plasmas israther time-consuming, because of the large number of spectral lines whichhave to be considered. A rigorous method has been applied [15] to calculateradiative properties including line radiation, free–bound and free–free

FIG.34. Total radiation from a nitrogen plasma at 1 atm including estimates for the con-

tinuum and line contribution for l4200nm [43].


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continuum for both ions and neutral particles. The various broadeningmechanisms of spectral lines have been included in this analysis. As anexample, Fig. 37 shows the net emission coefficients for an argon plasmawhere L ¼ 0 refers to the optically thin case (no absorption) [15]. The netemission coefficient represents the radiative source term commonly used inthe energy equation, and it is defined as the difference between the radiativepower emitted and absorbed at a given location in a homogeneous,isothermal plasma of a given configuration [15]. It is measured in units of

FIG.35. Total radiation from an oxygen plasma at 1 atm including estimates for the con-

tinuum and line contributions for l4200nm [43].


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W/m3ster. As the optical path length, L, increases, the net emission coeffi-cients drop due to increasing absorption. Below 5000K, the emission froman argon plasma becomes negligible. Figure 38 shows for an optically thinargon plasma that the majority of the radiant energy is contributed byspectral lines with wavelengths below 0.2 mm [15]. Other contributions to thenet emission coefficient are also included in this graph.

There is a drastic change of the contributions of the various emissionmechanisms to the net emission coefficient of an optically thin argon plasmaif line radiation in the vacuum UV (o0.2 mm) is disregarded. Figure 39 [15]shows that line radiation does no longer dominate over the entire temper-ature region. This is a clear indication of the importance of line radiation inthe vacuum UV (o0.2 mm) in a thermal argon plasma.

FIG.36. Total radiation from an argon plasma at 1 atm including estimates for the con-

tinuum and line contributions for l4200nm [43].


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Figure 40 [12] shows a typical example of the net emission coefficient ofa pure nitrogen plasma of p ¼ 100kPa, where R ¼ 0 refers to the optically thincase. The net emission coefficient for R40 reflects the effect of absorption inthe plasma of various thicknesses. Similar as in the case of argon, a largefraction of the radiation is absorbed over a relatively short distance (RE1mm).

FIG.37. Net emission coefficients for a pure argon plasma at 1 atm for different geomet-

rical path lengths for the wavelength range 0.03–25mm [15].

FIG.38. Fractional contributions of the different emission mechanisms and wavelength

regions to the wavelength integrated emission coefficient for a pure argon plasma at 1 atm for

the wavelength range 0.03–25mm [15].


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Frequently, contamination of plasmas with electrode vapor and/ormetallic vapor from plasma processing is unavoidable. As an example,Fig. 41 shows the net emission coefficient for a 99% Ar/1% Cu plasmaat 100 kPa [15] and the results of Menart are compared with those of Gleizeset al. [44]. There is reasonable agreement between these results although themethods which have been used for calculating these emission coefficients arequite different. L ¼ 0 in Fig. 41 refers to the optically thin case. Again, thereis a substantial drop of the net emission coefficient for a larger thickness of0.1–1mm.

Figure 42 shows the optically thin total emission coefficient for differentlevels of Fe content in an argon plasma [12]. At low temperatures(To6,000K), there is a drastic increase of the total emission coefficienteven at rather low levels of Fe content (0.001%). The iron atom has manylow-lying energy levels which are excited at relatively low temperatures,giving rise to strong emission. At higher temperatures, the relative contri-bution of radiation from Fe diminishes and above 12,000K the total emis-sion coefficient is dominated by radiation from argon, even at high levels ofFe content in the plasma.

The last figure in this section (Fig. 43) refers to the effect of absorptionin a 99% Ar/1% Fe plasma at 100 kPa [12]. A layer thickness of 1mmleads to a drastic drop of the total emission coefficient at lower temper-atures (o8,000K) compared to the optically thin limit. Above 12,000K,there is a relatively small effect of absorption on the total emissioncoefficient.

FIG.39. Fractional contributions of the different emission mechanisms to the wavelength

integrated emission coefficient for a pure argon plasma at 1 atm for the wavelength range

0.2–25mm [15].


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At the end of this section, it should be emphasized that there is a wealth ofequilibrium transport property data available in the literature. Ref. [12]provides data in table form as well as some typical data in graphical form.In addition, [12] lists references of earlier work (before 1993) in this field.

Transport coefficients of argon, nitrogen, oxygen, argon/nitrogen, andargon/oxygen plasmas are presented in [18], whereas [19] refers to air andmixtures of nitrogen/air, and oxygen/air. Transport coefficients of He and Ar/He plasmas are given in Ref. [17] and Ref. [27] shows data for hydrogen andargon/hydrogen plasmas. The cited references also list previous work onplasma transport properties, including comparisons with experiments.

B. NON-EQUILIBRIUM PROPERTIES

Deviations from LTE in atmospheric pressure, high-intensity arcs mayoccur in the arc fringes as well as in the electrode regions. Such deviations

FIG.40. Net emission coefficient of a nitrogen plasma column for various plasma radii for

p ¼ 100kPa [12].


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may be due to deviations from kinetic equilibrium (Te4Th) and/or devi-ations from chemical (or composition) equilibrium.

In the case of LTE, the plasma can be described by two parameters, i.e.the temperature (T) which is the same for all the species in the plasma, and

FIG.41. Comparisons of Menart’s methods of net emission coefficients [15] for a 99%

Ar–1% Cu, 100 kPa plasma to the theoretical results of Gleizes et al. [44] for the wavelength

range 0.03–25mm.

FIG.42. Total volumetric emission coefficient of an Ar/Fe plasma (optically thin) for

different mole percent of Fe for p ¼ 100 kPa [12].


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the pressure (p). For plasmas which deviate from kinetic equilibrium, threeparameters are required for describing the plasma, i.e. the electron temper-ature (Te), the heavy-particle temperature (Th), and the pressure (p). Theplasma composition follows in this case from a modified Saha equation fora two-temperature plasma [12].

The situation becomes more complex for plasmas which deviate bothfrom kinetic and chemical equilibrium. The monatomic plasma descriptionrequires in this case four parameters: Te, Th, p, and ne or Te, Th, ne and n,where n is the number density of neutral particles. Deviations from chemicalequilibrium are primarily driven by diffusion, i.e. they will appear in regionsof steep gradients. The fact that such gradients are a function of the arcgeometry (for example, extreme constriction of the arc) precludes a moregeneral treatment of this situation. Therefore, the following discussion ofnon-equilibrium properties will be restricted to two-temperature plasmaswhere the plasma composition can be still described by modified Sahaequations.

Considering the collisional energy exchange between electrons and heavyparticles in an arc results in the following equation for the relative differencebetween electron and heavy-particle temperatures [12]:

T e � Th

T e¼ 3pmhðleeEÞ2

32me32kT e

�2 (46)

FIG.43. Total volumetric emission coefficient of an Ar/Fe plasma (1mol% Fe) for differ-

ent plasma radii at p ¼ 100kPa [12].


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where mh and me refer to the mass of heavy particles and electrons, respec-tively; le is the electron mfp length, e the elementary charge, and E theelectric field strength in the arc. The term (leeE) represents the energy gainof electrons over one mfp, and as this energy gain surpasses the averagekinetic energy of electrons (3

2kT e), electron and heavy-particle temperature

separate. Since lep1/p, Eq. (46) shows that

T e � Th

T e/ E

p

� �2

(47)

depends very sensitively on (E/p), i.e. high values of E and/or low values of pencourage deviations from kinetic equilibrium. This criterion also explainswhy such deviations are more likely in the arc fringes rather than in the arccore. The electron density in the arc fringes is substantially smaller thanin the arc core and, therefore, le is much larger there, i.e. the collisionalcoupling between electrons and heavy particles is diminished in the arcfringes, resulting in substantial deviations from kinetic equilibrium.

For the derivation of Eq. (46), it has been assumed that all heavy particles(ions and neutrals) have the same temperature, Th. The same type ofassumption is applied for the pressure, i.e.

p ¼ nekT e þXi

nikTh (48)

where ne is the number density of electrons and ni represents neutral par-ticles as well as ions.

1. Plasma Composition of a Two-Temperature Plasma

As shown previously (Section III.A.1), calculations of the plasma compo-sition requires knowledge of the p.f.s which, in the case of two-temperatureplasmas, will depend on both Te and Th. Considering a plasma which containsmolecular, atomic, and ionic species as well as electrons, two differenttemperature regions may be specified, according to the prevailing chemicalreactions:

� A low temperature regime in which dissociation and recombination ofmolecular and atomic species dominate, respectively. For this case theinternal p.f. may be written as [12]

QintðTe;ThÞ ¼ QintðThÞ (49)

because these reactions are mainly caused by collisions among heavyparticles.


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� A higher temperature region in which ionization and recombinationbetween atomic ions and electrons becomes important. For this casethe internal p.f. may be approximated by [45]

QintðT e;ThÞ � QintðTeÞ (50)

Using these p.fs. the plasma compositions can be calculated from themodified Saha equations for two-temperature plasmas in combination withDalton’s law (Eq. (48)) and the condition of quasi-neutrality [12]. As anexample, Fig. 44 shows the number densities of argon atoms and ions(Ar+ ¼ ne) as function of the electron temperature at p ¼ 100 kPa and forvalues of Y(Y ¼ Te/Th) from 1 to 6 [45]. For Teo14,000K, the densityof argon ions (or electrons) fall below the equilibrium values (Y ¼ 1) but forTe414,000K they exceed these values [45,46].

Mixtures of argon with hydrogen as plasma gases are of interest for someapplications, because the addition of hydrogen leads to a substantialincrease of the plasma enthalpy. Figures 45 and 46 show examples of theplasma composition for argon/hydrogen (25/75%) mixtures at p ¼ 100 kPaand for Y ¼ 2 and 3, respectively [12]. For comparison, Fig. 47 shows thecorresponding equilibrium values (Y ¼ 1).

It should be pointed out that the approach used for generatingFigs. 44–46 is only valid for relatively small deviations from kinetic equi-librium (Yr3). For larger values of Y, a kinetic model must be used, taking

FIG.44. Number densities of Ar and Ar+ for a two-temperature plasma at p ¼ 100kPa

with Y as parameter [45].


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FIG.45. Number densities of an Ar/H2 mixture (75mol% of H2) at p ¼ 100 kPa for Y ¼ 2

[12].

FIG.46. Number densities of an Ar/H2 mixture (75mol% of H2) at p ¼ 100 kPa for Y ¼ 3

[12].


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all possible reactions into account [47]. The validity of the previousapproach has been confirmed from an Ar/H2 plasma for Yr3 [48].

In the case of a molecular plasma gas, there may be additional complex-ities due to non-equilibrium effects on the internal p.f.s of molecules.As pointed out previously, the p.f.s in the case of two-temperature plasmaswill depend both on Te and Th. In addition, they may also dependon rotational (Tr) and vibrational (Tv) temperatures [49,50]. As shown in[50], it may be assumed that the dominating rotational energy is the same asthat of the vibrational ground state (v ¼ 0). Based on this assumption, theplasma composition will depend on two parameters, i.e. Yv ¼ Tv/Th

and Y ¼ Te/Th. The effect of Yv on the plasma composition is shown inFigs. 48–50 [50]. The last figure refers to the equilibrium situation. A com-parison of Figs. 48 and 49 shows that an increase of the vibrational tem-perature from Yv ¼ 1 to Yv ¼ 2 has only a minor effect on the speciesdensities. In contrast, an increase from Y ¼ 1 (Fig. 50) to Y ¼ 2 (Figs. 48and 49) reveals a drastic change of the particle density distributions.

2. Thermodynamic Properties of Two-Temperature Plasmas

After determining the composition of two-temperature plasmas, the ther-modynamic properties can be calculated for different values of Y using thepreviously discussed p.f.s. In the following, some typical examples will beshown.

FIG.47. Number densities of an Ar/H2 mixture (75mol% of H2) at p ¼ 100 kPa for equi-

librium conditions (Y ¼ 1) [12].


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FIG.48. Number densities of a two-temperature nitrogen plasma at p ¼ 100 kPa for Y ¼ 2

and Yv ¼ 1 [50].

FIG.49. Number densities of a two-temperature nitrogen plasma at p ¼ 100 kPa for

Y ¼ Yv ¼ 2 [50].


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a. Enthalpy and Specific Heat. Figure 51 shows the enthalpy of a pure hy-drogen plasma as a function of Te with Y as parameter [12]. For equilibriumconditions (Y ¼ 1) and p ¼ 100 kPa, the change of enthalpy due to disso-ciation falls in the temperature range from 3000 to 4000K which is notcovered in this diagram. Since dissociation is primarily a function of theheavy-particle temperature, variations of the enthalpy with increasingY dueto dissociation become visible at higher values of Te. For Y ¼ 2, this changeoccurs at Te between 6000 and 8000K, and for Y ¼ 3 this change shifts tovalues of Te beyond 12,000K.

Figure 52 shows the enthalpy of a 50% Ar, 50% H2 mixture as a functionof Th and Y as parameter [49]. For this calculation it has been assumed thatthe rotational temperature of the H2 molecule is the same as the heavy-particle temperature and the excitation and vibrational temperature hasbeen equated with the electron temperature.

Figure 53 shows the enthalpy of a pure nitrogen plasma at p ¼ 100 kPa asa function of the heavy-particle temperature for both Y ¼ 1 and Y ¼ 2 [50].The latter with the vibrational temperature Tv of the nitrogen molecule as aparameter. Variations of this parameter exert only a minor effect on theenthalpy which is primarily due to enhanced ionization at higher electrontemperatures beyond Th ¼ 6000K [50].

FIG.50. Number densities of a nitrogen plasma at p ¼ 100 kPa for Y ¼ Yv ¼ 1 [50].


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FIG.51. Enthalpy of two-temperature hydrogen plasma at p ¼ 100kPa with Y as param-

eter [12].

FIG.52. Enthalpy of a two-temperature Ar/H2 mixture (50% Ar, 50% H2) at p ¼ 100 kPa

with Y as parameter and the assumption T rot ¼ Thtr and Tex ¼ Tvib ¼ Te [49].


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The specific enthalpy of a pure oxygen plasma at p ¼ 1 atm and with Y asparameter is shown in Fig. 54, but in this case as a function of Te [51]. WithincreasingY the curves shift to higher values of Te. This is especially visible inthe dissociation regime of the oxygen molecule. As expected, the specific heatat constant pressure reveals a similar behavior as shown in Fig. 55 for thesame oxygen plasma [51]. The shift of the curves to higher Te with increasingY is very obvious in the dissociation regime of the oxygen molecule.

As an example of a gas mixture, Fig. 56 shows the specific heat of a 50%Ar/50% H2 mixture as a function of Th with Y as parameter [49]. The sameassumptions as listed in Fig. 52 have been retained for this figure. Forequilibrium conditions (Y ¼ 1), there is only one peak in this graph close toTh ¼ 4000K which is due to dissociation of hydrogen. For Y ¼ 1.5, thereare two peaks with the second peak around Th ¼ 9500K which accounts forionization, because the corresponding electron temperature exceeds already14,000K. As Y further increases, the ionization peaks shift to lower valuesof Th with the electron temperature remaining at values around 15,000K.

Since the derivation of the specific heat follows directly from the enthalpyaccording to Eq. (30), the specific heat for other plasma gases and gasmixtures will not be further discussed.

b. Entropy, Helmholtz Function, and Gibbs Function of Two-Temperature

Plasmas. As an example Fig. 57 shows the entropy of an argon/hydrogenplasma (50% Ar, 50% H2) as a function of Th with Y as parameter [49]. The

FIG.53. Enthalpy of a two-temperature nitrogen plasma at p ¼ 100 kPa [50].


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same assumptions made for rotational and vibrational temperature in Figs.49 and 53 are retained for this case. The entropy increases substantially withincreasing Y as soon as ionization becomes important.

After enthalpy and entropy are known for a plasma, the Helmholtz andGibbs function which are both derived functions, can be easily calculated aspointed out in Section III.A.2. Therefore, these functions will not be furtherdiscussed.

3. Transport Properties of Two-Temperature Plasmas

a. Diffusion Coefficients for Two-Temperature Plasmas. Combined ordinarydiffusion coefficients in an Ar/He plasma have been calculated as a functionof Te at p ¼ 100 kPa for different Ar/He compositions and with Y asparameter [52]. These calculations have been based on plasma compositionsgiven in Ref. [53]. Figure 58 shows the combined ordinary diffusion coeffi-cient for different molar percentages of argon for a relatively small deviationfrom kinetic equilibrium (Y ¼ 1.5). The diffusion coefficient dependsstrongly on the percentage of argon because the degree of ionizationdepends on this percentage. Figure 59 shows the combined ordinary diffu-sion coefficient for a fixed Ar/He composition (50% by mole) for different

FIG.54. Enthalpy of a two-temperature oxygen plasma at p ¼ 1 atm with Y as parameter

[51].


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FIG.55. Specific heat at constant pressure for a two-temperature oxygen plasma at

p ¼ 1 atm with Y as parameter [51].

FIG.56. Specific heat at constant pressure for a two-temperature Ar 50%/H2 50% mixture

at p ¼ 100 kPa with Y as parameter and the assumption; T rot ¼ Thtr; Tex ¼ Tvib ¼ Te [49].


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values of Y. The diffusion coefficient drops substantially as Y increases.Figure 60 shows the combined thermal diffusion coefficients for the sameparameters as in Fig. 59 [52]. Thermal diffusion refers to diffusion fluxesdriven by temperature gradients with f as the thermal diffusion coefficient.

FIG.57. Entropy of a two-temperature Ar 50%/H2 50%mixture for p ¼ 100kPa withY as

parameter and the assumption T rot ¼ Thtr; Tex ¼ Tvib ¼ Te [49].

FIG.58. Combined ordinary diffusion coefficient at p ¼ 100 kPa, Y ¼ 1.5 for an Ar/He

mixture with the molar percentages as parameter [52] (compositions according to [53]).


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Similar as in Fig. 56, the thermal diffusion coefficient drops sharply as Yincreases.

The most important contribution to thermal diffusion in a pure oxygenplasma is due to singly ionized oxygen atoms. Figure 61 shows the correspond-ing diffusion coefficient as a function of Te withY as parameter. Again, there isa substantial drop of the thermal diffusion coefficient as Y increases [51].

FIG.59. Combined ordinary diffusion coefficient at p ¼ 100 kPa, for an Ar/H2 mixture

(50% by mole) with Y as parameter [52] (composition according to [53]).

FIG.60. Combined thermal diffusion coefficient at p ¼ 100kPa, for an Ar/H2 mixture

(50% by mole) with Y as parameter [52] (composition according to [53]).


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b. Electrical Conductivity of Two-Temperature Plasmas. The electrical con-ductivity of a two-temperature argon plasma at p ¼ 1 atm is shownin Fig. 62 [46] as a function of Te with Y as parameter. For temperaturesbelow 10,000K (low degree of ionization), the electrical conductivitydecreases substantially with increasing Y, but for temperatures exceeding15,000K, there is little dependence on Y. For high degrees of ionization(Te415,000K), the electrical conductivity is only a function of Te.

The electrical conductivity in a pure two-temperature oxygen plasmareveals similar trends as shown in Fig. 63 [54].

c. Thermal Conductivity of Two-Temperature Plasmas. As pointed out inSection III.A.3 (LTE plasmas), the reactive part of the thermal conductivitywill play a dominating role in temperature regions where these reactionsoccur. The same holds for two-temperature plasmas, but the peaks dueto these reactions may shift to higher values of Te as Y increases. Thisis shown, for example, in Fig. 64 which refers to the thermal conductivityof a pure oxygen plasma at p ¼ 1 atm with Y as parameter [51]. There is

FIG.61. Thermal diffusion coefficient of singly ionized oxygen atoms in a two-temperature

oxygen plasma at p ¼ 100 kPa with Y as parameter [51].


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a pronounced shift of the dissociation peaks to higher values of Te as Yincreases. In addition, the peak values also increase with increasing Y.

The same trend may be observed in Fig. 65 which shows the thermalconductivity of a two-temperature argon plasma at p ¼ 100 kPa with Yas parameter [12]. For temperatures below around 13,000K, the thermalconductivity decreases with increasing Y, but this trend reverses for tem-peratures exceeding 13,000K.

Figure 66 shows the behavior of the thermal conductivity of an Ar/H2

two-temperature plasma at p ¼ 100 kPa with Y as parameter [12].For Y ¼ 1, the dissociation peak for hydrogen would be close to 3500K(not shown in this graph). As mentioned before, this dissociation peak shiftsto higher values of Te as Y increases.

d. Viscosity of Two-Temperature Plasmas. As in the case of LTE, the viscosityof a two-temperature plasma is determined by collisions among heavy par-ticles. Figure 67 shows the viscosity of a two-temperature argon plasma atp ¼ 100kPa with Y as parameter [12]. The viscosity decreases as Y increasesbecause of the decrease of the heavy-particle density with increasing Y.

FIG.62. Electrical conductivity of a two-temperature argon plasma at p ¼ 1 atm with Y as

parameter [46].


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Figure 68 shows a very similar behavior of the viscosity of a pure oxygenplasma at p ¼ 1 atm and withY as parameter [51]. Again, there is a substantialdecrease of the viscosity as Y increases.

Figure 69 shows the behavior of the viscosity of a two-temperatureplasma generated from a mixture (50% Ar, 50% H2 by volume) [12].Although the viscosity is in this case dominated by the heavier argon atoms,the presence of hydrogen causes a shift of the viscosity maxima to highervalues of Te as Y increases, because of delayed ionization. This delayedionization is due to the required dissociation of hydrogen (which depends onTh) before ionization can take place.

e. Radiative Transport Coefficients for Two-Temperature Plasmas. As of thiswriting, the authors of this chapter are not aware of any published data ontwo-temperature radiative transport coefficients. One may only speculateabout radiative properties if Y41. Two cases will be considered in thefollowing:

(i) Y41 caused by substantial lowering of Th.

FIG.63. Electrical conductivity of a two-temperature oxygen plasma at p ¼ 1 atm with Yas parameter [54].


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FIG.64. Thermal conductivity of a two-temperature oxygen plasma at p ¼ 1 atm with Y as

parameter [51].

FIG.65. Thermal conductivity of a two-temperature argon plasma at p ¼ 100kPa with Yas parameter [12].


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This situation is experienced in the fringes and in the electrode boundarylayers of high-intensity arcs. The electron temperature may show a smalldecrease only, as for example, in the anode boundary layer of high-intensityarcs. The drastic decrease of Th, however, ensures values of Y41 in theanode boundary layer.

FIG.66. Thermal conductivity of a two-temperature Ar/H2 (25%/75%) plasma at

p ¼ 100kPa with Y as parameter [12].

FIG.67. Viscosity of a two-temperature argon plasma at p ¼ 100 kPa with Y as parameter

[12].


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FIG.68. Viscosity of a two-temperature oxygen plasma at p ¼ 1 atm with Y as parameter

[51].

FIG.69. Viscosity of a two-temperature Ar/H2 (50%/50%) plasma at p ¼ 100 kPa with Yas parameter [12].


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The radiation intensity from such regions appears to be diminished com-pared to the adjacent plasma, i.e. radiative transport will be reduced fromsuch regions.

(ii) Y41 caused by substantial increase of Te.

Such increases are linked to the electric field in the arc, or to E/p (Eqs. (46)and (47)). Strong increases of the electric field are caused by extreme con-striction of the arc or strong convective cooling. The radiation intensityfrom regions of such high electric fields appears to be enhanced, i.e.radiative transport from such regions is expected to be larger.

No quantitative assessment of the effects described in (i) and (ii) is avail-able today.

At the end of this section it should be pointed out that the importance ofdeviations from kinetic equilibrium in ‘‘thermal’’ plasmas has been recog-nized many years ago. In spite of this fact, there is still a lack of compre-hensive property data for two-temperature plasmas, especially for plasmasgenerated from gas mixtures.

IV. Modeling of Thermal Arcs

In principle, the behavior of any arc may be determined by solving theconservation equations with appropriate boundary conditions, providedthat the thermodynamic state of the plasma and the transport coefficientsare known (see Section III). Even if the assumption of LTE for the coreof the arc column can be justified, there may be severe deviations from LTEin the fringes of the arc as well as in the electrode regions. Specifications ofrealistic boundary conditions imposes a serious problem, in addition to themathematical difficulties of solving a system of coupled non-linear partialdifferential equations possibly in three dimensions. It is customary in suchsituations to introduce simplifications, which facilitate solutions of the gov-erning equations. Although such solutions cannot describe the actualbehavior of the arc, they frequently reveal important physical trends.

A. SIMPLE MODELS BASED ON LTE

1. The Elenbaas–Heller model

The first attempt to solve the conservation equations for an arc columnhas been reported by Elenbaas and Heller in 1935 [1,2]. They considereda rotationally symmetric arc column in an asymptotic equilibrium flowregime, which leads to a decoupling of the energy equation from the


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momentum equation. As far as the energy equation is concerned this sit-uation is identical with the case of no flow. Neglecting radiation losses fromthe arc entirely, the energy balance may be written as:

div ~F � seE2 ¼ 0 (51)

where

~F ¼ �k grad T (52)

~F is the heat flow vector, k the thermal conductivity, se the electricalconductivity and ~E the electric field strength. According to this equation theheat source term, seE

2, is balanced by heat conduction, i.e. heat transfer bythermal diffusion effects is also neglected. For a rotationally symmetric arccolumn Eq. (52) transforms into (cylindrical coordinates, r, z),

1

r

d

drrk

dT

dr

� �þ seE2

z ¼ 0 (53)

which is known as the Elenbaas–Heller equation. Ez represents the fieldstrength in axial direction. By introducing the heat flux potential.

S ¼Z T

T0

kðsÞ ds (54)

where s is a dummy variable, Eq. (53) reduces to

1

r

d

drrdS

dr

� �þ seE2

z ¼ 0 (55)

where S may be considered as a function of se. Conservation of current inthe arc column may be expressed by Ohm’s law

I ¼ 2pEz

Z R

0

ser dr (56)

where R represents the arc radius.In spite of severe simplifications of the Elenbaas–Heller model, solutions

of Eqs. (55) and (56) are still complex because of strong non-linearities ofthe transport coefficients, S, and se.

In order to facilitate closed form solutions of Eqs. (55) and (56), variousapproximations of S(se) have been proposed, ranging from linear to highorder polynomial approximations and corresponding solutions have been


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reported. These solutions provide basic trends for arc column behavior. Forexample, Fig. 70 shows that solution of Eqs. (55) and (56) provide a rea-sonable approximation of the maximum temperature, which is feasible ina hydrogen arc, neglecting radiation.

An extension of the Elenbaas–Heller model with radiation lossesincluded, results in the following energy balance:

1

r

d

drrdS

dr

� �þ sE2

z � Pr ¼ 0 (57)

where Pr represents radiative energy losses per unit volume and unit time(Pr ¼ 4peT for optically thin plasmas). It is assumed in this model that thearc column is optically thin, i.e. there is no appreciable reabsorption ofradiation within the arc column. Attempts were also made to represent theradiation source term by polynomial approximations in Eq. (57) for facil-itating closed form solutions of this equation combined with Eq. (56).

For an accurate assessment of the behavior and properties of an arccolumn, exact values of the transport coefficients must be introduced whichnecessitates numerical solutions of Eqs. (56) and (57).

Although arcs with little or no superimposed gas flow are frequently usedin the laboratory, arcs exposed to substantial flows are of great practicalinterest as, for example, in the development of plasma torches or arc gasheaters. The wall-stabilized cascaded arc with superimposed laminar flowreceived particular attention because it offers the opportunity to applyscaling laws. Figure 71 shows a schematic arrangement of a wall-stabilizedarc. In this over simplified representation of the arc, the arc attachmentat the anode is assumed to be fixed and rotationally symmetric which doesnot reflect the actual continuous motion of the arc root over the surface ofthe anode.

FIG.70. Calculated and measured maximum temperatures in a wall-stabilized arc.


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2. The Stine–Watson Model

A simple, single-fluid description may be applied for modeling of the arccolumn if it is assumed to be in LTE and rotationally symmetric [55]. Forthis situation the conservation equations expressed in cylindrical coordi-nates may be written as:

Mass :@

@zruð Þ þ 1

r

@

@rrrvð Þ ¼ 0 (58)

Momentum : r u@u

@zþ v

@u

@r

� �¼ � @p

@zþ 1

r

@

@rrm

@u

@r

� �(59)

Energy : r u@h

@zþ v

@h

@r

� �¼ 1

r

@

@rrkcp

@h

@r

� �þ seE2

z � Pr (60)

Current : I ¼ 2pEz

Z R

0

se dr (61)

FIG.71. Schematic of a cascaded, wall-established arc configuration [12].


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The mass density of the plasma is expressed by r; u and v are the velocitycomponents in axial and radial directions, respectively; p is the pressure, Ez

the axial field strength, h, m, k, cp, se, and Pr are the plasma enthalpy, theviscosity, the thermal conductivity, the specific heat at constant pressure,the electrical conductivity and the radiative energy emitted per unit volumeand unit time, respectively. Eq. (61) implies that the radial component of thecurrent is negligible. The plasma is treated as a perfect gas so that:

h� h0 ¼Z T

T0

cp dT (62)

and

p ¼Xr

nrkT (63)

where, k, represents the Boltzmann constant and, nr, the particle densityof species r (electrons, ions, neutrals).

In addition to the previously stated assumptions, viscous dissipationin the plasma is neglected as well as self-induced magnetic field effects. Theflow is assumed to be steady and axially symmetric without swirl compo-nents, and reabsorption of radiation within the arc is neglected. In themomentum (Eq. (59)) and energy (Eq. (60)) equations, the usual hydrody-namic and thermal boundary layer approximations have been introduced.

For solving the conservation equations, the temperature dependence ofthermodynamic and transport properties must be known. Because of severegradients of the temperature and associated species densities in an arc,diffusion effects play an important role. Energy transport due to chemicalreactions in the plasma (e.g. dissociation and ionization) may have a dom-inating effect on the total energy transfer in certain temperature intervals.These conditions, however, are included in the thermal conductivity(see Section III) which, in general, becomes a strongly non-linear functionof temperature (see, for example, Fig. 27).

It should be pointed out that the conservation Eqs. (58)–(61) apply to theentrance region of a plasma torch. In the fully developed region whereð@h=@zÞ ¼ ð@u=@zÞ ¼ 0 and also v ¼ 0, a corresponding modification of Eqs.(58)–(60) adapts these equations for the fully developed (asymptotic) regionof the arc. The energy equation, for example, reduces to Eq. (57) andbecomes decoupled from the momentum equation.

Analytical solutions of the conservation equations for the entrance regionhave been reported by Stine and Watson [55]. In their original arc model,radiation has been entirely neglected among other simplifications. Although


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the results of this analysis are only qualitative without accurate predictionsof local property variations, they provide valuable guidelines for generaltrends. During the 1960s many attempts were made to remove some of thesimplifications in the Stine–Watson model in order to improve the stilllacking agreement between experiment and theory. Unfortunately, theseattempts had only limited success because the previously mentioned strongvariations of thermodynamic and transport properties do not lend them-selves to simple modeling.

Accurate predictions can only be expected from numerical solutions ofthe unaltered system of conservation equations. Such solutions have beenreported by Watson and Pegot [56] for the entrance as well as for theasymptotic region of arcs in laminar flow. Figure 72 shows selected results ofthe calculations by Watson and Pegot [56] for a nitrogen arc. The plasma

FIG.72. Selected properties of a nitrogen arc in LTE with superimposed flow [56].


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enthalpy (Fig. 72a) increases rapidly in the entrance region, reaches a peakand then levels off toward the fully developed (asymptotic) region of the arc.In spite of the high axial velocities (see Fig. 72d), the mass flow within theconstrictor (Fig. 72b) is essentially confined to a relatively cold layer closeto the wall, especially in the vicinity of the entrance. This effect is due tothe low mass density in the arc core which is a consequence of the highenthalpies (temperatures) in the arc axis. With increasing distance from theentrance, more and more of the cold gas permeates into the arc.

The crucial test for the validity of these predictions is, of course, a com-parison with pertinent experiments. Taking the uncertainties into accountinvolved in the determination of the transport properties, the agreementbetween theory and experiment is reasonable as long as the assumption ofLTE holds.

3. Further Developments of LTE Arc Models

Numerous modifications to the basic two-dimensional arc model havebeen pursued to make it more representative for specific applications. Deal-ing with radiative transport has led to the development of the net emissioncoefficient concept [44,57–59], where the absorption within an arc of spec-ified geometry and temperature distribution is calculated and the net radi-ation leaving the arc is determined for specific arc radii and temperaturedistributions. A further development of radiation transport mechanisms hasbeen presented by Sevastyanenko et al. [60]. In his method of ‘‘partialcharacteristics’’ the calculation of the radiative characteristics of the plasmacan be separated from the calculation of the gas dynamic characteristics[61,62]. Simplifying assumptions have been made for the electrode regions,e.g. an assumed current density distribution at the cathode as a boundarycondition for the thermionically emitting cathode. Refinements of thesemodels concentrated on making the electrode boundary conditions morerealistic [63], however, the column conditions of a stable free-burning archave not been strongly affected by different assumptions for the electroderegions.

Further developments were pursued for arcs within nozzles with highsuperimposed flow velocities, a situation encountered in circuit breakers.Consequently, these models are time dependent with a varying current, andconcentrate on determining the energy loss rate when the current ap-proaches zero [64]. Large-scale turbulence has been found to be a dominantfactor.

Modeling of arcs in plasma torches poses the problem that no real com-parison with experiments can be obtained because of the inaccessibility ofthe arc to diagnostics. In this geometry, the arc is between a cathode rod and


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a cylindrical anode, with a superimposed flow from the direction of thecathode through the anode nozzle. The arc axis is parallel to the anodesurface, and the arc has to penetrate a cold boundary layer between thecooled anode surface and the arc column plasma. This situation is depictedin Fig. 73 [65] where the details of the various fluid dynamic and magneticforces are indicated, i.e. the fluid dynamic drag on the high temperature, lowdensity, and high viscosity channel between the arc column and the anodewall exerted by the cold gas flow perpendicular to this channel, andthe forces generated by the self-magnetic field due to changes in currentdensity and curvature of the current path. Paik et al. [66] used a two-dimensional steady state model, and approximated the anode region byassuming a high electron temperature in the boundary layer at the locationof the anode attachment, and determined the location of the anode attach-ment from calculating the minimum of the sum of the voltage drops alongthe column and across the boundary layer (according to Steenbeck’sminimum principle).

The arc instabilities encountered in this type of plasma torches have led tothe development of time-dependent three-dimensional descriptions of thearc inside the torch [67–71]. These three-dimensional simulations have aprofound impact on our understanding of arc behavior inside plasmatorches, because a two-dimensional description necessarily violates physicalreality by assuming a circumferentially uniform arc attachment, since cir-cumferential symmetry poses the physical dilemma of having current

FIG.73. Illustration of forces acting on arc attachment to a cylindrical anode [65].


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transfer through a cold boundary layer or high mass transfer through a lowdensity region. Since these instabilities are predominantly in the frequencyrange of a few kilohertz to a few tens of kilohertz, a range that correspondsto the critical particle residence time during a plasma spray process, thesimulations have been developed for plasma spray torch conditions. Atpresent, all of the models use the assumption of LTE conditions, and usedifferent approaches for describing the non-equilibrium conditions that arenecessary for transferring the current through the cold boundary layer to theanode surface. Usually, a high temperature channel is imposed at a locationof a high electric field strength, or a region of high electrical conductivity.Both finite volume [70] and finite element [71] discretizations have beenused. While the arc motion can be simulated quite realistically, the changeto a different type of motion, as characterized by a different appearance ofthe voltage trace, has not yet been reproduced by changing the inputparameters arc current and plasma gas flow rate. Development of non-equilibrium models for this situation is necessary to describe the upstreambreakdown realistically. Figure 74 shows an example of the calculated tem-perature distributions at a specific instant in the horizontal and the verticalplanes [72].

B. MODELS FOR NON-LTE ARCS

The existence of LTE in ‘‘thermal’’ arcs is rather the exception than the rule.There are several effects that cause departures from LTE conditions. The mostfrequently encountered non-equilibrium is the kinetic non-equilibrium, theexistence of different heavy particle and electron temperatures. Because ofthe relatively long equilibration time between electrons and heavy particles(in the order of a few microseconds), steep gradients in the axial or radialdirections usually result in kinetic non-equilibrium. Chemical non-equilibrium,i.e. a composition deviating from that predicted by the Saha equation or themass action law for dissociation, is also frequently encountered with steepgradients or high flow velocities. A third cause for non-equilibrium is thetrapping of radiation resulting in distributions of excited states deviating froma Boltzmann distribution. An example is the overpopulation of excited statesin the arc fringes or in the jet [73]. On the other hand, in the region where thecold gas is heated to plasma temperatures, e.g. in the cathode region of a free-burning arc, an overpopulation of ground states is found compared toa Boltzmann distribution [74]. These latter departures from equilibrium can betreated by using a collisional–radiative model for the excited states or a ratekinetic model for the various excitation and ionization processes. Since thesecases are important primarily for interpreting diagnostic results, they will notbe treated in this article.


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FIG.74. Temperature distributions in a plasma torch obtained with a 3D time dependant

modeling approach [72].


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1. Laminar Flow in Non-LTE Arcs

The model for this case will encompass a wall-stabilized arc (Fig. 71) withsuperimposed laminar flow. In addition, the following assumptions will beincorporated into this model:

1. the arc is steady and rotationally symmetric;2. thermal diffusion, gravity, and viscous dissipation are negligible;3. the plasma is optically thin;4. no external magnetic fields are considered;5. both the electron gas and the heavy species are treated as perfect

gases and thermal equilibrium shall prevail among electrons (Te) andamong heavy species (Th). Species densities are governed by a gen-eralized mass action law.

Based on these assumptions, the conservation equations are expressed interms of cylindrical coordinates (r, z, j). It should be emphasized that onlythose conservation equations which contain the enthalpy or temperaturewill differ from those which apply to LTE situations.

Mass conservation

@

@zðruÞ þ 1

r

@

@rðrrvÞ ¼ 0 (64)

Momentum equations

ru@u

@zþ rv

@u

@r¼ � @r

@zþ 2

@

@zm@u

@z

� �þ 1

r

@

@rmr

@u

@r

� �

þ 1

r

@

@rmr

@v

@z

� �þ jrBj ð65Þ

ru@v

@zþ rv

@v

@r¼ � @p

@rþ @

@zm@v

@z

� �þ 2

r

@

@rmr

@v

@r

� �

þ @

@zm@u

@r

� �� 2mv

r2� jzBj ð66Þ

Since jzcjr, the self-induced magnetic field may be written as

Bj ¼ m0r

Z r

0

jzz dz (67)


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Current continuity requires

@jz@z

þ 1

r

@

@rðrjrÞ ¼ 0 (68)

The electron energy equation assumes the form

@

@z

5

2nekT eu

� �þ 1

r

@

@rr5

2nekT ev

� �¼ 5

2

k

ejz@T e

@zþ jr

@Te

@r

� �

þ @

@zke@T e

@z

� �þ 1

r

@

@rker

@T e

@r

� �

þ j2z þ j2rse

� SR � _Eeh þ5

2_nekT e þ _Qc ð69Þ

where ke is the thermal conductivity of electrons, _ne the rate of electronproduction, and _Qc represents the energy loss of electrons due to chemicalreactions.

The energy-exchange term between electrons and heavy particles may bewritten as

_Eeh ¼ 3

2kðT e � ThÞne

2me

ma

� �8kT e

pme

� �1=2

ðnaQea þ niQeiÞ (70)

where Th is the heavy-particle temperature, ma is the mass of the heavyspecies, na is the number density of atoms, and Qea, Qei are the collisioncross-sections of electron–atom and electron–ion collisions, respectively.

The heavy-particle energy equation may be written as

@

@z

5

2nhkTh þ niEI

� �u

� �þ 1

r

@

@rr

5

2nhkTh þ niEI

� �v

� �

¼ @

@zkeff

@T

@z

� �þ 1

r

@

@rkeffr

@T

@r

� �þ _Eeh ð71Þ

The enthalpy of the heavy species includes the ionization energy EI. Thequantity keff is the effective thermal conductivity, which is the sum of thetranslational thermal conductivity of the heavy species, kh, and the reactivethermal conductivity, kr. The electrons transfer energy to the heavy speciesby collisions and they pick up energy readily from the electric field due totheir high mobility.

For solving these conservation equations, thermodynamic and transportproperties are required which have been already discussed in Section III.


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Considering a similar arc configuration as shown in Fig. 71, temperatureand current density distributions have been calculated for a fully developedargon arc [75]. The results are shown in Fig. 75. Since deviations fromkinetic equilibrium occur primarily in the arc fringes where the temperaturedrops below 12,000K, the current density distribution also suffersdistortions in the arc fringes. The two-temperature model providesa substantially higher electrical conductivity close to the wall and, as aconsequence, the current density will also be higher close to the wall. This

FIG.75. Temperature and current density distribution in a fully developed argon arc at

p ¼ 1 and I-200A. T1, J1 refer to the one-temperature (LTE) model; Te, T2, J2 refer to the two-

temperature model [75].


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fact gives rise to a rearrangement of the entire current density distribution,although the effect on the arc core remains small.

If chemical non-equilibrium effects become important, in addition todeviations from kinetic equilibrium, the ensuing model becomes considerablymore complex. Deviations from ionization equilibrium, for example, requireseparate species continuity equations and, therefore, a multi-fluid model has tobe adopted in contrast to the simple one-fluid model for LTE conditions.

For the sake of simplicity, a three-component, optically thin plasmaconsisting of electrons, singly ionized atoms, and neutral atoms will beconsidered, exposed to a steady, laminar, rotationally symmetric flow.Viscous dissipation and pressure work shall be negligible. Since miEma,me � ma, and ni ¼ ne, the mass density becomes

r ¼ maðne þ naÞ (72)

Using a cylindrical coordinate system (r, z, j), the electron continuityequation may be written as [76]

@

@zðneuÞ þ 1

r

@

@r½rneðvþ vambÞ� ¼ _ne (73)

where _ne is the rate of generation of electrons (and positive ions) and vamb isthe ambipolar diffusion velocity. Equation (73) implies that ambipolardiffusion in z-direction is negligible compared to the r-direction, becauseð@ne=@zÞ � ð@ne=@rÞ. This is in particular true for the fully developed(asymptotic) regime where @ne=@z ¼ 0.

The total mass conservation equation assumes the form

@

@z½ðne þ naÞu� þ

1

r

@

@r½rðne þ naÞv� ¼ 0 (74)

and the global momentum equation becomes

maðne þ naÞ u@u

@zþ v

@u

@r

� �¼ � dp

dzþ 1

r

@

@rm@u

@r

� �(75)

Conservation of energy requires two separate, but coupled energyequations for electrons and for heavy particles. Assuming that jr � jz and


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~j � rTe ¼ 0, the electron energy equation which is equivalent to Eq. (69)becomes

@

@z

5

2nekT eðuþ udÞ

� �þ 1

r

@

@r

5

2nekT eðvþ vambÞ

� �

¼ 1

r

@

@rrke

@T e

@r

� �þ j2

se� _Eeh þ _Ei:c: þ

5

2kT e _ne

� �ð76Þ

In this equation, ud represents the electron drift velocity which isnegligible in r-direction consistent with the assumption jr � jz. _E i:c:

represents the net energy loss rate per unit volume due to inelastic collisionsof the electrons with heavy particles and the term ð52kT e _neÞ accounts for theenergy of the electrons liberated by the ionization process. The term _Eeh

which accounts for elastic collisions of the electrons with heavy particles inthe same as in Eq. (70).

The l.h.s. of Eq. (76) describes net convection and diffusion of the thermalenergy of electrons which is balanced by electron heat conduction, Jouleheat dissipation, and the effects of elastic and inelastic collisions of theelectrons.

The energy equation for heavy species which is equivalent to Eq. (71) maybe expressed by [76]:

5

2kðne þ naÞ u

@Th

@zþ v

r

@

@rðrThÞ

� ¼ 1

r

@

@rrkh

@Th

@r

� �þ _Eeh (77)

where kh is the thermal conductivity of heavy species and _Eeh is given byEq. (70). The effect of inelastic collisions by heavy species have beenneglected. For solving Eqs. (75)–(77), Dalton’s law and the condition ofquasi-neutrality (ne ¼ ni) are required. In addition, non-equilibrium trans-port properties must be introduced (see Section III.B).

A comparison of measured and calculated field strength–currentcharacteristics of a fully developed argon arc shows that the measurementsdeviate substantially from the calculated characteristics based on LTE, butthey are in reasonable agreement with non-equilibrium calculations [76].

2. Turbulent Flow in Non-LTE Arcs

Turbulence is one of the most puzzling phenomena in fluid dynamics andeven more so in thermal plasma technology which is, to a large degree,governed by turbulent flow situations. In spite of many successfulcommercial developments over the years, the underlying physics of


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turbulence in plasma flows is still poorly understood. Therefore, it is notsurprising that the presence of turbulence adds another dimensionof complexity to the already complex situation in thermal plasma systems.

Turbulence is characterized by highly random, non-steady, and three-dimensional effects in the flow. Turbulent flow, in principle, can bedescribed by the Navier–Stokes (NS) equations. Unfortunately, theseequations cannot be solved for most practical problems, because suchturbulent flows encompass a wide range of turbulent eddy sizes from the sizeof the domain of interest, down to sizes below those at which viscousdissipation and chemical reactions occur. This fact translates intocorresponding requirements in terms of the number of spatial grid cellsand the resultant time steps for all-scale resolution which is far beyond thecapacity and speed of available computers today.

Two alternate routes for the prediction of turbulent flows have beensuggested, i.e. large-eddy simulation (LES) and a statistical approach. LES is arelatively new approach that involves the solution of the three-dimensionaltime-dependent NS equations for large-scale turbulent motion together witha subgrid model for the statistics of the small-scale motion. These methods arestill under development. Although they can provide rather accurate results,they are prohibitively expensive for engineering applications. Furthermore,predicting the interaction between large eddies and small or subgrid eddies bymeans of a subgrid model imposes the closure problem which has beenaddressed in a number of turbulence models.

The statistical models have been classified according to the number ofturbulence parameters that appear as dependent variables in the differentialequations. All these models have been reviewed in detailed surveys [77–80].The simplest models relate the turbulence correlations directly to the localmean flow quantities, while the most complex models solve differentialtransport equations for the individual turbulence correlations. The choice ofthe proper turbulence model depends on the requirements of the problem andthus on the compromise between two factors: (1) the complexity of the modeland the availability of computational resources, and (2) the applicability andaccuracy of the information needed. A good turbulence model should providesufficient universality, but should not be too complex to use.

There has been substantial progress in using the turbulence models formodeling of turbulent flows under plasma conditions. Schaeffer [81]reported a theoretical model for a swirl arc using the mixing lengthhypothesis. Ushio et al. [82] and McKelliget et al. [83] incorporated atwo-equation k– e turbulence model into their investigations. Correa [84]combined a k–e turbulence model with a mass-weighted averaging conceptin his model. A multiple time scale turbulence model, using one time scalefor velocity fields and another for scalar fields, was first proposed for


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parabolic-type plasma flows [85]. The ability to predict both unweighted andmass-weighted mean temperatures can be achieved by adopting mass-weighted averaging for transport equations and a probability density func-tion. This model offers a linkage for correlating different measurementmethods, e.g. spectroscopy and enthalpy probes for plasma temperatures.The aforementioned parabolic model has been extended to more generalsituations for two-dimensional plasma flows, allowing, for example, thepresence of a swirl component, a cross-stream pressure gradient, or evenrecirculations [86]. However, the coefficients involved in the closure modelmust be re-optimized to achieve better overall agreement with availableexperimental data. Caution has to be exercised in applying the variousturbulence models.

It should be emphasized that most of the turbulence models have beenapplied for modeling of plasma jets rather than arcs. In this overview,modeling of plasma jets will not be considered.

V. Heat Transfer Processes in Thermal Arcs

A. GENERAL CONSIDERATIONS

For a proper assessment of plasma heat transfer it is useful to evaluatequalitatively how much heat transfer in a plasma is expected to differ fromheat transfer in an ordinary gas at low temperature. The following consid-erations will be based on a plasma without net current flow.

The heat transfer phenomenon and, in particular, the thermal boundarylayer are well understood for a cool, solid body immersed in a laminar hotgas stream in which no chemical reactions occur. In this simple situation, theheat transfer can be predicted by a dimensionless parameter, the Nusseltnumber

Nu ¼ f ðPr; ReÞ (78)

where Pr is Prandtl number and Re is Reynolds number. With some mod-ifications, similar relationships hold for dissociating gases, provided that theLewis number which describes the diffusion of the species is close to unity.

If one now considers heat transfer in a temperature range high enough forionization to occur, one might expect a strong increase of the heat transfercoefficient, because the free electrons contribute strongly to the thermalconductivity as they do in a metal. But this is not the case – at least not ona cold catalytic wall – because its surface is always separated by a cool, lessionized layer from the hotter part of the boundary layer and from the mainstream. This layer will be thicker when chemical equilibrium exists than for a


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chemically frozen boundary layer as shown in Fig. 76. A chemically frozensituation refers to an extreme case of chemical non-equilibrium, which islikely to occur close to the wall of a highly constricted arc. Although theelectron density may be rather high close to the wall due to diffusion, theelectron temperature gradient at the wall will be zero as shown analytically[75] and experimentally [87]. This prevents a strong increase of electron heatconduction to the wall. There is, however, another mechanism, which makesa strong or even dominating contribution to the wall heat flux. Neglectingthermal diffusion and the diffusion thermo effect, the heat flux equation forthe simple case of a two-component mixture (fully ionized plasma) may bewritten as

~q ¼ �kI¼0rT þ ðh1 � h2Þ~I1 (79)

where kI¼0 is the heat conductivity for pure conduction (without massfluxes), h1 and h2 are the enthalpies of component 1 and 2, respectively, and~I1 is the mass flux of component 1. The role of the second term in Eq. (79)may be illustrated by considering the simple example of a high-intensityargon arc enclosed in a tube which is kept at a relatively low temperature Tw

(Fig. 77). Because of the high degree of ionization in the hot core of the arcthere will be density gradients of argon atoms and ions (electrons) asindicated in Fig. 77. These gradients will give rise to mass fluxes of atomsand ions, i.e.

~IA ¼ �L1rhA (80)

FIG.76. Schematic of the electron density attribution on a plasma-wall boundary layer.


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I*

Aþ ¼ �L2rhAþ (81)

where hA and hAþ are the enthalpies of argon atoms and ions, respectively,and L1 and L2 are coefficients. But there will be no net mass fluxes(~IA ¼ �~IAþ). Since the opposite equal mass fluxes carry different enthalpieshA and hAþ , there will be a net flux to the confining wall so that the total heattransfer may be written as

~q ¼ �kI¼0rT þ ðhAþ � hAÞ~IA (82)

and

q ¼ hAþ � hA (83)

is known as the heat of transition which is in this case the excess enthalpywhich the ions and electrons carry with respect to the neutral atoms. In thiscase, this enthalpy is essentially the ionization energy. In such an arc there isa continuous flow of ions and electrons by ambipolar diffusion toward the wallwhere electrons and ions recombine releasing their ionization energy and theneutral atoms diffuse simultaneously in the opposite direction so that thereis no net mass flow. For a detailed analysis of the heat transfer situation in aplasma flowing toward or over the wall, the equations for mass and energyfluxes have to be introduced into the boundary layer equations [88].

Similar considerations apply for heat transfer to particles injected into aplasma [89]. Although there have been several studies of heat transfer from

FIG.77. Temperature distribution in an argon arc (schematically) and corresponding den-

sity gradients.


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an arc to neighboring walls [88,90] the emphasis in this article is on heattransfer to the electrodes which will be discussed in the following sections.

B. ANODE HEAT TRANSFER

As pointed out in Section II, modeling the region between the arc plasmaand the anode surface faces the difficulty that the plasma gas will cool fromtemperatures above 10,000K to the anode surface temperature in the orderof 1000K. Consequently, the equilibrium electrical conductivity is reducedfrom appreciable values in the arc column to effectively zero, and currenttransfer to the anode requires non-equilibrium conditions. The current den-sity in this region is given by the generalized Ohm’s law

j ¼ se E þ 1

e � nedpedx

� �þ f

dT e

dx(84)

where je is the electron current density, se the electron electrical conduc-tivity, E the electric field, ne, pe, and Te the electron density, partial pressureand temperature, respectively, and f the thermodiffusion coefficient.Because of very steep electron partial pressure and temperature gradients,diffusion effects, i.e. the second and third term in Eq. (84), dominate thecurrent transfer. However, the density and temperature gradients in front ofthe anode depend on the flow field in the arc. In general, the heat loss fromthe arc to the cold anode is compensated by increased heat dissipation dueto arc constriction, increased current density and electric field strength.However, considering that the total current is constant, i.e. (neglectingthermodiffusion effects)

I ¼ 2pZ R

0

se E þ 1

e � nedpedx

� �r dr ¼ const (85)

where R is the arc radius, it can be seen that the electric field is reduced forincreased density or temperature gradients, or for an increase of the areaover which these gradients exist. A flow directed toward the anode surfacewill provide these conditions, eliminating the need for a constriction of thearc. Under these conditions, the energy lost to the anode is replenished inthe anode region by convective fluxes from the arc column.

Several detailed models of the anode region exist. Nemchinsky and Peretts[91] and Dinulescu and Pfender [92] showed with one-dimensional models thathigh electron density gradients can lead to a negative anode fall, i.e. to areversal of the electric field in front of the anode surface. Following the for-mulation by Jenista et al. [93] and Amakawa et al. [94], a two-dimensional


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model has to consider kinetic non-equilibrium and diffusion effects. Conse-quently, energy equations for the heavy particles and for the electrons are used(Eqs. (69)–(71)).

The electron density is derived from an ionization rate equation:

_ne ¼ ann S Teð Þ � n2enn

� �(86)

Diffusion fluxes are expressed in an equation for the conservation of species:

u@ne@x

þ u@ne@r

þ @

@x

eneDin

kThEx �

1

ene

@pi@x

� ��

þ 1

r

@

@rreneDin

kThEe �

1

ene

@piar

� �� ¼ _ne ð87Þ

Solutions were obtained for either a free-burning arc or for a configu-ration where the anode region consists of a region bounded by a constrictedarc and an anode surface perpendicular to the arc axis, with the distancebetween the constrictor and the anode being 10mm. The upstream bound-ary conditions were given by a solution for a fully developed arc with pre-scribed current and mass flow rate. The anode was assumed to be at 1000K,and the outflow to the side boundaries was given by the conservationof mass and the vanishing of all gradients.

Figure 78 shows the resulting distribution of the magnitude of the differ-ent terms contributing to the current flow (Eq. (84)) for a free-burning arc

FIG.78. Contributions to current density in front of anode (right-hand side) [93].


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[93]. In this figure, the arc column is on the left-hand side and the anodesurface on the right. It can be seen that in the column, the current transportdue to the potential gradient dominates. Within the last millimeter, however,the diffusion effects take over, and a reversal of the electric field is observed,leading to a deceleration of the electrons and to an ion flux to the anode.

Figure 79 shows the kinetic non-equilibrium for a similar configuration[93]. It is seen that only a slight drop of the electron temperature occurs,while the heavy-particle temperature drops to the anode surface temperature(no-slip continuum conditions have been assumed).

The differences between a constricted and a diffuse attachment are illus-trated in Figs. 80–82 for the configuration of a constricted arc with a gapbetween the constrictor and the anode [95]. Figure 80a and b shows thestream lines for a constricted and a diffuse attachment (only the right half ofthe attachment is shown), respectively, indicating how an increase in theflow toward the anode can force the fluid stagnation layer to the anodesurface, eliminating the inflow of cold gas along the anode surface.Figure 81a and b shows the corresponding distributions of the heavy-particle temperatures. Figure 82 shows the calculated potential distributionsfor the constricted and the diffuse arc, with the anode being at zeropotential, indicating [95]:

(a) a voltage drop immediately in front of the anode for both situations,(b) a higher potential difference between the column potential and the

anode for the constricted mode,

FIG.79. Electron temperature and heavy-particle temperature distribution in anode

boundary layer [93].


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(c) a monotonic decrease in the potential gradient toward the anode fora diffuse attachment; while for the constricted arc an initial increaseof the gradient is followed by the drop immediately in front of thesurface.

FIG.80. Streamlines in anode boundary layer (a) constricted attachment and (b) diffuse

attachment [95].

FIG.81. Heavy-particle temperature distributions in anode boundary layer (a) constricted

attachment and (b) diffuse attachment [95].


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If the potential is extrapolated from the column to the anode surface, thedifference to the anode potential is positive for the constricted attachment(positive anode fall), but negative for the diffuse attachment (negative anodefall).

For description of the anode region as part of a model of an entire arc,usually simplifying assumptions are made. Lowke and his co-workers[96–98] developed an approach for calculating the electron and ion densitydistributions separately when proceeding from the column toward the anodesurface, while assuming a constant electric field until the difference betweenthe electron and ion densities reaches a given value. This way the solutionof Poisson’s equation for small space charges is avoided. Constant values forthe mobility and the electrical conductivity throughout the boundary layerare assumed. Based on comparison of the results with experimental data,further simplifications are introduced in later models, neglecting spacecharge effects and assuming a constant effective electrical conductivity in theboundary layer that includes the diffusion terms. Similar approaches havebeen used in many of the recent arc models, where the arc is described forLTE conditions, and a somewhat arbitrary high electrical conductivityis assumed for most of the boundary layer. Differences between constrictedand diffuse attachments are not calculated with this approach. Moredetailed descriptions of anode boundary layer calculations are reported in aforthcoming review by Heberlein et al. [99].

The energy transfer to the anode has been modeled and determined ex-perimentally with a wide range of approaches. Besides the heat transfer

FIG.82. Potential distribution in anode boundary layer [95].


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mechanisms due to temperature gradients and radiative transport, the en-ergy transfer due to the current flow must be considered. In general, thespecific heat flux can be expressed by

qa ¼ jelfa þ qel � kedTe

dx� kh

dTh

dxþ jiðEi � faÞ þ qR (88)

where qa is the specific anode heat flux, je the electron current density, fa theanode work function, qel the heat flux associated with the electron flux intothe anode, ke, kh, and Te and Th are electron and heavy-particle thermalconductivities and temperatures, respectively; ji is the ion current density, Ei

the ionization energy, and qR the radiative flux from the arc.The first term on the right-hand side is the energy released due to incor-

poration of the electrons into the metal lattice. The third and fourth termsare the regular heat conduction terms. The fifth term represents the energyreleased when gas ions reach the anode surface and recombine there. Theterm qel associated with the electron flux to the anode can be easily definedwhen a diffuse attachment and no or slightly negative anode falls are as-sumed. It becomes then

qel ¼ jel5

2þ ef

kse

� �kT e

e(89)

where e is the electronic charge, k the Boltzmann constant, Te the electrontemperature, se the electrical conductivity, and f the thermodiffusioncoefficient. The first term in the bracket represents the electron enthalpyflowing into the anode, while the second term represents thermodiffusionfluxes. For a positive anode fall, it has been customary to add the energygain by the electrons in the anode fall region, je�Ua, with Ua the anode fallvoltage drop. However, as shown in Fig. 82, there should be alwaysa reversal of the potential gradient, i.e. a negative anode fall immediately infront of the anode, and the increase in the potential for a constricted arcshould be converted into an increase in electron enthalpy. However, it isuncertain that this can happen with relatively few electron collisions in thesheath, i.e. with a possible breakdown of the continuum concept.

Consequently, the energy flux associated with the current flow in the caseof a constricted attachment with positive anode fall can be approximated by

qel ¼ jel5

2

kT e

eþUa

� �(90)

with Te the electron temperature value at the boundary layer edge.


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The term associated with the ion flux is usually small because the ion fluxis small.

Figure 83 shows calculated results for the radial distributions of thedifferent contributions of a diffuse anode attachment [95]. It is apparent thatthe term associated with incorporation of the electrons into the anode metallattice dominates (electron condensation energy), followed by the electronenthalpy flux and the heavy-particle conduction terms. For different con-ditions, the relative magnitude of these terms may change. It is interesting tonote that the radial distribution of the anode heat flux changes drasticallywhen the type of attachment changes. As seen in Fig. 84, the heat flux on theaxis of a constricted attachment is about four times that of a diffuseattachment, with significant radial gradients, while the total heat transfer isapproximately the same [95].

It is difficult to experimentally verify the relative importance of the var-ious terms in Eq. (88). However, radial distributions of the heat flux to theanode have been measured [15,100]. In Fig. 85, such distributions are shownfor a free-burning arc [95]. They have been obtained with a heat flux probeimbedded in the anode while the arc was moved across the probe location[15]. Since the radial distribution was usually asymmetric, both sides of theheat flux distribution are shown together with a calculated heat flux profilefor an arc at the same conditions. The agreement is acceptable.

Estimates of the relative magnitude of the heat transfer terms have beenderived from measurements by Sanders and Pfender [101] for atmospheric

FIG.83. Contributions to anode heat flux [95].


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FIG.84. Heat flux distribution to the anode surface for diffuse and constricted attachment

[95].

FIG.85. Heat flux distribution to the anode of a free-burning arc comparison of prediction

and measurement [15,95].


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pressure argon arcs operating between 50 and 350A for constricted and fordiffuse attachments. It has been found that the pure conduction termsamount to about 12% and the radiative terms to 5% of the total heat flux.The terms associated with the electron flux contribute about 83% to the fluxin the case of a constricted attachment. In the case of a diffuse attachment,this term was split up into a term associated with the current density at thearc axis (53%) and into a term associated with the mass flow into the anoderegion (about 32%).

C. CATHODE HEAT TRANSFER

Numerous approaches have been published for describing the cathoderegion of electric arcs, including several books and review articles [102–105].Consequently, only a brief overview of the physics of a couple differentapproaches will be given here.

In general, the modeling of the cathode region is divided into two separateapproaches according to the emission mechanism of the electrons from thecathode surface. For a thermionic cathode, the cathode material has a meltingpoint which is sufficiently high that it can operate without melting at a tem-perature where electrons are emitted with a sufficiently high current density.For current densities in the order of 108A/m2 this will require a temperature inexcess of 3000K for most materials. The other mechanism, frequently calledan explosive or evaporative emission, is started by field emission from a site onthe cathode surface that provides some form of field enhancement. The veryhigh current density at this site leads to rapid evaporation of the cathodematerial, and ionization of this metal vapor yields the charge carrier densitythat allows the current transfer. This emission mechanism is usually transient,with rapid succession of the evaporation at ever changing sites. However, forextremely high current and heat flux densities, a continuous evaporation of thecathode material may occur forming a stationary vapor jet. These conditionsmay also occur with thermionic cathodes. No detailed description will bepresented of this emission mechanism.

The models describing the attachment to a thermionic cathode divide theregion between the cathode surface and the arc column (cathode boundarylayer) into a collisionless space charge zone immediately adjacent to thecathode surface (sheath region) and into a presheath or ionization zone. Thepresheath is frequently subdivided [106,107] into an ionization zone anda thermal relaxation zone. A further subdivision of the ionization zone caninclude a ‘‘Knudsen zone’’ [108] where charge exchange is the dominantinteraction mechanism. The sheath voltage drop accelerates ions toward thecathode and electrons toward the ionization zone. The extent of the sheath isin the order of one Debye length (0.05–0.5 mm for most cathode conditions).


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Electrons are thermalized in the ionization region and ionizing collisionsexceed recombinations. Its extent can be given as (li� lcx)

0.5 [108], with liand lcx the mfps for ionization and charge exchange collisions, respectively.The ‘‘Knudsen layer’’ essentially reduces the ion energy by heating theneutrals from the cathode surface recombination. Finally, in the thermalrelaxation zone, Saha equilibrium is assumed, and the electron temperatureequalizes with the ion temperature. The extent of this zone may be as largeas 100 mm [109].

The fluxes in the different regions are indicated in Fig. 86. Heat flux q isentering the cathode material. Electron emission results in an electron fluxleaving the surface. There can also be an electron current contribution dueto secondary electron release, but also a negative contribution to the currentflow from electron back diffusion from the ionization region toward thecathode surface. Additionally, material evaporation may take place, as wellas heat loss by radiation. The principal flux into the cathode surface is theion flux.

Accordingly, the energy input into the cathode can be written as

jiðVe þ E i � feff þ 2kT c=eÞ þ jedðfeff þ 2:5kT e=eÞ¼ jem feff þ 2:5kT c=e

�þ qþ qevap(91)

where ji is the ion current, jed the electron back diffusion, jem the electronemission current, Vc the sheath potential drop, Ei the ionization energyof the plasma gas, feff the effective work function, i.e. the cathode materialwork function reduced by the electric field in front of it (see below), Te isthe electron temperature at the sheath edge, and Tc the cathode surface

FIG.86. Energy fluxes in the cathode boundary layer [120].


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temperature; q is the heat flux inside the cathode, and qevap the heat loss byevaporation.

On the left-hand side is the heat input into the cathode. Associated withthe ion current are the ion directed energy gained in the cathode fall,the ionization energy gained due to recombination at the cathode surface,reduced by the work function, and the ion enthalpy at the sheath edge.Corresponding terms apply to the energy transport by the back-diffusingelectrons. On the right-hand side, the first term describes the energy flux dueto electron emission, the second the heat flux from the cathode surface, andthe third the heat loss by evaporation.

It has been shown that the evaporation heat loss is for most conditionsnegligible, in particular if one considers that under normal conditions muchof the evaporated material will be rapidly ionized in the arc and re-depositedon the cathode [110]. In case of strong secondary electron emission, this fluxjse will have to be added to jem.

The emission current is given by the Richardson–Dushman equation

Jem ¼ AT2c exp � efeff

kT e

� �(92)

Here, A has the theoretical value of 12� 105Am�2K�2; however, formany materials including pure tungsten, a value of 6.02� 105Am�2K�2

has given results closer to experimental results. For thoriated tungsten,Dushman recommends a value of 3.0� 105Am�2K�2 combined witha work function of 2.63V [111]. The effective work function feff takes intoaccount that the work function value is reduced due to the electric field infront of the cathode (Schottky effect), and is given by

feff ¼ fe �eEc

4p�0

� �1=2

(93)

With fe the regular work function of the cathode and Ec the electric fieldin front of the cathode.

For calculation of the other fluxes determining the heat transfer to thecathode, the energy balances and the flux balances for the different regionsof the cathode boundary layer have to be solved [106,107]. Some approachesuse an integral balance for the boundary layer or for part of the boundarylayer with input of some experimentally determined quantities to verify theresults [108], or make use of Steenbeck’s minimum principle [120]. For de-tails of these approaches, the reader is referred to the literature [96,106–109].


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In spite of the difference in the approaches, the results agree in principle,even though they were derived for vastly different conditions, e.g. lamp arcsat 5A and plasma torch arcs at 200A.

A very extensive theoretical and experimental study of thermionic cath-odes in high-intensity discharge applications has been performed by Menteland his co-workers [108,112,113], and experimental results have been com-pared with model results obtained by Benilov and his co-workers [114–116].Using 2D and 3D models of the cathode and the energy input from the arcusing a slightly modified Eq. (91), different types of attachments have beenidentified as diffuse mode, low temperature spot mode, and high temper-ature spot mode. The theoretically predicted conditions for the diffuse andthe low temperature spot modes were experimentally verified. A highlyconstricted attachment, the ‘‘superspot mode’’ [117] was observed, however,it was not possible to ascertain that it could be represented by the hightemperature spot mode results. Typical cathode parameter values that wereobtained for the diffuse mode were a current density of about 106A/m2 andan electron temperature in front of the cathode of about 13,000K ata current of 6A and a cathode diameter of 1.5mm. For the low temperaturespot mode these values were 3� 108A/m2, about 25,000K, and a cathodetip temperature of about 3800K. It is interesting to compare these resultswith those obtained by [110,118] at arc currents between 50 and 300Aand cathode diameters of 3.2 and 6.4mm. Electron temperatures of23,000–25,000K, current densities of about 108A/m2, and similar cathodetip temperatures were observed, close to the values for the spot mode atcurrents smaller by more than an order of magnitude. No diffuse or otherspot modes were observed in these experiments.

Recently, Benilov et al. [119] carried out an analysis showing the existenceof several different types of cathode attachments, up to currents of 500A,found from bifurcation points for steady state solutions for the current-voltage characteristic. To our knowledge, these different attachment modeshave not been observed at these high currents.

As an example, some calculated results of cathode fall values are pre-sented taken from Ref. [120] and obtained for an atmospheric pressureargon arc. Figure 87 shows the calculated cathode fall voltage as functionof the arc current on the basis of having a minimum voltage drop over theentire cathode region. This figure shows the experimentally observedbehavior, however, the value of 11.5V for higher currents appears to behigh. A similar dependence was obtained by Dabringhausen et al. [113] forarc currents between 1 and 6A and argon at 260 kPa. Figure 88 shows thecontributions to the total current of the electron emission current, the ionflux and the electron back diffusion. It is clear that the electron back diffu-sion is negligible under these conditions, while the ion current can reach


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50% of the total current at low arc currents and remains above 20% athigher currents. Again, these results are comparable to those obtained forlow currents [113]. Figure 89 shows the contributions to the heat transferfrom the cathode surface. For low current, heat conduction toward thecathode base and radiation from the cathode surface dominate, while at

FIG.87. Calculated cathode fall values for free-burning argon arc [120].

FIG.88. Contribution to total current in front of the cathode in a free-burning argon arc

[120].


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higher currents cooling by electron emission is prevalent. For arcs withhigher current densities, e.g. with different gases and at higher pressure, thetransition to dominant electron emission cooling occurs at lower temper-atures. Values for the heat transfer from the cathode surface in the lowcurrent experiments with a 4A arc and diffuse attachment were given, due toconduction in the 1mm diameter cathode, as 10W, and due to radiationfrom the cathode as 16W, and cooling by electron emission can be estimatedby the data given to be about 18W, i.e. 41%.

It should be mentioned that once the current densities become so highthat the cathode surface becomes molten, different effects need to be con-sidered, and the fluid dynamics of the arc gas will play a major rolein determining the dominant heat transfer mechanisms [121]. Under theseconditions, a delicate balance exists between the various forces acting on theliquid metal pool, and ejection of liquid metal droplets are a major loss ofheat. We do not know of any model describing such a situation.

VI. Conclusions

This contribution concentrated on describing the heat transfer processesassociated with electric arcs. However, one of the major parts, the review ofthe thermodynamic and transport properties for LTE and non-equilibrium

FIG.89. Contributions to the heat flux from the cathode surface in a free-burning argon arc

[120].


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plasmas at high pressures have a wider application range. It is clear that inparticular the non-equilibrium properties of gas mixtures at high temper-atures require more effort in order to make modeling efforts more appli-cable to realistic conditions. But chemical non-equilibrium, as well asradiation, are strongly dependent on the specific configuration that onlygeneral approaches for their determination can be given.

What concerns the description of the arc column and the heat transferto the surroundings, the various effects that cause non-equilibrium have tobe of concern and need to be described in detail. A major effort is requiredin a three dimensional description of plasma dynamic instabilities, includinginstabilities of the shear layer between the arc or jet and the cold gas sur-roundings, and the entrainment of cold gas into the arc column or the jetand its mixing with the plasma. No practical approach is available at presentfor describing such conditions. Another area of uncertainty is encounteredwhen the process time constants are in the same order as the plasmadynamic instabilities, e.g. in plasma spraying. Time-dependent dynamicsimulations in three dimensions need to be provided, and the powers ofpresent computers are stretched to their limits.

The description of the electrode regions still suffers from a number ofuncertainties. While models exist to provide acceptable predictability forsome specific applications, e.g. in lamps or in welding arcs, in numerousother cases, our capabilities are insufficient to provide such predictions.In particular when high currents and high current densities are encountered,present models are inadequate to predict the arc-electrode heat fluxes. Fur-thermore, temperature and density gradients near an electrode surface canbe sufficiently high to pose questions about the validity of a continuumapproach for describing the heat and mass transfer. Also here newapproaches are needed for achieving predictability.

In summary, while the present modeling capability is significant and ad-equate to provide predictability for many plasma applications, no generalapproach can be defined for all arc applications, and areas exist where notonly more powerful computers are needed but also new approaches.

Acknowledgement

The author of this review gratefully acknowledges granting of permissionto reproduce figures from previous publications of individual authors (P.Fauchais, A.B. Murphy, J.A. Menart) and of copyright holders (Springer,IEEE). Figures 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 22, 23, 24, 28, 29,30, 31, 33, 40, 42, 43, 45, 46, 47, 51, 65, 66, 67, 69, 71 [ref. 12], 25, 26 [ref. 18],48, 49, 50, 53 [ref. 50], 52, 56, 57 [ref. 49], 75 [ref. 75] are reproduced with


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kind permission of Springer Science and Business Media, Figs. 19, 20, 21[ref. 17], 78, 79 [ref. 93] are reproduced with kind permission of IEEETransactions on Plasma Science.

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Heat and Mass Transfer in Plasma Jets

S.V. DRESVIN1and J. AMOUROUX

2

1St. Petersburg State Technical University, Polytechnicheskaya Str. 29, St. Petersburg

195251, Russia2Paris University Pierre et Marie Curie, France

Abstract

The chapter is devoted to systematization and generalization of the dataon the convective heat transfer between small solid particles and plasma jetsfrom arc or high-frequency plasma torches. The chapter gives numericalmethods and scattered experimental data on heat transfer and heat resistanceduring the motion of small particles with different resistance terms in plasmajets. The main criterial relations and correlations describing the heat transferare analyzed. The experimental data are compared with the criterial rela-tionships, and the choice of the most appropriate formulas is suggested.

Calculation methods for the motion and heating of a single particle inplasma jets and the plasma jet loaded with a great quantity of small-sizedparticles are given.

The general parameters of plasma torches and technological setups forprocessing small refractory particles in the plasma jets are also given.

The chapter is intended for students, postgraduates, engineers and re-searchers involved in the applications of plasma torch technology in plasmachemistry, plasma dusting and processing dispersed materials.

I. The General Concepts of Convective Heat Transfer

The wind blows to the south, it veers to the north, round and round it goes and

returns full circle. Bible, Ecclesiastes

A. WHAT IS A CONVECTIVE HEAT TRANSFER? THE NEWTON’S FORMULA

The first notion of heat and cold one gets from the sun and wind: the coldwind, the warm wind, the cool wind it is that which really affect our clothing,plans and behavior.




The heat transfer by air and water masses in the world’s oceans govern theclimate of continents, the weather of the day, week, winter and summer.

In the technology, especially in plasma technology, the heat conductionby flowing plasma constitutes the basis of technological treatment of thematerial treatment during its production. It also defines the plasma state inthe plasma torch itself.

Metal cutting and welding by an electrical arc, plasma spraying of pro-tective coatings and treatment of hard melting materials, surface treatmentby plasma jets arc furnaces; all these processes are based on the heating byheat transfer from flowing plasma to immobile technological objects.

This kind of heat transfer from a moving heat carrier with respect to aheated object is called a convective heat transfer.

This definition, although lacking in its correctness, is due to the fact that thefirst investigations of the heat transfer from immobile objects to flowing gas orfluid jets were devoted to cooling of warmed bodies by natural convection.

In spite of the long history on convective heat transfer, experimentalresearch procedures and relationships are still the principal way of itsdescription.

The historical development of heat transfer description between flowingmedium gas or liquid and an immobile heated or cooled object began withqualitative estimates and later resulted in the establishment of the principalquantitative regularities. It began with the definition of the basic factsaffecting the effectiveness of such heat transfer.

The experiment shows that the amount of energy (heat) Q amount trans-ferred during the convective heating is proportional to the difference betweenthe flow gas temperature Tp (plasma temperature ‘‘p’’) and that of the heatedbody Ts (solid walls ‘‘s’’):

Q � Tp � T s

�. (1)

It is obvious that during that process the quantity Q is proportional to theheating time t and to the area of the interface solid-fluid S:

Q � Tp � T s

�St (2)

A little remained has to be done: to assess the character of the flow, itscontact with the solid body (wall) and to express all this by the main factorsof the flow, in order to find mathematical expressions giving the completemodel of the convective heat transfer.

But ‘‘yThe wind blows to the south, it veers to the north, round andround it goes and returns full circle’’.

Not a single weather-station is still capable of calculating the motion of anatmospheric cyclone with reasonable accuracy.

452 S.V. DRESVIN AND J. AMOUROUX

Similarly, it turned out to be impossible to describe the multiformity ofmicrocyclones, the turbulence near the solid wall and in the boundary layer,and so.

This is the reason for an experimental study being the principal methodfor convective heat transfer description, and its results are attemptedly car-ried over to the real objects by similarity considerations.

The peculiarity of the approach of flow is considered by the introductioninto formula (2) of a proportionality factor a called heat transfer coefficient.It contains all the information about the heat transfer which we would liketo have

Q ¼ a Tp � T s

�St (3)

It is this heat transfer coefficient a which is the subject of thorough ex-perimental study.

In order to carry over the model experimental results to real objects usingsimilarity considerations, the coefficient a is usually expressed by similaritycriteria. This makes the basis of the teaching on convective heat transfer.

Formula (3) is called the Newtonian formula which was originally set upfor the natural convective cooling of heated bodies.

The Newtonian formula makes the basis of the study of convective heattransfer. Although seemingly simple, the difficulties of the study of thisproblem are not solved in this formula, they are only concentrated in thedetermination of the heat transfer coefficient a.

While the difference of temperature of the flowing medium and the heatedbody [Tp�Ts] (3) is called the ‘‘temperature pressure’’, the heat transfercoefficient qualifies the main information on the character of the fluid nearthe body and the data of the boundary layer.

B. THE ENERGY CONSERVATION LAW AT THE SOLID WALL INTERFACE

Let us consider the processes of energy transfer (heat transfer) at the solidheated body interface with the flowing heat carrier (gas or plasma).

1. The heat transfer inside the solid body (wall) is carried out by the heatconduction mechanism, which is described by the experimental Fourier’s law.

‘‘This heat energy amount Qs’’ transferred from the heated layer to a coldface is proportional to their difference of temperature which is called tem-perature pressure DT, the face area S, the heating time t, but it is inverselyproportional to the thickness of the layer Dx, while the medium propertiesand the micromechanism are taken into account through the thermal con-ductivity coefficient ‘‘ls’’:

Qs ¼ �lsDT s

DxSt Joule½ � (4)

453HEAT AND MASS TRANSFER IN PLASMA JETS

The heat flux (the energy flux per unit time and unit surface) is equal to

qs ¼ �lsDT s

DxWatt

cm2

� �(5)

2. It was just postulated that the heat amount transferred from the flow ofmoving heat carrier to the immovable body is described by the Newtonianlaw (formula (3)):

Qp ¼ a Tp � T s

�St Joule½ �

Hence the heat flux (the energy flux per unit time and unit surface) isequal to:

qp ¼ a Tp � T s

� Watt

cm2

� �(6)

In these conditions, taking into account the energy (or heat) conservation(moving medium2solid body), we obtain:

qp ¼ qs

which holds at the boundary of the solid body.Hence:

a Tp � T s

� ¼ �lsDT s

Dx(7)

This energy (or heat amount) conservation law at the interface forms thebasic relationship of the convective heat transfer.

In thermal physics textbooks it is sometimes formulated only as theboundary condition for the heat transfer problem (the boundary conditionof the 3rd kind). But for the studies of the heat transfer in the flowing mediathis law is the key and should be formulated as an independent law.

C. SIMILARITY CRITERIA (NUMBERS): REYNOLDS AND NUSSELT’S NUMBERS

So, the principal method of the convective heat transfer studies is theexperimental determination of the heat transfer coefficient a.

It is needed to establish the rules for the similarity of heat conductionprocesses and the similarity criteria or adimensional numbers allowing tomodify the results for real objects.


It is well known from geometry criteria that two triangles, having sidesx1, y1, z1 and x2, y2, z2, are similar if the ratio of their sides are equal to aconstant number C:

x1

x2¼ y1

y2¼ z1

z2¼ C

The number C is called the constant of the geometric similarity of thetriangles.

One can ask, how can the constants be established for hydrodynamic andheat transfer similarity? These processes present complex physical phenom-ena and at first sight an attempt to establish such constants seems to befruitless.

Nevertheless, the first such similarity criterion for hydrodynamic flowswas experimentally obtained by the English physicist, O. Reynolds.

O. Reynolds studied the flows into cylindrical tubes and the conditions oftransition of laminar flow into turbulent one. He established that the motionof the liquid having density r1, viscosity m1 and velocity u1 in the tube ofdiameter d1 is similar to the flow of another liquid having density r2, viscositym2 and velocity u2 in the tube of diameter d2 provided the following com-binations of these parameters are equal:

r1u1d1

m1¼ r2u2d2

m2

This dimensionless complex has got the name of Reynolds number orcriterion:

Re ¼ rudm

¼ udn

(8)

Here n ¼ m=r is the kinetic viscosity coefficient.This criterion proved to be the most important and successful criterion of

hydrodynamic flow similarity. The laminar flow transition into a turbulentone for gases and liquids is observed at the very specific value of thatnumber for different media, velocities and tube diameters. For smooth tubesthis transition takes place at ReE2000.

Now, we shall attempt to construct a criterion or a number with a constantvalue which would show the similarity of the conditions of the convectiveheat transfer.

Let us consider the first model of heating phenomena in a flowing mediumhaving parameters T1, u1, l1, r1 (temperature, velocity, thermal conductivity,density). This medium and this model have the heat transfer coefficient a1.


The second model with the dimensions d2 is heated in the medium withdifferent parameters T2, u2, l2, r2 and this model is described by the heattransfer coefficient a2.

We introduce the simplest scales of similarity (just as in geometry) for allthese quantities:

T1

T2¼ CT ;

l1l2

¼ Cl;a1a2

¼ Ca; etc (9)

where CT , Cl, Ca are constants (as in the case of triangles).The simplified form of the energy (heat) conservation law for the con-

vective heat transfer (formula (7)) for both first and second models can bewritten as:

a1DT1 ¼ �l1DT1

Dd1(10)

for the first model, and

a2DT2 ¼ �l2DT2

Dd2(11)

for the second model.Now, let us express the energy conservation condition of the first model

using the variables of the second model and the scalar constants CT, Cl, Ca.So, for the first model we obtain the equality

CaCT½ �a2T2 ¼ � ClCT

Cd

� �l2

DT2

Dd2(12)

The condition of similarity of the heat transfer of the first model to that ofthe second model is satisfied, if the equations (11) and (12) are absolutelyidentical. This is fulfilled, if the expressions in square brackets in both theright and left sides of (12) are equal and so can be cancelled out.

So, the condition of similarity of the heat transfer in both first and secondmodels leads to the following equality for scaling constants:

CaCT ¼ ClCT

Cd(13)

or

CaCd

Cl¼ a1d1l2

a2d2l1¼ 1 (14)


Introducing the values of the medium parameters expressed by the scalingconstants from (9), we get:

a1d1

l1¼ a2d2

l2(15)

so that the conditions of similarity of the heat transfer in both models aresatisfied, if they both have the same value of the dimensionless complex:

adl

¼ Nu (16)

This complex is called Nusselt number or dimensionless heat transfercoefficient and represents the ratio of the convective heat transfer over theconductive one.

The introduction of this criterion in the convective heat transfer brings theNewtonian formula (6) to the form:

qp ¼ a Tp � T s

� ¼ Nuld

Tp � T s

�(17)

All the experimental data on convective heat transfer are also expressedby the values of the Nusselt number in hope that the above mentionedsimilarity considerations are powerful.

We shall note without discussion that the heat (energy) conservation law(10) and (11), which was obtained earlier for the interface of the solid bodyand the medium (7) is written down here for the medium itself with theassumption that the temperature changes from Tp to Ts within the thinsublayer adjacent to the solid body (boundary layer). Inside this sublayer theheat is transferred mostly by the heat conduction of the medium and so thissublayer is almost immovable.

D. ON THE BOUNDARY LAYER AND SIMILARITY THEORY

The considerations given above on the similarity of heat transfer andhydrodynamic flow for different models and heat carriers allow somehow togeneralize individual experimental results. The dimensionless parameters orsimilarity criteria give hope that the basic concepts of the convective heattransfer have the same theoretical basis.

The methods of the similarity theory have been elaborated, and the gen-eralization of experimental results with the use of dimensionless numbershas become a routine practice of the scientific research. But, still

‘‘The wind blows to the south, it veers to the north, round and round itgoes and returns full circle’’.


The similarity theory and the generalization of these experimental resultsby using similarity numbers is an approach which describes these pheno-mena but does not qualify hidden fundamental phenomena.

This approach allows to describe the phenomenon but not to reveal itsmechanism. It is like a patch on the beggar’s rags which preserves him fromcold but does not change the miserable state of its owner.

No doubt, the similarity theory proved to be successful in investigatingthe heat transfer mechanisms. But the dream of a physical model of con-vective heat transfer that could express the connection of the heat flow into asolid body with the physical parameters of the moving heat carrier is stillunrealizable. The Newtonian formula (3), (6) should not be postulated butshould stem out from the physical model of the flows and heat transfermechanism!

The boundary layer. The liquid, plasma, gas (or other medium) near theplate surface, or, exactly at the boundary itself may be regarded as immov-able. Such an assumption of the medium sticking at the boundary holds truein most cases except for rarefied gas where the concept of a continuousmedium is not valid.

So, the dynamic boundary layer can be approximately described as theregion, where the medium plasma velocity u decreases from the velocity ofthe outer free flow to zero at the body surface.

Although such a definition does not specify any exact thickness of theboundary layer Du. It can be assumed that this thickness is equal to thedistance over which the most part of the velocity change is observed. Forplasma high-temperature jets the same is true for the plasma temperature.

The thermal boundary layer is the region where the plasma (or any me-dium) temperature varies from the temperature of the outer free flow plasmaTp to that of the solid body surface Ts.

The thickness of the dynamic layer du may not coincide with that of thethermal boundary layer dT.

The relative immobility of the fluid medium within the boundary layerallows to substitute the Newtonian formula (6) within the boundary layerfor convective heat transfer by the Fourier formula (5) and to consider theheat transfer through the boundary layer is in agreement with the heat con-duction law

q ¼ a Tp � T s

� � lpTp � T s

�dT

Here lp is the medium plasma conductivity, in contrast to the body con-ductivity that we have in formula (7).


This transition within the similarity theory considerations has led to thefirst physical model of the heat transfer through the boundary layer. This isthe simple conductive heat conductivity model:

a � lpdT

But it should not be over estimated because the heat transfer mechanismfrom the moving medium to an movable one was shifted only to a boundarylayer thickness dT and all the difficulties of calculating the heat transfercoefficient a were switched to the calculation of dT.

It should be noted also that the heat transfer dimensionless coefficient Nu(Nusselt number) was developed under the tacit assumption of the existenceof such immobile sublayer. Therefore, the conductivity of the plasma gasappears in formulas (10) and (11) in place of the solid body.

E. BOUNDARY LAYER THICKNESS EVALUATION AND THE FIRST POSSIBILITY OF

EXPRESSING THE HEAT TRANSFER COEFFICIENT WITH FLOW PARAMETERS

So, the hydrodynamic boundary layer is the narrow region near the in-terface between the flowing plasma medium and the solid body where thevelocity of the fluid decreases from the free flow velocity u to zero at the wall.

Let us examine now the simplest boundary layer case, when the mediumflows past the surface of a plane plate. This definition assumes that theviscous friction forces within that layer which suppress the inertial force ofthe free flow to its zero value at the wall are comparable with the inertialforce. These forces may be expressed as follows:

Friction:

F friction ¼ md2uxdy2

(18)

Inertial force:

F inertial ¼ ruxduxdx

(19)

The x-axis is oriented along the motion direction, and y is directed across it,r is the medium density, ux is the velocity x-component along the plate.

To evaluate these forces, we denote the boundary layer thickness by duand the characteristics body dimension along the flow direction by d.


Then

F friction � mupd2u

F inertial � ru2pd

(20)

Equalling F friction ¼ F inertial, we get:

mupd2u

� ru2pd

(21)

It follows from here

du ¼ffiffiffiffiffiffiffiffiffiffim

rupd

r(22)

But the complex rud=m ¼ Re is the Reynolds number, hence

dud’ 1ffiffiffiffiffiffi

Rep (23)

So, the order of magnitude of a dynamic boundary layer thickness dudivided by the characteristic dimension of the body d is the inverse of thesquare root of the Reynolds number. This simplest estimate allows to drawtwo very important inferences:

1. The boundary layer thickness is small only for large Reynolds numbers.For small Reynolds numbers the boundary layer thickness is comparablewith the body dimension characteristic, e.g. with the diameter of the smallparticles in the plasma jet.

It should be noted that all other conclusions of the boundary layer theoryare also based on this assumption.

2. The second conclusion which can be drawn from this estimation, is thepossibility to establish the relationship (although rather approximately) ofthe convective heat transfer coefficient a with the flow parameters. Thispossibility seems to be very important because within the similarity theoryboundaries, which does not take into account any mechanism of heat trans-fer it seems to be impossible.

So, under the assumption of the immovability of the sublayer adjacentto the wall, it was shown that the Newtonian formula for a convectiveheat transfer between the medium and the body inside that sublayer canbe substituted by the Fourier formula in the case of simple heat


conductivity:

a Tp � T s

� ’ lTp � T s

dT(24)

If we substitute the thickness of the dynamic hydrodynamic boundarylayer assuming du ’ dT from (23) to (24), we obtain:

a Tp � T s

� ’ ffiffiffiffiffiffiRe

p ld

Tp � T s

�(25)

It follows from here that in a very rough estimate the convective heat trans-fer coefficient a can be expressed by the flow parameters in the following way:

a ’ffiffiffiffiffiffiRe

p ld

(26)

Comparing (26) and (17) it follows from here that the dimensionless con-vective heat transfer coefficient – the Nusselt number is proportional to thesquare root of the Reynolds number:

Nu �ffiffiffiffiffiffiRe

p(27)

The most striking fact that the intensity of the heat transfer (Nu) is ex-pressed by the flow parameters (Re) without any complex physical modelsusing only speculative supposition of immobility of the sublayer and its smallthickness!

This shows one of the greatest merits of the similarity theory and of thesimilarity criteria.

Further of formulas (26) and (27) will not reject but confirm this dependence!

F. THE FULL ENERGY OF THE ONCOMING FLOW: THE STANTON’S NUMBER

When the description of a physical phenomenon is difficult, a possibleway for understanding the mechanism is an external qualitative approach.Power engineering gives as a typical example of such an external approachto the problem. Whatever the specific ways of using power by individualconsumers, power engineering evaluates its useful amount and lossesthrough the concept of efficiency.

Let us pose a similar question for the problem of convective heat transfer:what amount of energy carried by the oncoming stream can be transferredto the solid body and assumed by?

This requires specifying the initial value – the energy content of the streamitself.


It will be shown later in Section II that it is the enthalpy H that qualifiesthe energy content of the immovable plasma flow:

HJoule

kg

� �

In the case of plasma moving with a velocity u, the energy content is equal to:

ruHpWatt

cm2

� �(28)

Here r is the density; u is the velocity and Hp is the enthalpy of the stream.If we consider the problem of heat transfer, we do not operate with the

absolute value of the stream enthalpy Hp but with some difference betweenthe medium at the body wall Hs, i.e. enthalpy pressure, which was alreadydiscussed

Hp �Hs

�Let us evaluate the amount of energy delivered into the front surface of a

spherical particle inserted into a plasma flow.

ru Hp �Hs

�S Watt½ � (29)

S being the middle section of the sphere.So, we get the energy of the flow per unit surface equal to:

q � ru Hp �Hs

� Watt

cm2

� �(30)

This quantity gives us the total of energy transfered by the flow to theparticle surface.

The amount of heat gained by the spherical particle is defined byNewton’s formula:1

q ¼ aHp �Hs

Cps(31)

The ratio of these thermal fluxes leads to the Stanton number:

aruCps

¼ St (32)

This number is dimensionless and stands for the heating efficiency in heatengineering. For low-temperature subsonic plasma jets and flows it can

1 Here the enthalpy pressure is used rather than the temperature pressure.


be expressed by the temperature pressure which, naturally, yields the sameresults:

St ¼ a Tp � T s

�ruCp Tp � T s

� ¼ aruCp

(33)

G. THE PRANDTL AND PEKLET NUMBERS

It can be easily shown that all principal similarity numbers of the con-vective heat transfer (Nu, Re, St) are combined in single common expression:

St ¼ Nu

Re Pr. (34)

From this we derive a new similarity number (complex) – the Prandtlnumber. It is equal to:

Pr ¼ mCps

l. (35)

Multiplication and division by the density r of a heat carrier gives us

Pr ¼ mrrCps

l¼ n

a(36)

where n is the kinematic viscosity coefficient: n ¼ m=r; a is the thermaldiffusivity, a ¼ l=rCps.

The Prandlt number is defined completely by the physical properties ofthe medium: specific heat Cps, thermal conductivity l viscosity m. Therefore,it characterizes the physical properties of the thermal carrier. It may beexpressed as the ratio of two characteristics of the transfer: (1) the kinematicviscosity n and (2) the temperature conductivity coefficient a.

The impulse transfer, related to the quantity u is defined by the velocitydifference and the heat transfer in the same way depends on the temperaturedifference. Hence, the Prandtl number defines the similarity of temperatureand velocity fields. If Pr ¼ 1, the fields are similar.

It will be shown in the next section that the Prandtl number expresses theratio of thicknesses of temperature and velocity boundary layers for con-vective heat transfer within the theory of the boundary layers.

dTdu

� 1ffiffiffiffiffiffiPr

p (37)


To end the discussion of similarity numbers and criteria, we introduce onemore important number which characterizes the ratio of the share of theconvective heat transfer (ruCps) to the thermal conductivity heat transfer l.

Let the process in two models and two media be described by the twoequations respecting the convective heat transfer and heat conductivity:

The first model:

r1Cp1u1dT1

dx1¼ l1

d2T1

dx21

u1dT1

dx1¼ a1

d2T1

dx21ð38Þ

The second model is described respectively by

r2Cp2u2dT2

dx2¼ l2

d2T2

dx22

u2dT2

dx2¼ a2

d2T2

dx22ð39Þ

Using the similarity scales

T1

T2¼ CT ;

d1

d2¼ Cd ;

a1a2

¼ Ca;u1u2

¼ Cu

we expressed the processes in the first model by the variables of the secondone and by the scales

Cu � CT

Cd

� �u2

dT2

dx2¼ CaCT

C2d

" #a2

d2T2

dx22(40)

It follows from the identity of the processes in the media and models thatas in (11) and (12) the terms in square brackets are equal and may becancelled out

CuCT

Cd

� �¼ CaCT

C2d

" #(41)

or

CuCd

Ca¼ 1 (42)


It follows from here:

u1d1

a1¼ u2d2

a2(43)

This dimensionless number is called Peklet number

Pe ¼ uda

(44)

So, the Peklet number describes the comparative intensity of the convec-tive and conductive heat transfer.

It can be easily seen that only two derived numbers – the Peklet numberPe and the Prandtl number Pr are connected with the Reynolds number bythe following relation:

Pe

Re¼ Pr (45)

which along with the relation

St ¼ Nu

Re Pr¼ Nu

Pe(46)

ends the search for the numbers and complexes of thermal and dynamicsimilarity. We can hope that the problems treated here can be successfullysolved with the use of only these five similarity numbers.

H. THE EQUATIONS OF THE LAMINAR BOUNDARY LAYER

One of the cases where the flow and temperature field in the boundary layerand hence the heat transfer coefficient a can be defined exactly, is the flownear to a plane thin plate. In this case the structure of the flow is not disturbedbut the whole peculiarity of the adjacent boundary layer is revealed.

The equations for the boundary layer will be setup for this model below.The thermal problem cannot be solved without solving the motion equa-

tions. Therefore we begin with the formulation of the general stationaryequations of the heat transfer for the plane two-dimensional motion of themedium:

1. The equations of motion for the plane stationary motion of real non-compressible medium have the form:

ux@ux@x

þ uy@ux@y

¼ � 1

r@p

@xþ v

@2ux@x2

þ @2ux@y2

� �

ux@uy@x

þ uy@uy@y

¼ � 1

r@p

@xþ v

@2uy@x2

þ @2uy@y2

� �ð47Þ


2. Continuity equation (the mass conservation law) is

@ux@x

þ @uy@y

¼ 0 (48)

3. The heat transfer equation:

ux@T

@xþ uy

@T

@y¼ a

@2T

@x2þ @2T

@y2

� �(49)

Here ux is the x-component of the velocity along the plate, uy is the y-component of the velocity in the transverse direction. At the wall (at theplate) Ts ¼ const. In the free flow

ux ¼ up; T ¼ Tp

This system of equations written down for the whole flow is further re-written for the thin boundary layer adjacent to the plate using some estimatesand simplifications. In this new form, the equations will be called boundarylayer equations.

The transformation of the general Navier–Stokes equations into boundarylayer equations means their simplification based on a single assumption thatthe use of these equations is restricted to the very small region of theboundary layer. This can be done in the most simple and clear manner whileinspecting the plane non-vertical motion along the plate.

Within the boundary layer longitudinal (directed along the plate) distancesand velocities are of order 1 compared to the plate length, whereas thetransversal velocity and distance is of order d (the boundary layer thickness)which is substantially less than unity.

So in a good approximation, the flow in the boundary layer can be des-cribed by the velocity ux�component which can be called the main flow.

1. We begin with the estimate of the continuity equation in the boundarylayer

@ux@x

þ @uy@y

¼ 0 (50)

The order of the quantities

1

1þ d

d¼ 0

Hence, both the terms in the continuity equations are of the same orderand so it remains unchanged.


2. The first motion equation:

ux@ux@x

þ uy@ux@y

¼ � 1

r@p

@xþ v

@2ux@x2

þ @2ux@y2

� �(51)

has the order of the terms

11

1þ d

1

d¼ 1

1þ 1

12þ 1

d2

� �

The second equation:

ux@uy@x

þ uy@uy@y

¼ � 1

r@p

@xþ v

@2uy@x2

þ @2uy@y2

� �(52)

has the following order of the terms

1d1þ d

dd¼ dþ d

12þ d

d2

� �

(more precise evaluation of terms should be based on the dimensionlessform of the equations).

All the left-hand terms in the first equation have order of unity, and thevelocity change in the brackets ux with respect to x is naturally substantiallyless than its change with respect to y

@2ux@x2

� @2ux@y2

Hence, the term @2ux=@x2 can be neglected compared to @[email protected] of the second equation with the first one, we see that all the

terms of that second equation are small (d51) compared to the terms ofthe first one. This estimate holds true also for the pressure. That means thatthe second equation can be neglected in the boundary layer altogether com-pared to the first one!

3. We assess now the terms in the heat transfer equations:

ux@T

@xþ uy

@T

@y¼ a

@2T

@x2þ @2T

@y2

� �(53)

In individual terms have the order:

11

1þ d

1

d¼ 1

12þ 1

d2


On the left-hand side all the terms have the order of unity, and on theright-hand side the temperature variation with respect to x-along the platecan be neglected compared to its variation in the transverse y-direction.

So, the assessment of the terms of the equations (50)–(53) based on theonly assumption of the small thickness of the boundary layer d compared tothe plate length L

dd� 1ffiffiffiffiffiffi

Rep � 1 ðfor Re � 1Þ

gives us the equations which are called boundary layer equations:1. The motion equation:

ux@ux@x

þ uy@ux@y

¼ � 1

r@p

@xþ v

@2ux@y2

(54)

2. The continuity equation:

@ux@x

þ @uy@y

¼ 0. (55)

3. The heat transfer equation:

ux@T

@xþ uy

@T

@y¼ a

@2T

@y2. (56)

This is just the form which was originally set up by L. Prandtl.The systems of equations of motion in their general form (47) consisting of

two equations includes three unknown quantities ux, uy and r. This uncer-tainty is usually overcome excluding from (47) to (54) of the pressure gra-dient. This is based on the following assumptions.

If we neglect the influence of the plate and its boundary layer on the wholeflow, the outer flow can be regarded as a motion of ideal non-viscous fluidhaving the only velocity component ux ¼ ufl. Then the first equation

ux@ux@x

þ uy@ux@y

¼ � 1

r@p

@xþ v

@2ux@y2

is reduced to the equality

up@up@x

¼ � 1

r@p

@xas

@ux@y

¼ 0

� �(57)


So, the pressure gradient in the boundary layer equation can be expressedby the velocity gradient of the outer flow

ux@ux@x

þ uy@ux@y

¼ up@up@x

þ v@2ux@y2

(58)

Thus, in this section we have set up the simplified boundary layer equations.

I. ESTIMATION OF THE THERMAL BOUNDARY LAYER THICKNESS

Earlier, for the estimation of the thickness of hydrodynamic (dynamic)boundary layer we made the assumption that the viscous forces inside thislayer are of the same order as the inertial forces. It was shown that the ratioof the thickness of this layer du to the characteristic dimension of the bodyalong the x-axis d is equal to


Rep (59)

Now, after setting up the heat transfer equation for the boundary layer wecan attempt to estimate the thermal boundary layer thickness dT.

To this end, we make the assumption that within the boundary layer theprocesses of heat transfer by conduction are of the same order as the con-vective heat transfer. It is evident from equation (56) that the convectiveheat transfer is defined by the first term of (56)

rCpuxDTDx

whereas the term

lD2T

Dy2

stands for the heat conduction.These terms have the order

rCpsuxDTDx

� rCpsupTp

d(60)

lD2T

Dy2� l

Tp

dT(61)

respectively.


Setting equal the right-hand sides of (60) and (61) we get

dTd

� �2� l

rCpsup(62)

Here dT is the thermal boundary layer thickness.This yields

dTd

� �2� l

rCpsupL¼ 1

Pe(63)

Hence

dTd

¼ 1ffiffiffiffiffiffiPe

p

Comparing the dynamic du and thermal boundary layer thickness (63) we get

dTdu

¼ffiffiffiffiffiffiRe

Pe

r¼ 1ffiffiffiffiffi

Prp (64)

Here Pr is the Prandtl number, Pe the Peklet number and Re the Reynoldsnumber.

J. THE APPROXIMATE EXPRESSION FOR THE CONVECTIVE HEAT TRANSFER

COEFFICIENT AS FUNCTION OF MEDIUM AND FLOW PARAMETERS

The main goal for this topic is how to express the heat transfer intensity(the coefficient a or Nu number) as a function of the medium parametersand characteristics of the flow: the velocity u, the density r, the viscosity m,the thermal conductivity l, the specific heat Cp etc. It seems impossible toderive such expression on the basis of simple estimations without getting theexact solution of the equations (54)–(56). But similarity considerations andsimilarity numbers offer unexpectedly such a possibility. They allowto establish the structure of the expression sought using the most simpleestimations.

It was shown above (Section I.E) that the simple estimate for the (hydro)dynamic boundary layer thickness yields


Rep (65)


It was shown that under the assumption of the medium immobility withinthe boundary layer we get from

a Tp � T s

� � lp �Tp � T s

dT(66)

and approximate equality dT� du a rough estimation for the heat transferintensity (a) expressions by the flow parameters described by the Reynoldsnumber (Re).

Substitution of (65) into (66) yielded:

a Tp � T s

� ’ ffiffiffiffiffiffiRe

p ld

Tp � T s

�(67)

It follows from here

a �ffiffiffiffiffiffiRe

p ld

The Nusselt number has proved to be proportional toffiffiffiffiffiffiRe

p:

Nu ’ffiffiffiffiffiffiRe

p(68a)

A similar estimation can also be made for dT, which was just obtainedusing simple considerations on equality of conductive and convective heattransfer in the boundary layer. The quantity dT proved to be expressed by duand the Prandtl number (64)

dT � duffiffiffiffiffiffiPr

p

Using the estimate for du from (65) and substituting it into (64) we get

dT � dffiffiffiffiffiffiRe

p ffiffiffiffiffiffiPr

p (68b)

From here, using equation (66) one can obtain

a Tp � T s

� � ffiffiffiffiffiffiRe


p ld

Tp � T s

�(69)

Hence, the heat transfer coefficient a in the rough estimate can be ex-pressed by the flow parameters (Re) and medium parameters (Pr) in thefollowing way:

a ’ffiffiffiffiffiffiRe


p ld

(70)


The Nusselt number equals:

Nu ’ffiffiffiffiffiffiRe


p(71)

We should remark that such an estimate is contradictory in itself. On theone hand, it is assumed that the medium in the boundary layer is immovableand there is no heat transfer by convection (equality (66)). On the other hand,the estimate for the thermal boundary layer was obtained from an approxi-mate equality of convective and conductive heat transfer (equality (62)).

This estimate of the structure of the expression of a by Re and Pr numbersis given here as a mere illustration of effectiveness of similarity consider-ations and numbers.

Further the exact solution of the problem of thermal boundary layer willonly make the character of the expression for Nu ¼ f (Re, Pr) more precisebut not refute it.

K. THE EXACT CALCULATION OF THE HEAT TRANSFER COEFFICIENT a(LAMINAR THERMAL BOUNDARY LAYER AT THE PLANE PLATE)

The previous section of this chapter have introduced the reader to thescope of basic concepts and definitions of convective heat transfer. Now, wehave come up to the statement of the key problem which will use all thesesimilarity numbers, criteria and estimates as mere tools.

The problem is to establish the expression for the heat transfer coefficientand its dependence on the medium and motion parameters. This means thatwe will attempt to setup a physical model of heat transfer in the boundarylayer discussed at the beginning of the chapter.

Because of the complexity of the medium motion near the solid wall thiscannot be done in a general form. But there are some particular simpler caseswhich lead to both exact and approximate solutions. This is the case of theboundary layer of the plane plate. We can obtain here analytical expressionsfor the heat transfer coefficient represented by the medium and motionparameters.

Further, the composition of the derived formulas yields to their exten-sions on more complex models using similarity considerations.

Modern theories of the boundary layer originate from the studies ofKarman and Pohlhansen. In the later contributions they were substantiallyimproved, became more simple and exact, and in some aspects were sub-stantially modified.

The substance of this idea is based upon an assumption that the velocitydistribution in the regions of the boundary layer is represented by thefunctions which are given in advance and not obtained as a result of theintegration of the boundary layer differential equations.


The choice of these functions is stipulated by consequent considerations,which are sometimes rather subtle and complex. Anyway, the problem isreduced to the reasonable choice of the functions and not to defining them byintegrating the basic equations. The use of the approximate procedures leavesout the necessity of direct integration of the boundary layer equations alto-gether. It should be noted that the subject of the investigation is only the mainflow orientated along the x-coordinate (and, consequently, the longitudinalvelocity ux). The transversal velocity component is not considered at all.

The functions used as approximations of actual velocity distribution,should possess a fair degree of flexibility which would allow to representmultiformity of really existing types of boundary layer flows. They shouldserve as an instrument for the description of the process which allows todefine all the peculiarities of the flow pattern in different conditions. Theseinclude an accelerated flow with decreasing pressure (convergent flow) and adecelerated one with increasing pressure (divergent flow).

The one-parametric function that proved to be suitable for the velocity isdefined as an explicit function of the transversal coordinate and it includesone more parameter depending on the longitudinal coordinate. The variationof this parameter which is usually called the form parameter along the flowallows to represent the pattern of velocity factor restructuring. It was un-derlined above that the boundary conditions are to some extent indefinitebecause the very concept of the boundary layer thickness is not strictlydefined. This makes it impossible to specify its outer boundary in an exactmathematical form. These conditions may be formulated only in an asymp-totical form.

The approximate theory of the boundary layer in its initial form wascontrasted to the precise theory as the teaching about the boundary layer offinite thickness. It contrast to the characteristic for exact theory definition ofthe boundary layer thickness based on the agreement about the acceptabledifference between the longitudinal velocity ux and the velocity of the outerflow up the approximate theory directly introduces some specific value ofordinate y ¼ d at which both conditions

ux ¼ up and@ux@y

¼ 0 with y ¼ d

are satisfied. Here d is the function of longitudinal coordinate x.Such concept of the boundary layer thickness as some finite quantity,

which is an unspecified function of x-coordinate, is useful in many aspects.Nowadays, although the modern theory does not necessarily involve thefinite thickness concept, it is still true. As long as the modern theory wasdeveloped, the main concept shifted from the boundary layer thickness to


more accurate integral layer characteristics – the thickness of impulse lossand the thickness of mass extrusion.

Both these integral characteristics – the thickness of mass extrusion d* andthe thickness of impulse loss d** – retain their sense within the system ofnotions of the boundary layer theory with finite thickness. The expressionsdefining them are somewhat modified (because the upper integration limitbecomes a finite value d):

d ¼Z d

0

1� uxup

� �dy; d ¼

Z d

0

uxup

1� uxup

� �dy

But it is absolutely clear that all the definitions remain unaffected by suchsubstitution, because both integrants for y4d are equal to zero as followsfrom their definition.

The question arises, why do we need some extra dimensions in addition tothe ones defined above: the thickness of the thermal boundary layer dT and(hydro) dynamic one du.

The fact is that the quantities dT and du were defined in a speculative way.Their only definition rests upon the position of the boundary between the non-gradient flow and the boundary layer adjacent to the plate. The quantities dTand du can be hardly incorporated into some equations which would be usedfor their definition. On the other hand, the quantities d* and d** can be insertedinto mathematical equations, because the first of them is related, to the massconservation law and the second one to the impulse conservation law.

In further analysis it will be d* and d** which are defined from the equa-tions and serve as a key which allows to penetrate into boundary layer.2

Using the methods of the boundary layer theory one can obtain for thelocal value of the heat transfer coefficient between the plate and the flow:

a ¼ 0:323 lffiffiffiffiffiffiPr

3p ffiffiffiffiffi

upnx

r(72)

In practice one usually employs not local, but the mean value of heattransfer coefficient amean, which is equal to

lmean ¼ 1

x

Z x

0

a dx ¼ 0:646 lffiffiffiffiffiffiPr

3p ffiffiffiffiffi

upnx

r. (73)

The mean value of the heat transfer coefficient is always equal to thedoubled value of the local coefficient for a given plate length.

2 We do not place here very complicated calculations. They can be found in textbooks of gasand hydromechanics.


If we multiply the local coefficient in equation (72) by x/l, it becomes

Nu ¼ axl

¼ 0:323 lffiffiffiffiffiffiPr

3p ffiffiffiffiffiffi

Rep

(74)

or for the mean value of the Nusselt number

Nu ¼ ameand

l¼ 0:646

ffiffiffiffiffiffiPr

3p ffiffiffiffiffiffi

Rep

. (75)

Here for the plate 0rxrd, where d is the characteristic longitudinaldimension of the plate.

So, we can obtain the result which was sought from the very beginning.We succeeded for the simple model case to establish the relationship of

the convective heat transfer intensity a with the energy carrier parameters(Pr) and the flow parameters (Re).

Formula (75) expresses the heat transfer coefficient a by the similaritynumbers Pr and Re. We recall that the structure of formula (75) differs fromformula (71) only in the power of the Pr number and the numerical factor.So, all the earlier estimates are thereby confirmed.

In such a manner the relationship of the heat transfer coefficient with themedium and flow parameters were established using only a limited number ofmodel assumptions. For solving the problem it was necessary to introducealong with the thermal boundary layer thickness dT and the dynamic one dutwo more quantities: the thickness of impulse loss dv and the enthalpy lossthickness dT . Both these quantities allowed to set up the impulse equationand energy conservation equation and to solve them.

It should be noted that the definition of du and dT as a boundary, dividingthe non-gradiental free flow and the boundary layer adjacent to the plate hasretained it sense.

The quantity du is expressed by du and du in the following way:

the mass extrusion thickness du ¼ 1=2du;the impulse loss thickness du ¼ 1=6du;the energy (enthalpy) loss thickness dT ¼ 1=4du.

So the goal has been reachedy , but only for the simplest case. And howabout more complex cases? What shall we do if the character of the flowchanges along the surface (e.g. the face is formed by the rear of the sphericalparticle)? How can we treat turbulent flow?

In the case of the complex character of the flow, non-isothermic jets,turbulent flow and the main procedures of the heat transfer investigationsare experimental procedures.


Therefore the similarity considerations (the similarity theory), similaritynumbers and the heat transfer formulas expressed in the terms of similaritycriteria are of still greater importance.

The derived above formula (75) including Nu, Re and Pr numbers is usedfurther as a basis for all further analysis.

The structure of the expression of the Nu-number is generalized into theform:

Nu ¼ A RemPrn (76)

where the constant A and exponents m and n are defined experimentally foreach individual model and flow type. Different correction factors are oftenadded to this formula. They are also defined experimentally.

Now we have dozens, or in some cases hundreds, of different values of theconstants A, m, n and correction factors in formula (76) for every modelbody, flow character, velocity and temperature range. One can hardly find athermo physicist, who would not try to establish the values of A, m and n ofhis own for his particular model and flow type.

Sometimes it is difficult to be orientated in this ocean of values of A, mand n.

The a-values expressed by medium and flow parameters are rather scarce.Is this a merit or a disadvantage?

On the one hand, it is a merit, because we get a tool to describe theconvective heat transfer. On the other hand, it is a disadvantage, because theproblem of multiformity of heat transfer mechanisms in the boundary layerdoes not ever arise. Even if that question is posed, it is within the similaritynumber considerations.

L. HEAT TRANSFER FORMULAS FOR SPHERE, CYLINDER AND PLATE3

The end of this section devoted to fundamentals of convective heattransfer at low (subplasma) temperatures there will be a review of formulaspresented in tabular form, describing the heat transfer of subplasma jets andflows with spherical bodies, with a cylinder in the transversal flow and with aplane normal to the jet according to the data of different authors.

1. The Heat Transfer in the Spherical Bodies with the Flow

The criterial formulas for the heat transfer between the spherical bodiesand subplasma flows presented in different papers, are listed in Table I. Inaddition to the different values of A and exponents m and n of the Reynolds

3 This section includes the reference data.


and Prandtl numbers caused by different conditions of the flow and heattransfer, the different forms of the mathematical expression for the Nusseltnumber should be noted. So, in some cases that number is defined by theformula Nu ¼ 2+A Rem Prn, in other formulas the term 2 does not appear.Spherical case allows to establish theoretically the limit (lowest) value ofthe heat transfer coefficient in an immobile fluid. So we have for the sphereNumin ¼ 2. This is the reason for representing the correlation for the spherein the two-term form. One term stands for a conductive form and anotherfor a convective one. But the value Numin ¼ 2 is obtained for the case whenthe heat transfer conditions (the medium parameters) are close to thespherical wall temperature (the inner boundary of the layer). In the caseswhere the authors neglect this rule and define the heat transfer parameters at

TABLE I

CORRELATIONS FOR THE HEAT TRANSFER WITH THE SPHERE

Nu Range

Nu ¼ 0:37 Re0:6 Re ¼ 17270� 103

Nu ¼ 2þ 4:12 Re0:31 Re ¼ 5022000

(For the front point)

Nu ¼ 0:945 Re0:54 Re ¼ 1600290; 000

(For the front point)

Nu ¼ 2þ 0:493 Re0:5 Re ¼ 1021800

Nu ¼ 2þ 0:3 Re0:54 Re ¼ 18002150; 000

Nu ¼ 1:44 Re0:5 For the front point

Nu ¼ 0:7 Re0:5 Pr0:33 K

K ¼ sin2 2 xð Þ12cosð2xÞ � 3

2cosð2xÞ � 1

�0:5 For any point, local values Nu

Nu ¼ 0:93 Re0:5 Pr0:33

Nu ¼ 0:19 Re0:64 Re ¼ 1042105

Nu ¼ 0:54 Re0:5 Re ¼ 20023000

Nu ¼ 2þ 0:6 Re0:5 Pr0:33 Re ¼ 02200

Nu ¼ 2þ 0:55 Re0:5 Pr0:33 Re ¼ 22750

Nu ¼ 0:62 Re0:5 Re ¼ 103212� 103

(The sphere is hung up)

Nu ¼ 1:06 Re0:457 Re ¼ 1032123

(The sphere on the stretches)

Nu ¼ 0:2 Re0:83 The falling particles

Nu ¼ 2þ 0:03 Re0:54 Pr0:33 þ 0:35 Re0:58 Pr0:35 Re ¼ 0215� 104


the outer boundary layer, their experimental data are described by the for-mula Nu ¼ ARemPrn. Several heat transfer researches for spherical bodieswith subplasma temperatures was carried out, in transient conditions (forthe body in the flow). In these cases, the differences in the correlations arecaused not only by the different character of the heat transfer but also bytransient character of the dynamic and thermal boundary layers.

2. The Heat Transfer to a Cylinder Target in Cross Flow

The case of a cylinder target in a subplasma cross flow is the most widelyinvestigated geometrical form. Some of the results obtained for the subplasmaflow in different sources are presented in Table II. As in the case of a plane ora sphere target the coefficients A, m and n vary for the different conditions ofthe heat transfer. It follows from this table that for increased values of Re theA-values decrease and those of m increase. The divergence of correlationsdeveloped in different sources is caused not only by the difference in theheat transfer conditions, but also by the different form of the temperaturecorrection factor. So, some authors define the reference temperature asthe mean value for the boundary layer (Tp+Ts)/2, while others define theheat transfer parameters based on the flow temperature Tp to the walltemperature Ts.

For some correlations the choice of the reference temperature has only asmall influence on the a value. This is due to the mutual compensation oftemperature changes of transfer coefficients and thermodynamic functionsinvolved in Re and Pr. So, the value of a for air at m ¼ 0.47 is almostindependent of the reference temperature. In some cases this fact allows todefine the reference temperature arbitrarily. (At m ¼ 0.4–0.6, the a-values aremore markedly affected by the reference temperature.) In these cases if thecorrelation with certain values of C, m and n leads to a substantial error whenused in a wide temperature range, some authors introduce the special cor-rection factor, so-called temperature correction, allowing to compensate thearising error. Such a correlation is written down in the form Nu ¼ CRem

Prn � f (T), where f(T) is the temperature correction factor. It can be seen fromTable II how different the values and the ways of introducing the correctionare. In some cases the temperature correction represents the ratio of the walland flow temperatures, in other cases it is expressed by the ratio of the Prandtlnumbers calculated for the outer and inner interface of the boundary layer. Itwill be shown further that for the ionized and dissociated boundary layer thetemperature correction is defined by the ratio ðrpmp=rsmsÞk, where r and m arethe density and velocity at the both interfaces of the boundary layer.

The flow turbulence factor affects markedly the heat transfer coefficient.Coefficient C is supposed to be dependent on the degree of turbulence of the


TABLE II

CORRELATIONS FOR THE HEAT TRANSFER FOR A TRANSVERSELY PLACED CYLINDER IN A CROSS-FLOW AND CONDITIONS UNDER WHICH WERE OBTAINED

Correlation Re-number range Temperature range (K) Reference temperature Medium

ð0:35þ 0:47 Re0:52Þ Pr0:3 1�105 300�1300 0:5 ðTp þ T sÞ Water, air

ð0:36þ 0:37 Re0:5 þ 0:057 Re0:67Þ Pr0:33 1�105 300�1300 0:5 ðTp þ T sÞ Air

0:86 Re0:41 Pr0:35 4�50 T soTp 0:5 ðTp þ T sÞ Air

0:891 Re0:33 ðT s=TpÞ0:08 1�4 T s � 300

Tp ¼ 40021300

0:5 ðTp þ T sÞ Air

0:821 Re0:389 ðT s=TpÞ0:1 4�40

0:615 Re0:466 ðT s=TpÞ0:12 40�4000

0:174 Re0:618 � ðT s=TpÞ0:16 4� 103�4� 104

0:0239 Re0:805 ðT s=TpÞ0:12 4� 104�2.5� 105

0:5 Re0:5 Pr0:38 ðPrp=PrsÞ0:25 5� 103 Tp ¼ 2912323 Water, air, transformer oil

T s ¼ 2932342

0:25 Re0:6 Pr0:38 ðPrp=PrsÞ0:25 103�2� 105

0:59 Re0:47 Pr0:38 ðPrp=PrsÞ0:25 8�103

0:25 Re0:6 Pr0:38 ðPrp=PrsÞ0:25 103�20� 105 T s ¼ 2902350 The same

0:945 Re0:33 ðT s=TpÞ0:21 10�30 T s � 300 0:5 ðTp þ T sÞ Air

0:68 Re0:42 ðT s=TpÞ0:12 40�60 Tp ¼ 35021300 0:5 ðTp þ T sÞ Air

0:6 Re0:5 Pr0:33 � ðT s=TpÞ0:12 10 Ts ¼ 311 Nitrogen

Tp ¼ (6�13)� 102

479

HEATAND

MASSTRANSFER

INPLASMA

JETS

flow:

C ¼ 0:5 1þ ffiffi�

p �(77)

For the laminar flows C ¼ 0:5, for the turbulent ones C ¼ 0:521. In thiscase the values of m and n and the temperature correction factor remainunchanged. This is not the only way of considering the flow turbulence. Someauthors (Table III) introduce the corrections into both values of A and m.

3. The Heat Transfer Coefficient to a Flat Target with the Gas Flow or a Jet

The correlations of the heat transfer of axi-symmetrical jets with the plateperpendicular to the flow are presented in Table III. Experiments with jetsongoing on a plate are carried out in two ways. The first one uses the coolingof the hot plate by the jet. The second one uses heating of the cold or cooledplate. The local and mean values of the heat transfer coefficient can bedefined. The value of the heat transfer coefficient a in these experimentsdepends substantially on the distance from the plate to the nozzle h, i.e.whether the plate is positioned in the initial or main section of the jet.Therefore, in some papers the Nusselt number is treated as a function ofh/d, where d is the nozzle diameter. In these cases, the dimensionless length ofthe jet h/d also appears in the correlation along with the usual similaritycriteria. In the cases when the heat transfer is investigated for the initialsection of the jet or the h-value in the experiments is fixed and the jet velocityand temperature are variable parameters. The experimental data are treatedon the basis of the usual correlation Nu ¼ CRem �Prn. As follows fromTable III, the analysis of the heat transfer conditions with the plate shoulddistinguish two substantially different cases:

1. The plate dimensions are close to or less than that of the jet.2. The plate dimensions are substantially larger than the jet diameter.

In the first case, the criteria and the heat transfer coefficient are related tothe plate dimensions. In the second case they are related to the jet dimen-sion, usually, to the nozzle diameter. The data make an exception. Here themean heat transfer coefficient was defined for the whole plate surface.

The heat transfer was studied from a heated plate l to the air flow fordifferent diameters d of nozzles and distances h. The criterial processing ofthe results was based on the formula

Nu ¼ CRenh

d

� �ml

d

� �k

(78)


TABLE III

CORRELATIONS FOR THE HEAT TRANSFER OF THE JET WITH THE PLATE NORMAL TO THE FLOW

Nu Re Medium,

experimental

conditions

Reference diameter Comment

0.181 Re0.7 Pr0.33 1.1� 104�3� 104 Air, heating, 8 Nozzle diameter d Jet coming on the

infinite obstacle300–6001C

C Re0:33 exp �0:037h

d

� �C ¼ 1:06; C ¼ 0:33

2.2� 104�6� 104 Air, heating, � 10 Nozzle diameter d Jet coming on the

infinite obstacle50–201C

0:55 Re0:5 Pr0:33 50�3.1� 104 Water, cooling � 0:5 Nozzle diameter d Jet coming on the

infinite obstacleC Re0:64 Pr0:33

� exp �0:037 hd

� 50�3.1� 104 Water, cooling 0.5�10 Nozzle diameter d Jet coming on the

infinite obstacle

C Re0:33 Pr0:33

� exp �0:037 hd

� 50�3.1� 104 Water, cooling � 10 Nozzle diameter d Jet coming on the

infinite obstacle

1:41 Re0:451 2.5� 103�105 Air, cooling Disk diameter R Plate in the flow

0:724 Re0:5 103�105 Air, cooling Half-width of the plate Plate in the flow

0:82 Re0:5 Pr0:33 104�105 Calculation hþ R � 6:2 The current radius of the

point

Jet, local Nu

1:54 Re0:5 Re0:33 104�105 Calculation 2R Get, mean Nu

1:54 Re0:5 Pr0:33 104�105 Air, cooling 2R Get, mean Nu

1:26 Re0:5 Pr0:33 103�105 Calculation 2R Get, mean Nu

481

HEATAND

MASSTRANSFER

INPLASMA

JETS

One of the most important parameters of the convective heat transferis the Stanton criterion which defines the ratio of the heat transfer intensityto the specific enthalpy of the jet St ¼ a=Cpsru. Representing the a-valuein the criterial form a ¼ l=d ARemPrn one can obtain the analyticalformula for the Stanton criterion: St ¼ ARem�1 Prn�1. So, for the valuem ¼ 0.5 and n ¼ 0.33 St ¼ CRe�0:5 Pr�0:67. The function St ¼ f ðReÞwas investigated in many studies. The different functional expressions forSt ¼ f ðReÞ were derived in a similar manner to those of Nu in variousconditions.

The local values of the thermal flux, velocity and jet temperature weremeasured. For the range of Re ¼ 1500210000 the authors obtained thevalues of the Stanton’s criterion ranking from 0:0420:15. Statistical treat-ment of the obtained data the authors approximated the functionSt ¼ f ðReÞ by the expression St ¼ 3.8 Re�0.6.

The data of Tables I–III show striking differences in the values of A, mand n. This may lead to confusion but let us keep courage and move on to amore complex system, we will treat plasma.

II. The Convective Heat Transfer in Plasma

A. THE KEY CONCEPTS AND THEIR CONSIDERATIONS

1. Temperature or Enthalpy Heat?

When the basic formula (3) was derived by Newton, the concept oftemperature as the natural measure of the energy content of the movingmedium, was used. This statement is no doubt true for the gas temperaturerange up to two thousand degrees. But in plasma jets with temperaturefrom 5 to 50 thousand K, the energy is stored not only in the kinetic formresulting from the motion of electrons, ions and atoms 3/2kT, but also inthe form of rotationally excited molecules ER, vibrationally EV, or dissoci-ated molecules ED and ionized atoms Eioniz. These processes have to beincluded for the complex relationship between the energy gas flow and itstemperature.

All the energy stored accumulated in a plasma is transfered into theboundary layer and after diffusing through it reaches the wall of the heatedtarget. To describe all these mechanisms included in each event of thesemicroprocesses we have to calculate the exact flow and temperature patternin the boundary layer.

The simplest way to describe ionization, dissociation and excitation in agas phase is the insertion into the Newtonian formula of the enthalpy


difference [Hp�Hs] instead of the temperature difference between the gasflow and the surface of the target [Tp�Ts].

So, the concept of temperature in the formula is replaced by theenthalpy:

Tp � T s

�! Hp �Hs

� ¼ DH

In order to retain the dimension of the heat transfer coefficient a, theenthalpy heat is divided by the specific heat at the wall (Cps):

4

Tp � T s ¼Hp �Hs

Cps¼ Hp

Cps� T s

In this case the Newtonian formula takes the following form:

q ¼ aHp �Hs

Cps¼ Nu

ld

Hs

Cps� T s

� �(79)

Now the question arises: why is the enthalpy heat used rather than anyother function?

It is because in the ionized and dissociated flows of high-temperatureplasma, the enthalpy summarizes all the kinds of stored energy. The plasmaenthalpy is the thermodynamic function in agreement with the kinetic energyof the translational motion but we have to take into account the energy ofmolecular dissociation ED, the ionization phenomenon for molecule, atomEioniz, the energy of the excited state Eexc, and the vibrational and rotationalenergy of molecules EV, ER.

However, the plasma temperature takes into account only the kineticenergy of the chaotic translation (Brownian) motion having a velocity equalto u. But for a temperature range up to TZ3000K, that means when themolecule dissociation starts, the temperature can in no way represent theenergy content of the plasma gas.

So, the enthalpy is one of the most important thermodynamic functionsof a plasma.

This quantity may be also called plasma heat content, or energy content.It is measured in energy units per medium mass unit [Joule/kg].

The enthalpy of a plasma gives a substantially larger amount of infor-mation than the temperature.

4 We use the plasma specific heat at the wall temperature Cps, but not the temperature of theincident flow.


The enthalpy calculation results in a summation of all energies stored, byall plasma particles:

1. The kinetic energy (with the expansion work included) 5/2kT of allatoms, ions, electrons and molecules:

Hkin ¼ 1

r5

2kT na þ ne þ ni þ nm½ �

� �

where na, nm, ne are the concentrations, r is the atomic density (spe-cific weight).

2. The dissociation energy ED (for dissociated plasma):

HD ¼ 1

ranaED½ �

where na is the dissociated molecule concentration.3. The ionization energy:

H ioniz ¼1

riniEi½ �

where ni is the concentration of ionized atoms (molecules).4. The energy of rotational ER and oscillational EV motion of molecules.5. The energy of excited atoms nBa and that of excited ions nBi(�Eecc):

Hexc ¼1

rainBaE

0exc þ nBiE

00exc

�This is the general procedure of calculation for the plasma enthalpy. Whenperforming specific calculations for the complex plasma composition oneshould carefully summarize the contribution of all the particles and chemicalcomponents: molecules and molecular ions, atoms and atomic ions, excitedmolecules, atoms, ions, etc. The individual component terms of concentra-tion are defined by the effective mass law. So, the full enthalpy per unitplasma mass is equal to the sum of all possible kinds of energy accumulatedby plasma.

2. What are Similarity Criteria in Plasma?

It was declared above that the heat transfer analysis in plasma will befirmly based on the concepts and criteria of thermal and dynamic similarity.A sound confidence in that has come later when the formulas of heattransfer in their criterial form did not reveal any substantial discrepancieswith the experimental data. But there were many doubts at the beginning,


and we cannot say that they have disappeared now. One of the main prob-lems is how to calculate the similarity criterion for a plasma. Which tem-perature value should be used for determining the physical parameters ofplasma? Should it be the temperature of the incident flow Tp, which usuallyis of the order of tens of thousands of degrees, or the temperature of theheated wall Ts, which reaches hundreds of degrees, and is always substan-tially less at a temperature less than the incident flow.

Experimental and theoretical studies of the heat transfer in plasma arelike an Italian opera, where each author sings his own aria. Some authorsdefine the physical properties of plasma at the incident flow temperature Tp,others use the wall temperature Ts, sometimes the average temperature isintroduced, etc.

Formula (79) used as a basis for convective heat transfer descriptioncontains three principal similarity criteria: the Reynolds number (Re), thePrandtl number (Pr), and the Nusselt number (Nu):

q ¼ aHp �Hs

Cps

� �or q ¼ aðTp � T sÞ

a ¼ Nuld¼ A Re0:5 Pr0:3

ld

ð80Þ

Let us examine the variation of the similarity criteria with varying referencetemperature.

The Prandtl number ðPr ¼ mCp=lÞ, (Table IV) for an argon and an airplasma varies. It follows from Table IV that in the field of temperatureranging from 300 to 11000K the Prandtl number variations are within 30%range. In formula (81) this criterion is raised to a power of 0.3 (the cubicroot is extracted). Therefore the variations of Pr0.3 do not exceed 10%. Thatmeans that Pr0.3 is only slightly dependent on the reference temperature, andthe quantities q and a are not markedly affected by the choice of the ref-erence temperature for calculating the number.

The Reynolds number ðRe ¼ rud=mÞ. We will define the number for tworeference temperature values Tp ¼ 10000K, which is characteristic forplasma temperature, and 300K which, at the initial stage of the heating, isclose to room temperature. We shall consider the heating of a small particlehaving diameter ds ¼ 10�2 cm in the typical argon and air jet for a velocityof u ¼ 100m/s (104 cm/s). The Reynolds number of argon and air defined at10,000K is equal to Rej10000 ¼ 1:5� 2. The corresponding value calcu-lated at the wall temperature of a plasma at wall temperature Ts isRe300 ’ 500� 900. As we see, these values differ greatly. The numericalvalue Re0.5 defining the heat flow for the defined particle under the sameconditions differs approximately 30 times!


This means that the formula (80) can describe almost any experimentalresult, if the reference temperature is chosen in some way or another. It isprobably one of the most vulnerable points of application of the similaritytheory for the heat transfer description under plasma conditions. The defi-nition of Re number should be determined more carefully, but it needsthoughtful and intensive analysis.

Any work on plasma heat transfer should necessarily include specific dataon the definition of the reference temperature for Re-number calculation. If itis not the case, the work is suitable only for the waste-paper basket.

The Nusselt criterion. As the Nusselt criterion is defined as Nu ¼ ARe0:5

Pr0:3, all stated above about the Reynolds and Prandtl numbers should beremembered and considered.

The heat transfer coefficient a and conductivity l. When we have to cal-culate the heat transfer coefficient a, one further important problem arises inaddition to the difficulties of defining the Reynolds number: it is the choiceof the reference temperature for calculations of l in formula (80).

For the atomic argon plasma this function is rather monotonic, and so thecalculation of a in the form a ¼ Nu l=d will encounter no surprises, if the lvalue is defined at the flow temperature.

For a plasma of molecular gases the conductivity reaches a maximumwith the dissociation zone, that means in the temperature range between3000 and 5000K. Therefore, in that range, the l-value based on the flow

TABLE IV

THE PRANDTL NUMBER FOR ARGON AND AIR

T (K) Pr

Air Argon

300 0.723 0.675

1000 0.720 0.680

2000 0.680 0.685

3000 0.535 0.690

4000 0.660 0.695

5000 0.605 0.700

6000 0.585 0.705

7000 0.820 0.710

8000 1.210 0.715

9000 0.820 0.720

10,000 0.877 0.800

11,000 1.000 0.900

12,000 1.120 1.010

13,000 1.160 0.950


temperature will have a sharp maximum. On the other hand, if the tem-perature is chosen within 6000 to 10,000K, the heat flow sharply decreases(about 5 times!).

No such sharp variations of the heat flow q with an increasing temperaturecannot be either guessed, or experimentally observed. They are absurd.

Therefore, the second very important part of the author’s attentionshould be paid to the definition of the conductivity in formula (80), espe-cially for molecular gases.

So, the major problem in the application of the theory and numbers ofsimilarity to a plasma is not the composition of the correlation, but thechoice of the reference temperature used for the calculation of the similaritycriteria.

3. The Boundary Layer: Equilibrium or Frozen? The Catalycity of the Wall

An ionized conductive gas (nitrogen) heated to a temperature of 10,000K,is close to the thermal equilibrium state, and at atmospheric pressure,the overall concentration is nS ¼ 0:7� 1018 cm�3, with a molecular concen-tration nN2

¼ 3:4� 1015 cm�3, an atom concentration (dissociated molecules)nN ¼ 6:9� 1017 cm�3, an ionized molecule concentration nN2þ ¼ 1:8�1016 cm�3, an ionized atom concentration 1:8� 1016 cm�3 and a concentra-tion of electrons ne ¼ 1:8� 1016 cm�3.

It should be guessed, that the nitrogen plasma composition near the outerinterface of the boundary layer will have the same composition as in the freeflow. But what kind of change appear within the boundary layer? Wheredoes the recombination appear? Where does the recombination of ions andelectrons take place? Is it inside the boundary layer or in the plasma or onthe surface of the target because of the large difference of reaction speedbetween these different parts.

In this last case, the boundary layer is called a frozen zone for the re-combination reactions. That is why it is called frozen boundary layer incontrast with the equilibrium boundary layer where the reaction speed issufficiently low in front of the particle transversal velocity in the layer.

The estimate of the boundary layer state is based on the comparison of thetime (rate) of atomic recombination ta, defined by dnN2

=dt ¼ n2NKa, or theionic recombination time tr, from dnN=dt ¼ nineK r with the particle transittime tr ¼ dT=u. The dimensionless Damkler numberDk or the inverse quantity

Dk ¼ tr

tT

describes the equilibrium or the frozen state of the boundary layer.


The catalycity of the wall. If two nitrogen plasma atoms arrive at the wallsurface through the boundary layer, the rate of their association and for-mation of the new molecule is defined by the nature of the wall material andthe characteristics of its surface. Can the wall be a catalyst of the recom-bination or not? And what about the association reaction?

The ability of the wall to accelerate the recombination or associationreactions and the energy accomodation of such reactions is usually calledcatalicity of the wall.

It can be needed to choose a material able to absorb the atomic nitrogen(oxygen), i.e. to prevent nitrogen atoms to build up into molecules and so tofree the large amount of energy at the surface. This means that such wallcould hinder the dissociation of molecules (sometimes an opposite solutionis necessary).

Just such possibility of substantial decrease of the heat flow from thedissociated air to the wall is used in the thermal protective covering of theSpace-Shuttles.

4. The Work of J. Fay and F. Riddell

During last 30 years one cannot find a single work on the plasma heattransfer not referring to the work or formula of J. Fay and F. Riddell.

It was published at the very start of the space era in 1958 when theproblem of the space vehicle reentry into the atmosphere was crucial for thewhole space program. The satellite reentering the dense atmosphere layerswith tremendous velocity extinguishes its energy not only with the use ofbraking devices but also by friction, turning the ambient air into plasma.Therefore, the said article was called ‘‘Theory of stagnation point heattransfer in wash dissociated air’’.

The authors used a routine approach of aerodynamics based on the con-cepts of the boundary layer. But it included, apparently for the first time, theprincipal plasma phenomena: recombination and association.

This work was also the first one which treated the problem of the state ofthe boundary layer. At what point of the boundary layer does the mainprocess of the heat generation, i.e. where the recombination of ions withelectrons take place? Is it at the surface or inside the boundary layer. Is theboundary layer frozen or equilibrated in these reactions? What is the state ofplasma inside the boundary layer? Is it in thermodynamical balance or not?And, finally, in this work without any special comments the enthalpy heatwas introduced into Newtonian formula for convective heat transfer insteadof the temperature heat.

In the same work all the similarity parameters were calculated using thewall temperature of the flow, and this fact was stated quite plainly.


This work may be regarded as the Bible for every one who is devoted tothe heat transfer in plasma.

Fay and Riddell obtained the solution of boundary layer equation re-specting the variation of gas parameters, atom diffusion, dissociation andrecombination (Table V).

The solution was obtained for the following principal cases:

1. balance of energy in the boundary layer;2. the boundary layer is frozen, and the conditions in the layer are

defined by its outer boundary; and3. for the intermediate case, the concentration of each component in the

boundary layer is defined by the ratio of flow and recombinationvelocities.

The heat flux in the front point of the body entering the atmosphere at ahypersonic speed is defined by the expression

q ¼ NuffiffiffiffiffiffiRe

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirsms

dudx

� �sDHPr

(81)

respecting the diffusion and conductivity heat transfer.The numerical solution of the boundary layer equations for Pr ¼ 0.71 and

Le ¼ 1 in the case of the equilibrium boundary layer yields.

NuffiffiffiffiffiffiRe

p ¼ 0:67rpmprsms

� �0:4

for Le ¼ 1; Le ¼ DarCps

l

� �(82)


p ¼ 0:67rpmprsms

� �0:4

1þ Le0:52 � 1� � �HD

Hp(83)

For the frozen boundary layer the influence of the parameters r and m isvery close to that for the case of the balanced layer. As to the influence of theLewis criterion, the best approximation in formula (83) easily be found to beLe0.63. So the heat flow in the braking point at Pr ¼ 0.71 may be expressedas follows:

q ¼ 0:94ðrsmsÞ0:1ðrpmpÞ0:4 1þ Le0:52 � 1� � �HD

Hp

� �DH

ffiffiffiffiffiffiffiffiffiffiffiffiffidudx

� �s(84)

For Pr 6¼ 0.71, it is recommended to substitute the factor 0.94 by (0.76 �Pr�0.6).The velocity gradient in the front point for the modified Newtonian flow is


TABLE V

THEORETICAL FORMULAS FOR THE PLASMA HEAT FLOW CALCULATION (CRITICAL POINT)

No. Source Formula Conditions

1 Rosner DorrenseCiPr

2=3ru DH 1þ ðLe� 1ÞHp

DH

� ��2=3 Heat transfer to the plate. Ci is friction coefficient. The

quantities with are calculated with the use of the flow

temperature. Pr is const; Le is const

2 Fay Riddell 0:76 Pr�0:6 ðrpmpÞ0:4ðrsmsÞ0:1

� 1þ ðLen � 1ÞHD

DH

� �dudx

� �0:5

DH

n ¼ 0:63 for frozen layer; n ¼ 0:52 for equilibrium layer

3 Fay KampPr�0:5 lp

Cp

� �0:5

DHNuffiffiffiffiffiffiRe

p dudx

� �0:5 NuffiffiffiffiRe

p from the numerical solution of the boundary layer

equation

4 Rayly0:76 Pr�0:2 la

Cpa

� �0:4

ðrsmsÞ0:1

�ðH �Hp �HsÞdudx

� �0:5

� lalCpa

� �0:41

1þ a

� �0:4

þ LenHp

ðH �HpÞ

" #

Subscript a is for frozen (atomic) value. lal is atomic and

electron conductivity; a is ionization rate; Hp is enthalpy

of characterizes body dimension

5 Bak0:87 Pr�1=3ðrmÞDH 1þ 1� zs

1� qs

� ��

�ðLe0:63 � 1ÞHp

H

�dudx

� �0:5

zs ¼H

Hs; qs ¼

aas

490

S.V.DRESVIN

AND

J.AMOUROUX

defined by the expression:

dudx

� �¼ 1

R

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 Pp � P1 �

rp

s¼ u

R(85)

where R is radius of the head; PN, the pressure far from the head; Pp, dynamichead of flow. With the use of (85) formula (81) may be transformed into

q ¼ NulsR

DHCps

(86)

where Nu is defined by (83). So, the numerical solution of the boundary layerequations resulted in the usual correlation of heat transfer, in which criteria Reand Pr are expressed for the plasma using wall temperature (Pr ¼ 0:71;Re ¼ upRms=rs). Rose and Stark on the base of the solution use the formula


p ¼ 0:76Pr0:4rp � mprs � ms

� �0:4

1þ Le0:52 � 1� � �HD

Hp(87)

allowing to calculate the heat flow for Pr 6¼ 0.71. Fros has carried out thecalculations of heat transfer near to the critical point of balanced boundarylayer plasma for nitrogen and air. It was shown that up to an accuracy of75% the results can be described by the following formula:


p ¼ 0:915 Pr0:25rpmprsms

� �0:43 up11; 300

� �(88)

Formula (88) was obtained with the use of the thermodynamical propertiesand transfer coefficients of plasma calculated by Fros. If the correspondingplasma parameters are adopted according to Hansen, the heat transfer isdescribed by the formula


p ¼ 0:9 Pr0:25rpmprsms

� �0:43 up9900

h i(89)

The expressions (88)–(89) were obtained for the velocities and u411,300and 9900m/s. For slower speeds of the flight or incidence the last term in theformulas should be substituted by unity.


B. EXPERIMENTAL STUDIES OF HEAT TRANSFER IN PLASMA

1. D-factor. What to Measure and How to Present the Experimental Results?

The experimental study of the heat transfer from a plasma jet to a target isa multilateral problem. In many works the heat transfer study qualifies thetechnological efficiency of small refractory particles (powders) treated byplasma. In these works, the authors determine the average velocity of theplasma flow over the plasma torch section, the average temperature, and theaverage powder consumption. We will not analyze these works.

In the present survey we are mainly interested in the works which studythe heat flow q to the model body for a plasma temperature Tp and avelocity up.

But we shall consider only the works which give us an experimentalfunctional relationship

q ¼ f ðTp; up; dÞ (90)

i.e. to express the heat flow to the model by the plasma parameters.Usually plasma jets have large axial and radial temperature and large

velocity gradients. Therefore, such relationships are proposed in the plasmazone where the model body is situated and is able to be described by theconstant parameters Tp and up.

The experimental studies of the heat transfer in plasma jets of arcand high-frequency plasma torches start more than 35 years ago. But afew works permit to compare the heat transfer in a local regime of theplasma fit with the exact temperature and velocity of the plasma. Moreover,one can definitely say that such studies are rather scarce. This is mainlycaused by the model body q and the local parameters of the plasma jet(Tp, up).

From a large number of experimental works we have picked up only those,where the dimensions of the heat flow allow to identify the quantity of theheat flow q correlated with the values of the velocity up and the temperatureTp of plasma in the target zone of the plasma jet. While consideringthe experimental studies we have encountered an important difficulty. Mostauthors do not report primary data (the values of q, up, Tp) but presentthem in a generalized form. The relationship Nu ¼ f (Re) is used in the mostcases, the way of calculations of Nu- and Re-criteria is not specified. Itremains unclear whether the incident plasma temperature or the averagevalue was used as a reference temperature. We attempted to represent all theexperimental data in their primary form: as the values of the heat flow to themodel q, the velocity up, and temperature Tp for which the q-value wasdetermined.


Such representation of the experimental data allows readers themselves toanalyze the relationship

q ¼ f ðTp; up; dÞ

So, what presents the main informative value when the plasma heattransfer is studied? It is the heat flow q (W/cm2) to the model or heatedbody. This quantity, if it is obtained in real jets of a real plasma torch, bringsin itself necessary and adequate information.

In the cases where the problem of generalization or determination of therelationship of q to plasma temperature Tp and its velocity up is stated, allthese three quantities should be measured simultaneously and in the samepoint of the plasma jet (the same holds for d). Authors should be recom-mended to present in tables, or graphically, just these primary quantities(their criterial interpretations could certainly follow).

For the plasma jets the D-factor permits to simplify the calculation:

q

ffiffiffiffiffids

u

rwhere u ¼ up � us (91)

The D-factor is a dimensional quantity. For plasma, we recommendto use the following dimensions: for q is the heat flow to the heated body(W/cm2); d, the particle diameter (cm2); u, plasma velocity (cm/s). In thiscase, the D-factor for plasma jets is expressed by a simple number of order1–10 having dimension Ws1/2/cm2.

We shall clarify the main idea of the D-factor definition for a plasma:The composition of the heat transfer formula for a plasma is as follows:

q ¼ aHp �Hs

Cps

� �¼ ARe0:5 Pr0:4

ldðTp � T sÞ (92)

We express Re- and Pr-numbers by the plasma parameters:

q ¼ Arudm

� �0:5 mCps

l

� �0:4 ldðTp � T sÞ (93)

If the principal experimental values q, u, d are brought into the left-handside of this equation, we get

q

ffiffiffid

u

r¼ A

rm

� �0:5 mCps

l

� �0:4

lðTp � T sÞ ¼ DðTÞ (94)

Then in the right side the plasma characteristics depending only on thetemperature are assembled (r is the density; m is the viscosity; Cps is the


specific heat; l is the thermal conductivity; H is the enthalpy). So we geta unique chance to trace the relationship of the right-hand side to thetemperature D(T).

This valuable property of the heat transfer correlation (81) proved to bevery effective for plasma jets. This is caused by the fact that it can link thefour main parameters by a single relationship or a graph. These four pa-rameters are the plasma temperature Tp, the velocity u, the particle diameterd and the heat flow q. So the preferential form of the representation of theexperimental data is the D-factor.

The merits of such representation are able to be defined in the amount ofthe heat flow transfered to a small particle of diameter d placed into anargon plasma. In a usual plasma torch (power 30–50 kW) the temperature ofthe plasma jet in its initial section is 12–13 thousand K. The D-factor takenfrom the nomograph for this temperature is equal to D ¼ 2–2.5. Then for agiven value of the plasma velocity (say, u ¼ 400m/s) the heat flow to theparticle of any diameter can be easily determined. For a particle of a di-ameter d ¼ 10�2 cm, q

ffiffiffiffiffiffiffiffid=u

p¼ 2:5, so that q ¼ 2:5

ffiffiffiffiffiffiffiffiu=d

p¼ 5000 W=cm2.

The D-factor is one of the most important functions of the heat transfer inplasma. Therefore, along with the primary data we always give the value ofqffiffiffiffiffiffiffiffid=u

pand a graph of the correlation (94) versus temperature.

2. Survey of the Principal Works and Experimental Data with an Arc PlasmaTorch P-1 (Argon)

The first experiments in St. Petersburg Technical University on theheat transfer of a plasma jet with the spherical probe model placed intoit were performed in 1965–1967. The arc plasma torch P-1 with a free arc wasused for spraying. The working gas was argon; the arc current was 250A, thediameter of the plasma torch channel was 7mm and its length 25mm.

The temperature distribution was found from spectral measurementsof the radiation intensity in the spectral range 4500A7100A which wasselected by an optical filter.

The velocity distribution was defined by a transient procedure using theprobe signal put into the plasma cross-flow and a non-cooled Pitot tube.The tube of diameter 1mm was shot through the plasma jet, while thepressure signal received by the capacitor microphone membrane was trans-formed into an electric pulse registered on the oscillograph.

Using the known gas density (temperature), the dynamic head data allowto define the velocity of plasma flow in a simple manner. The heat flow at thelocal point of the plasma jet was defined for a spherical body which wasperformed as a thermocouple weld having diameter � 0.8mm. The sphericalthermocouple was introduced for a short time into the axial zone of the


plasma jet and was kept there for 2–3 s. The temperature rise registered onthe oscilloscope screen as a rising thermo EMF. The heat flow was used, forthe determination of the sphere qex.

Such complex measurements allowed to obtain simultaneously the plasmajet parameters T, u and the heat flow for a spherical model q. The spectraland heat measurements performed on the plasma torch P-1 showed imme-diately that the heat flow q is very sensitive to the gas flow G. It is stronglyaffected by the choice of the measurement point along the jet. Meanwhile,the temperature of the plasma jet measured by spectral methods varies alongthe jet and is slightly dependent on the gas flow.

In 1967, we made the assumption that the argon jet plasma at atmos-pheric conditions is a non-equilibrium state. It was confirmed by the factthat the temperature of its atoms and ions can be substantially lower thanthat of its electrons (TaioTe). The spectral measurements really give thevalues of T close to the electron temperature Te. At the same time the valueof the heat flow q is defined mainly by the atom-ion temperature.

At this time, this result made a sensation, and our main attention wasconcentrated on the studies of very non-equilibrium state of the plasma jet.These results were repeatedly published. But the measurements of the heattransfer with the spherical mode were never published.

It follows that for an arc current 250A the increase of the gas flow from 14to 44L/mm modifies slightly the electron temperature: Te ¼ (10–11.5)� 103Kalong the jet length 0ozo2 cm. But at the same time, the atom-ion temper-ature decreases from 6 to 3 thousand K.

Table VI includes all the experimental data: the heat flux qex to the sphereprobe and the parameters of the plasma jet where the flux is measured (Te, u).

TABLE VI

HEAT TRANSFER DATA MEASURED BY A SPHERICAL PROBE OF A DIAMETER D ¼ 0.8MM IN THE

ARGON JET OF THE ARC PLASMA TORCH P-1 (ARGON FLOW RATE G ¼ 0.39 G/S, PLASMA TORCH

CURRENT 250A, DIAMETER OF THE PLASMA TORCH CHANNEL 7MM)

Distance to

the nozzle

exit (mm)

Temperature

of the electron,

thousands (K)

Temperature of

the atom-ion,

thousands (K)

Plasma

velocity u(m/s)

Experimental

values of heat

flow to the sphere

q (W/cm2)

Temperature of

the sphere wall

(K)

0.2 11.7 4.5 125 400–580 300–600

0.5 11.6 4.5 114 350–590

0.7 11.5 4.2 110 350–620

1.2 11.4 4.0 98 400–450

1.7 11.0 3.5 88 200–240

2.2 10.0 3.0 75 100–120


Some more comments concerning these data. The major disadvantages ofthe P-1 are plasma torch because the arc length is modified by the large scalepulsations mainly caused by the arc instability, thus affected the precision ofthe heat flow determination. However, the large amount of heat flow meas-urements obtained for no less than 100 experiments are given in Table VIand the results of the heat transfer qex point out the large fluctuation causedby the arc and jet pulsation.

We can expect that these pulsations explain the large difference betweenthe electrons and the ion-atom temperature in the plasma gas.

a. Experiments with the Arc Plasma Torch P-2 (Argon). The design of a newarc torch is needed to perform the real heat transfer in order to be sure thatthe instrument and its working parameters can be well controlled. This hassometimes such an importance that one can hardly describe the net heattransfer measurements as being pure. The scientific research in such casesturns out to be a technical measurement of some parameters under someconditions.

The experiments with the P-1 plasma torch have shown that: (1) Theq-value is strongly affected by the arc instability in the channel; (2) Thethermal instability of the argon plasma jet was established and the electronictemperature is much higher thant the atom-ion temperature (Te4Tai);(3). The necessity of the measurement of the turbulence rate and plasmapulsation became clear; and (4) The P-1 plasma torch was proved not to bethe most appropriate instrument for the net heat transfer measurements, sothat we have to create a new special plasma torch which takes care of thesemain recommendations. The new P-2 version was worked out with thechannel formed by cooled isolated sections which allowed to fix the arclength in the plasma torch. This technique eliminated the major sourceof the plasma torch pulsations caused by the variations of the arc length.The channel diameter in the P-2 version was enlarged up to 10mm, thearc then reached 5th section, its length was to 94–96mm. The plasma gaswas argon, its flow rate was G ¼ 5–30L/min (0.14–0.84 g/s), the arc currentI ¼ 50 and 200A. The channel diameter enlargement allowed to usestationary water-cooled probes (enthalpy probes) for measuring the gastemperature.

The following jet parameters were measured:

1. The electron temperature Te determined by the spectral method aswell as in the P-1 plasma torch.

2. The atom-ion (gas) temperature was established by the water-cooledenthalpy probe based on the gas suction and heat exhaustion fromthe specific jet region.


3. The gas velocity was determined by the dynamic head measurementwith the use of a non-cooled Pitot tube which was swiftly carriedthrough the jet by the pendulum.

The gas (atom-ion) temperature and its velocity in the plasma torch P-2are sufficiently affected, by the current I and gas flow rate G. The electrontemperature in different modes are not really modified for different oper-ation modes (Te ¼ 10,400–11,800K), as well as for the initial section (z ¼ 0)of the jet axis as shown in Table VII.

Compared with the plasma torch P-1, the electron (Te) and gas (T) tem-peratures in the P-2 version were carefully studied for a wide range of thecurrent and gas consumption values.

The measurements with the arc-plasma P-2 confirmed the hypothesis onthe separation mechanism with an electronic temperature higher than theion-atom temperature and on the current line extrusion into the jet region.Some operation modes are described with the assumption Te ¼ T in the jetregion. This is true if both the current and gas consumption are large enough(I ¼ 200A, G ¼ 0.84 g/s), and more than 25–30% of current lines areextruded into the jet zone. In this case the density of the extracted currentand the electron energy are sufficient for supporting the temperature equalityof electron and atom-ion components (Te ¼ Tai).

b. The Turbulence Measurements of the Plasma Jet at the Plasma Torch

P-2. The turbulence pulsations in the plasma jet were measured with theuse of a non-cooled Pitot tube of diameter 1mm, which was shotthrough the certain cross-section of the jet. The tube was connected to acapacitive probe (microphone). The pressure signal was transformed intoan electric pulse and registered on the oscillograph screen. The signalmagnitude calibration was based on steady-state dynamic head measure-ments at the cold flow. The response pictures distinct by the variation of

TABLE VII

ELECTRON TEMPERATURE (TE), ATOM-ION TEMPERATURE (T), AND FLOW VELOCITY (u) AT THE AXIS

IN THE INITIAL SECTION (Z ¼ 0) OF ARGON PLASMA JET IN THE P-2 PLASMA TORCH FOR DIFFERENT

MODES OF WORKING PROCEDURE

I (A) G (g/s) 0.14 0.28 0.42 0.56 0.84

50 Te (K) 10,400 10,600 10,700 10,700 10,700

T (K) 2900 3200 3400 3700 4600

u (m/s) 19 40 61 81 115

200 Te m/s 11,500 11,600 11,800 11,800 11,800

T (K) 4400 4600 7400 7700 10,900

u (m/s) 37 97 156 217 325


the average value of the velocity head and the value of the turbulentpulsations p0.

If we suppose that the pulsations are caused mainly by the pulsations ofthe longitudinal velocity u0 alone at the given point of the jet, the velocity atthe head is expressed by the sum of the average value p and pulsations p0:

pS ¼ pþ p0 ¼ rðuþ u0Þ22

p ¼ ru2

2

Hence:

p0 ¼ 1

2ru0 þ ruu0

The turbulence rate e may be expressed by the values p and p0 as follows:

� ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ

ffiffiffip

pp

s� 1 (95)

The measurement system assuming the pressure signal and its pulsationsp0 is qualified by the air volume in the Pitot tube, the gap between the tubeand the membrane, and the membrane itself with its own frequency re-sponses (peaks and falls). The frequency response having minimal frequencydistortions up to 6000Hz were obtained by the careful choice of the Pitottube diameter and the gap.

Tables VIII and IX give the turbulence rate value determined in that wayfor different sections of the plasma jet and different working parameters ofthe plasma arc P-2.

The design of the P-2 plasma torch prevented large-scale pulsations of thejet core caused by the arc length, so that we hope that the data of the TablesVIII and IX represent the plasma jet characteristics. The glowing jet coreconfined by the isotherm � 5000K proved to have small turbulence rate(0.1–0.03) for the current 200A and for gas flow rates (40.28 g/s). But forsmall currents (I ¼ 50A) and low gas consumptions (o0.28 g/s) the

TABLE VIII

TURBULENCE OF THE PLASMA JET e AT THE AXIS IN THE INITIAL SECTION OF THE PLASMA TORCH

(R ¼ 0, Z ¼ 0)

G (g/s) 0.14 0.28 0.42 0.56 0.84

e 50A 0.85 0.26 0.16 0.13 0.11

200A 0.20 0.10 0.03 0.03 0.03


turbulent pulsations are sufficiently greater even at the nozzle exit to reachthe value 0.85; this is probably caused by the arc instability in the channel.At low gas flow rates and for small currents the arc does not fill the wholesection of the channel, and can move freely inside it (screw and thermalinstability). When the current reaches 200A and the consumption, is morethan 0.28 g/s, the arc fills the whole channel section, a the layer of the densecold gas is formed near the wall, and all the instabilities disappear.

The heat flow to the copper sphere Ø 1.5mm and 1.8mm containing thewelded thermocouple was measured by the swift insertion for 2–5 s into agiven point of the plasma jet. The heat flow was determined by the rise of thetemperature registered with an oscilloscope.

The heat flow measurements q for spherical probes are presented inTable X with the plasma jet parameters at the same point. Earlier worksperformed in the 1960 s and in the early 1970 s are devoted to the heattransfer between a cylinder, plane or sphere probes with a plasma jet. Someexperiment conditions and results obtained are listed in Table X.

3. Short Survey of the Literature Data

Abu-Romia studied the heat transfer of an argon plasma jet with a plate(stagnation point). The plasma torch with the self-adjusting arc is charac-terized by a nozzle diameter of 7.92mm, an arc current between 100 and400A, and a voltage from 18 to 27V. The heat flow to the plane water-cooledobstacle were measured with the use of the heat tube probe. The experimentalresults for an argon plasma, compared to the theoretical calculations of Fay,are represented by the formula:

q ¼ 0:76 Pr0:62ðrpmpÞ0:4ðrsmsÞ0:1

b0:5DH 1þ ðLe0:63 � 1Þ aIHS

� �(96)

where a is ionization rate; b, velocity gradient; I, ionization potential.The Re-criterion was defined by the mean mass velocity across plasma

torch with a nozzle diameter d. The velocity gradient is b ¼ up=d. The dataobtained from (96) and the experimental ones for similar conditions but

TABLE IX

TURBULENCE OF THE PLASMA JET AT THE AXIS FOR THE DIFFERENT SECTIONS ALONG THE JET

LENGTH (G ¼ 0.42 G/S, I ¼ 200A)

z (cm) 0.2 1.0 2.5 4.0 6.0 10.0

e 0.03 0.04 0.08 0.2 0.43 0.65


TABLE X

DATA OF THE HEAT TRANSFER OF SPHERICAL PROBES WITH THE ARC ARGON JET P-2

Operation mode Distance from

the nozzle where

the heat flow

was measured

Diameter of

the spherical

probes

Electron

plasma

temperature

Atom-ion gas

temperature

Plasma

velocity

Turbulence

rate

Experimental

values of the

heat flow to the

spherical probe

Current Argon flow

rate

I (A) (g/s) Z (mm) d (mm) T e (K) Tai (K) u (m/s) e q (W/cm2)

50 0.14 2 1.5 10,400 2900 19 0.85 220

0.28 10,600 3200 40 0.26 360

0.42 10,700 3400 61 0.16 628

0.56 10,700 3700 81 0.13 414

0.84 10,800 4600 115 0.11 670

200 0.14 2 11,500 4400 37 0.2 650

0.28 11,600 4600 97 0.1 1050

0.42 11,800 7400 156 0.03 1700

0.56 11,800 7700 217 0.03 1600

0.84 11,800 10,900 325 0.03 –

200 0.42 10 1.8 11,100 6700 150 0.04 1010

25 10,300 5700 118 0.08 500

40 – 4800 96 0.20 480

60 – 2600 65 0.43 260

500

S.V.DRESVIN

AND

J.AMOUROUX

different average mass temperatures T and gas flow rates G are in a goodagreement at low gas flow rates. The heat flow rise with respect to thecalculated values at large flow rates is explained by the authors by theincrease of the turbulence rate of the plasma jet.

The peculiarities of the ionized gas heat transfer were analyzed by Klubni-kin. The problem of the criterial relationship and the choice of the referencetemperature has been examined. The ‘‘reference temperature’’ was shown tobe conveniently adopted as that of the incident flow. The criterial relation-ship is chosen in the form C �Rem Prn. The variations of flow parameterswithin the boundary layer should be accounted for by ‘‘the temperaturecorrection’’ factors. For m ¼ 0.5 the heat transfer coefficient is almost un-affected by the Tref -value. In a turbulent flow the exponent m is close to 0.8and so the choice of the Tref becomes more significant. The turbulence in-fluence on the q-value can be taken into account by the adoption of theproper value of the factor C. For large temperature gradients across theboundary layer when the physical constants of the gas flow show extremum,the calculation and the experimental heat-flow results may be brought closer,if the reference temperature should be taken as some effective value equal to

T eff ¼R d0TðrÞr drR d0 r dr

(97)

where r is the coordinate normal to the surface and d the boundary layerthickness.

In the work of Kimura and Kazava the heat flow to tungsten or platinumwires (d ¼ 0.3, 0.5 and 1mm) in the argon arc plasma with Tr20� 103Kand ur120m/s was determined on the base of the rate of their electricresistance variations. It was inferred that the cylinder heat transfer can becalculated from the familiar empirical relationship

Nu ¼ ð0:35þ 0:47 Re0:52ÞPr0:3 (98)

using T ref ¼ 0:5 ðTp þ T sÞ.The measurements have shown that the convective component of the heat

flow is sufficiently larger than the diffusion one and the boundary layer isclose to the frozen state.

Far less experimental studies examine molecular plasma such asN2 or O2 but the diagnostics are much more complex and one of thedifficulties is the stability of the thermal probes which can react with theplasma species.

One of such first works of W. Rother studied the convective heat transferto steel particles (d ¼ 1mm) in a nitrogen arc jet. Two series of the


experiments were performed. The first one examined balls freely fallingthrough the horizontal plasma jet at the rate of 2600 particles which arecollected in the calorimeter.

The q-value was calculated with the use of the Abel integral transform.The flow parameters were determined by spectral methods and with thewater-cooled Pitot tube. This procedure pointed out that a dynamic actionof the gas flow on each ball curved their trajectory, but to qualify the heattransfer, it needs many balls and long measurements.

Therefore, the second experimental series was performed with thermoprobes. They were made of steel balls with welded thermocouples placed intoglass capillaries. The cold thermoweld was put into the thermostat. Thethermocouple leads were attached to the device that enabled to more precisionthen through the plasma jet with the prescribed velocity. The amount of heattransferred to the ball was defined by its temperature rise, and recorded by anoscilloscope. The measurements were performed at Tp ¼ (2–5) � 103K andup ¼ 10–100m/s. The results obtained by W. Rother were, in the temperaturerange up to 4000K, approximated with reasonable accuracy by the familiarrelationship

Nu ¼ 1:32 Re0:5Pr0:4 (99)

which was established to be valid for the critical point where T ref ¼0:5ðTp þ T sÞ independently of the dissociation.

W. Gauvin also carried out the studies of the heat transfer of fixed spheresin nitrogen at a temperature up to 3000K and velocity up to 45m/s. Water-cooled steel spheres of Ø 25 and 16mm were placed in the flow axis, whichwas formed in a graphite chamber of 200mm diameter, attached to thedirect-current plasma torch. A thermocouple welded to the inner spheresurface in the equatorial plane was used to measure the temperature Ts. Thetotal heat flow was determined by the temperature difference of the coolingwater. The accuracy of the measurements was within 10%. The authorsproposed the formula

Nu ¼ 0:118 Re0:76Pr0:33 (100)

for the prediction of their obtained results. Here the average-mass temper-ature is used as reference one, and the heat flow is calculated from thetemperature head T ¼ TB�Ts. The exponent value of the Re-number showsthat, in their experimental work, the gas flow was turbulent. This was alsoconfirmed by the existence of the separation point, detected from the surfacetemperature distribution along the circumference of the spherical probe:within 90–120K from the head point where the Ts-value was about 70% ofits maximum value.


In the paper of S. Katta and W. Gauvin the influence of local flow pa-rameters on the heat flow to the sphere was studied in high-temperature argonand helium jets. The steel sphere of diameter 12.7mm used was cooledthrough capillary tubes. The three-layer probe made of thermosensitive semi-conductive material was attached to the sphere wall, for a diameter 3.18mmand a thickness 1.6mm. It was used for the heat flow measurements basedupon the temperature gradient along the probe. The sphere was put inside thevertical cooled reactor of 305mm diameter. The flow temperature and ve-locity were detected by the auxiliary spherical probe having the same diameteras the main sphere. The high-temperature thermocouple and the end of thetube attached to the micro manometer were situated at the probe surface.Turning the probe around the supports allowed to measure temperature andvelocity near to the sphere surface at different angular distances from thehead point. The local temperature in helium plasma was measured with theuse of the calorimetric probe. The temperature and velocity of the argon flowwere 130–1900K and 30–43m/s. It was found that the local values of Nucalculated by the local temperature within the range Re ¼ 1700–7500 are farmore scattered than those calculated by the mean-mass temperature when theflow-separation takes place at 120K from the head point.

The correlation for helium and argon

Nu ¼ 0:02 Re0:73 ðlB=lsÞ1:73

Nu ¼ 0:01 Re0:79 ðlB=lsÞ1:15 ð101Þ

for the heat flow calculation by the mean-mass temperature TB and DT wereproposed. They correspond to relatively low temperatures 1.6–2.2� 103K inthe range of Re ¼ 300–3000.

S. Dresvin studied the heat transfer of air-cooled copper spheres(d ¼ 6–8mm) in a turbulent flow of an RF air plasma torch. The heat flowwas determined calorimetrically with regard to the influence of cylindricalprobes. The temperature of the gas flow was evaluated by spectral meas-urements, and the velocity was determined by the dynamic head. The resultsobtained were 20–40% above those predicted by the formula and the dis-crepancy was attributed to the flow turbulence.

V. Klubnikin investigated the heat flow in ionized argon at Re ¼ 60–136.Two different procedures were employed. The first one used the calorimetricevaluation of the heat flow to copper spheres d ¼ 9.9mm and d ¼ 8mm inthe laminar flow of an HF plasma. The second one was based on measuringthe heating rate of spherical particles (diameters 1.5 and 1.8mm) in an arcdischarge by the dynamic thermocouple procedure. The non-steady proce-dure had better than 10% accuracy owing to the rapid establishment of


quasistationary state. The correlation

Nu ¼ 2lslp

þ 0:5Re1=2Pr1=3rpmprsms

� �1=5

(102)

was proposed. The factor ls/lp is introduced in order to match the con-ductive Nu-term with the adopted reference temperature Tp. The q-values in(92) are calculated with the use of the enthalpy head DH.

Sayegh and Gauvin studied the heat flow to immobile polished spheres ofmolybdenum (diameters 2.2, 3.3 and 5.6mm) which were introduced into anargon plasma jet on a tungsten wire stretched between two bars.

The argon plasma jet was produced by an RF plasma torch with a fre-quency 4.5MHz and a voltage 3–4 kV. The quartz water-cooled dischargechamber had diameter 40mm and outlet nozzle 25mm. The supplied powerwas 6 kW of which 1.6–2.4 kW was transferred to the plasma gas. Themolybdenum spheres were carefully polished (the molybdenum meltingtemperature is 2833K). The heat flow measurements were performed in fouroperation modes at different powers and gas supplies. The plasma temper-ature T was slightly above the wall temperature (Tp ¼ 2700–4500K;Tp ¼ 1200–2400K; up ¼ 7–11.5m/s; Re ¼ 10–80; Nu ¼ 3–6). The heat flowfrom the plasma jet to the molybdenum sphere was determined for steadystate heating conditions assuming that the heat flow plasma is equal to theradiation heat losses. In this case, the following equation holds true:

aðTp � T sÞ ¼ �sT4s (103)

(The heat flow plasma is equal to the radiation heat losses.)The sphere wall surface temperature Ts was determined using an optical

pyrometer with a high resolution (the authors claim the resolution up to0.1mm). The heat transfer coefficient a were defined directly by the meas-ured surface temperature from equation (104)

a ¼ �sT4s

ðTp � T sÞ(104)

where e is the emissivity coefficient of molybdenum. The surface polishing ofmolybdenum allowed the use of the data bank of that coefficient.

Different points of measurement of the temperature in the heat flow be-tween the plasma and the sphere are realized with the cylindrical wire. To dothat, we have to remember the well-known correlation of the heat transfercoefficient between a cylindrical model and a plasma jet. The plasma velocitymeasurements were based on the velocity head, and the established plasmatemperature (density). Results of that work are presented in Table XI in the


Nu-criterial form. The authors claim their results to be in good agreementwith the criterial equation

Nu ¼ 2f 0 þ 0:473 Re0:552Prm (105)

where

m ¼ 0:78 Re�0:145

2f 0 ¼2ð1� T1þx

0 Þð1þ xÞ ð1� T0ÞTx

T0 ¼T s

Tp; x ¼ 0:8 ðfor argonÞ

The reference temperature for evaluating the criteria was calculated from thefollowing formula:

T ref ¼ T0:19 ¼ T s þ 0:19 ðTp � T sÞ (106)

However, the experimental values of the heat flow q are not presented byN. Sayegh and W. Gauvin. To obtain a good standardization of all the experi-mental results published by different authors we had to recalculate theNu-values. N. Sayegh and W. Gauvin say that they did not consider the heatflow to the tungsten wire. This suggest that, according to the authors’estimates, that flow was negligible (this condition is difficult to achieve). Theexperimental values of a and Nu for the sphere yield criterial formula. At the

TABLE XI

THE HEAT FLOWS CALCULATED FROM THE EXPERIMENTAL NU-VALUE BY N. SAYEGH AND

W. GAUVIN

Sphere diameter (mm) Tp (K) up (m/s) Ts (K) Re Nu q (W/cm2)

2.2 4900 12.4 2400 13.6 4.4 69

4500 11.2 2360 15.4 4.5 57

4000 10.5 2240 18.1 4.6 44

3500 9.6 1920 20.8 4.3 38

5.6 4900 12.4 2150 34.7 5.7 39

4500 11.2 2090 39.2 5.9 33

4000 10.5 2020 46.1 6.0 56

3500 9.6 1760 54.2 5.2 22

3.3 4950 12.5 2200 22.0 3.8 45

4300 10.9 2080 26.0 4.4 37

3000 7.7 1640 33.9 5.0 20


same time, the gas temperature itself defined by the correlation for the cylin-drical model. This makes a vicious circle. The plasma temperature should beestablished by a procedure that is independent from the criterial considerations.

Some results. Table XII lists primary experimental data from the abovereviewed sources. The D-factor values calculated from these primary dataare also shown in the table. The heat flow quantities q are of special value.The primary data allow everybody to analyze them and to draw conclusionson his own.

4. One More Attempt to Assess and to Generalize

The systematization of the data in Table XII and authors’ remarks onthem produces no enthusiasm. It shows the discordance, and so in the finalpart of that review we present the results of systematic research of the heattransfer in plasma carried out by us in Leningrad Polytechnical Institute in1979–1986.

The experiments used both fixed metal models, and moving small spher-ical particles (0.3–0.8mm) of refractory oxides. The aim of the research wasto investigate the heat transfer of fixed and moving objects with metallic walland with refractory dielectrics such as MgO, Al2O3 and ZrO2.

The scope of our experimental data is about ten times larger than that ofall the published experimental results in the last two decades. Therefore, webring them in a special section.

Our experiments were carried out on an RF plasma torch of 60 kW, afrequency of 5.28MHz and we use a water-cooled induction plasma torch.The discharge plasma torch chamber made from profiled copper sectionswith quartz housing had inner diameter 68mm. HF-inductor with 4.5 turnsand inner diameter 100mm was placed at a distance of 30mm between thefirst turn and the plasma torch nozzle.

The design of the gas-former allowed the combined straight gas supplythrough the annular gap for producing the cold gas layer along the innersurface of the discharge chamber and axial supply. Such arrangement allowedto produce the laminar jet for durable and stable plasma torch operation in awide range of operation conditions.

The first set of experimental studies are conducted by calorimetricalheat flow measurements to the water-cooled spheres of different diameters(4.6, 6.0, 8.4 and 9.9mm, Table XIII). The cooling of the spheres was per-formed by the copper capillaries having diameters 0.8–1.5mm soldered to thesphere surfaces at the diametrally opposing points. The water was circulatedthrough the capillaries, which were also used as the support means, thecooling-water temperature was measured by the thermocouples placed atthe capillary inlets and outlets.


TABLE XII

EXPERIMENTAL DATA ON THE HEAT TRANSFER WITH A SPHERICAL PROBE

Source T (K) u (m/s) d (10�3, m) q (� 104, W/m2) qffiffiffiffiffiffiffiffid=u

p(� 104,

W s1/2/m2)

Referred to d ¼ 6mm and

u ¼ 25m/s

1 2 3 4 5 6 7 8

G. Kubanek W.

Gauvin

1170 11.9 25.4 11.2 0.517 33.4 Heat transfer

with

sphere

1350 20.8 22.0 0.769 49.4

1510 18.6 20.0 0.739 47.7

1600 15.0 21.2 0.872 56.3

2000 23.5 38.5 1.266 81.7

1580 25.6 15.9 20.5 0.511 33.0

1610 15.0 17.7 0.576 3.7

1800 29.3 27.7 0.645 41.6

2020 23.5 23.3 0.606 39.1

2360 38.0 41.0 0.839 54.2

2520 22.0 33.6 0.903 0.58

2660 31.0 58.2 1.320 85.2

2780 45.0 31.6 0.594 38.3

3060 39.0 64.0 1.290 83.2

W. Rother 1500 15 1 59 0.48 31.1

2000 20 88 0.62 40

2500 30 134 0.77 49.7

3000 40 190 0.95 61.3

3500 50 264 1.18 76.1

4000 60 336 1.37 88.4

4500 70 430 1.63 105.2

5000 80 560 1.98 127.8

Klubnikin 8000 22.1 8 56 1.06 69

9000 27.0 80 1.38 89

10,000 32.0 95 1.50 97

507

HEATAND

MASSTRANSFER

INPLASMA

JETS

TABLE XII. (Continued )

Source T (K) u (m/s) d (10�3, m) q (� 104, W/m2) qffiffiffiffiffiffiffiffid=u

p(� 104,

W s1/2/m2)

Referred to d ¼ 6mm and

u ¼ 25m/s

1 2 3 4 5 6 7 8

Klubnikin 8000 17.6 9.9 48 1.14 73.5

9000 21.6 63 1.35 87

10,000 25.6 77 1.51 98

S. Katta, W.

Gauvin

1060 45.2 12.7 16.5 0.277 17.9

1380 29.9 19.8 0.408 26.3

1400 31.6 21.3 0.427 27.6

1610 66.1 29.2 0.405 26.1

1630 51.9 64.4 0.538 34.7

1880 77.6 42.5 0.544 35.1

1910 45.8 33.2 0.553 35.7

q (� 104) q=ffiffiffiu

p(� 105)

S. Katta, W.

Gauvin

2000 7.4 Nozzle

diameter

7.92mm

15.0 0.551 Heat transfer with plane

3500 12.9 32.4 0.902

4200 6.2 16.8 0.675

4600 16.9 36.3 0.883

5800 4.3 17.5 0.844

5800 21.3 44.0 0.953

7000 10.3 35.0 1.091

9200 13.7 40.1 1.083

10,200 15.4 48.0 1.223

10,700 4.1 22.3 1.101

10,650 8.2 38.8 1.355

11,300 8.9 40.0 1.341

11,900 5.1 36.0 1.594

12,300 5.4 38.2 1.644

508

S.V.DRESVIN

AND

J.AMOUROUX

Model sphere sensors were introduced into the plasma jet at specific pointby the use of the coordinate device allowing to move the sphere smoothly inaxial and radial directions. The system was thermostatted and protectedfrom radiation by water-cooled shields at the end of each capillarie tube(Table XIV).

For the second set of the experiments we have chosen moving sphericalparticles of refractory oxides (MgO and Al2O3) with a range of diameter300–800 mm. The heat flows were defined from the temperature rise rate ofthe particles moving into the plasma jet, with the specific parameters of theplasma. The temperature and the velocity of the particles were correlatedwith the trajectory measurements. To do that we use a camera with a lightfilter at the wavelength of l ¼ 650 nm with a stroboscopic disk. The particleswere introduced into the jet at the nozzle through vertical quartz channelplaced in the middle plane. The distance between the jet axis and the filmplane was 0.4–0.6mm. The stroboscopic disk had a diameter of 360mm andequally spaced holes at its circumference. Its rotation speed was controlledup to 6000 rpm. The speed was measured by the electronic tachometer, withprovided the accuracy of 1%. The described photo registration system hadthe exposure time for one track of 0.5–1.8 ms (Table XV).

In order to qualify our measurements in a large range of temperature andvelocity we have modified the characteristics of the plasma torch (electricalparameters and gas flow) and at last the model sphere sensor into the torchat different axial positions.

TABLE XIII

HEAT FLOW (W/CM2) TO SPHERE PROBES FIXED IN AIR PLASMA

Jet parameters Tp (K) 6300 6600 6800 7000 7200 7400 7800

up (m/s) 31.0 34.8 37.6 39.5 44.6 49.3 53.0

Sphere diameter 9.9mm 184 190 266 283 304 342 409

8.4mm 212 240 311 294 369 368 451

6.0mm 208 264 301 330 378 448 505

4.6mm 312 345 432 435 498 538 655

TABLE XIV

HEAT FLOW (W/CM2) TO SPHERE PROBES FIXED IN ARGON PLASMA

Jet parameters Tp (K) 9300 10,000 10,700 11,200 11,500

up (m/s) 29.0 31.6 32.5 34.1 35.2

Sphere diameter 8.4mm 92.8 112 117 143 150

6.0mm 120 148 152 179 188

4.6mm 144 159 182 214 218


The electrical power supplied to the plasma torch Pe was 33–58 kW forair, and 18–29 kW for argon, the gas supply G was 0.5–1.1 g/s and 0.4–0.8 g/s, respectively.

The temperature was measured by three independent procedures.The spectral method using a small monochromator allowed to define the

whole temperature field of the jet from the absolute intensity of the electroncontinuum with the accuracy 5–10%. The intensity was defined by theblackening of the negative of the investigated region with the use of theroutine procedure.

The atom-ion gas temperature was evaluated by the enthalpy probes ofvarious designs with the 0.8–1.0mm gas inlet opening in diameter and with2–5mm outlet diameter. The gas temperature was also obtained by the linearcalorimeter procedure based on the measurement of the heat flow to the

TABLE XV

EXPERIMENTAL DATA ON THE HEAT TRANSFER OF MOVING PARTICLES IN AN AIR JET PLASMA

Material d (mm) Tp (K) Dup(m/s)

T (K) dT/dt

(� 103, K/s)

Wpart

(%)

q

(W/cm2)

q�

(W/cm2)

MgO 400 6600 34.4 2400 11.5 19.6 490 713

6700 35.9 2430 14.9 16.8 613 878

6700 35.5 2400 17.6 13.8 696 1003

6800 36.4 2450 18.3 14.7 734 1060

6900 38.7 2400 17.7 13.7 700 1014

7100 41.1 2360 21.0 10.8 802 1130

7200 42.2 2330 24.8 8.81 930 1247

670 6500 35.4 2360 7.23 17.3 499 733

6700 37.4 3350 9.08 14.0 603 843

6800 37.8 2320 9.43 12.8 618 826

7000 41.0 2290 11.2 10.3 714 945

7100 42.1 2270 9.4 11.4 607 797

750 6900 39.1 2310 6.73 15.3 508 701

7200 43.9 2280 8.67 11.5 627 818

7200 44.1 2280 8.06 12.3 587 766

820 6200 30.7 2280 4.31 19.3 373 522

Al2O3 330 6300 30.6 2340 13.3 18.4 508 743

6600 34.6 2430 14.9 19.9 584 845

6700 34.3 2440 20.8 15.4 769 1077

6800 35.9 2400 19.7 14.9 721 1030

7000 39.8 2360 24.4 11.4 861 1200

500 6800 36.8 2360 9.35 18.2 541 762

6900 37.8 2310 10.2 15.0 570 786

810 6300 30.8 2370 3.42 27.7 362 538

7000 40.3 2280 7.25 12.5 635 832

7100 41.3 2270 6.52 13.5 578 765

�Referred to Ts ¼ 300K.


cooled capillary moved across the jet, and the dynamic head at the corre-sponding point. The temperature is calculated from the measured values withthe use of the criterial relationship. This method has accuracy of 10–15%,the same as the former one. The jet velocity was evaluated from the dynamichead measured by the micro manometer with the help of a water-cooledprobe of axial design. The jet velocity measurements were also performed bythe injection of small particles (10–15mm) and the use of a stroboscopic diskto qualify on a photopicture their trajectories and the time.

The variations of the supplied power Pe and the plasma gas G2 in theabove chosen ranges allowed us to change the temperature and velocity ofthe gas flow within 6000–7800K and 28–53m/s for air plasma, and9000–11,500K and 27–36m/s for argon plasma.

The heat transfer to small spherical of moving particles was studied onlyfor air plasma at temperature 6200–7200K and flow velocity 30–43m/s.

In order to try to interpret all the data, the choice of the form of criterialrepresentation of the obtained results should be based on the brief survey ofthe available criterial relationship used to describe the heat transfer in plasma.

Many proposed correlations differing in the choice of the referencetemperature, the way of respecting pronounced non-isothermally at theboundary layer, and the contribution of chemical reaction energy into theresulting heat flow. The most common formulas for the Nu-criterion withthe brief description of the conditions under they were obtained are shownin Table XVI.

C. COMPARISON AND CONCLUSION

To calculate the Nusselt number, a great number of formulas exist and thecriterial dependences are correct for narrow ranges of temperatures andconditions at which they have been obtained. Therefore, using correlationsoften leads to errors difficult to be evaluated (an error of the heat fluxcalculation may exceed a hundred percent). That is why it seems to beimportant to compare the most generally used formulas with experimentaldata in a wide range of temperature.

To have a total notion of the process of heat transfer it is necessary tomeasure at the same time the following values: the heat flux to a target model,the plasma temperature and its velocity in a local point. Such investigation iscomplex to realize; therefore, data does not exist in large quantities. Figures 1and 2 present practically all well-known experimental data of a heat transferresearch in high temperature flows and plasma jets for traget models of metalwater-cooled spheres and for moving ceramic particles.

From those experimental data, the correlation between temperature andheat flux for argon and air plasma was calculated using the different


TABLE XVI

CORRELATIONS FOR HEAT TRANSFER AND TECHNICAL CONDITIONS OF THEIR USE IN HIGH-TEMPERATURE AND PLASMA FLOWS

No. Nu Reference

plasma

temperature

Medium wall temperature Re Source Conditions

1 0:181 Re0:76 Pr0:33 TB Nitrogen 100023000 K 60024300 Kubanek Gauvin Calorimetric measures for

fixed spheres + 15:9;25.4mm in the flow of

the arc plasma torch,

P ¼ 24235 kW; Ts – the

mean-mass jet

temperature

20:02 Re0:73

lpls

� �1:73 TB Helium 160022200 K 30023000 Katta Gauvin The heat flows were

evaluated with the use

of the temperature

gradient in the spherical

probe wall + 12:7 mm.

In the arc plasma torch

flow power 40 kW

30:01 Re0:79

lpls

� �1:15 Argon 160022200 K

512

S.V.DRESVIN

AND

J.AMOUROUX

4 1:32 Re0:5 Pr0:4 Tp+Ts/2 Nitrogen 150025000 K o200 Rother Moving the spherical

thermoprobes + 1 mm

through the jet of the

arc plasma torch,

I ¼ 14 A, P ¼ 3 kW

50:76 Re0:5 Pr0:4

rpmprsms

� �0:4

� 1þ ðLen � 1ÞHB

Hp

� �Ts Dissociated air Fay Riddell Theoretical calculation for

the critical point with

respect of chemical

reactions in the

boundary layer n ¼ 0:63for frozen; n ¼ 0:52 for

the equilibrium

boundary layer; q –

calculations for DH/Cps

60:5 Re0:5 Pr0:4

rpmprsms

� �0:2 Tp Argon Pt � Pp measured by a

thermocouple layer

+ 0:8 mm in the argon

jet of the arc plasma

torch; I ¼ 250 A

72lslp

þ B Re0:5 Prnrpmprsms

� �0:2 Tp Argon, air Katta Gauvin Calorimetrization of the

model spheres

+ 8; 10 mm in the jet

of the induction. B ¼0:6 and n ¼ 0:4 for

argon; calculation with

the use q by DH/Cps

82þ 0:6 Re0:5 Pr0:33

nsnp

� �0:15 Tp þ T s

2

Lewis Gauvin Analysis of the

experimental data of

various authors

513

HEATAND

MASSTRANSFER

INPLASMA

JETS

TABLE XVI. (Continued )

No. Nu Reference

plasma

temperature

Medium wall temperature Re Source Conditions

92þ 0:6 Re0:5 Pr0:33

nsnp

� �0:15Cp

Cps

� �Tp Lee Pfender Experiments in the arc

plasma jet

10 2 f 0 þ 0:473 Re0:552 Rem;

f 0 ¼1� ðT s=TpÞ1:8

1:8 ð1� T s=TpÞ ðT s=TpÞ0:8

T sðlÞTpðlÞ Argon 10280 Sayegh, Gauvin Temperature measurements

at the surface of M0

polished spheres,

+ 5:6222 mm in the

HF induction plasma

torch jet, q calculated.

P ¼ 6 kVA;

f ¼ 4:5 MHz;

+ 40 mm of SiO2

chamber;

U ind ¼ 324 kV;

dnozzle ¼ 25 mm

514

S.V.DRESVIN

AND

J.AMOUROUX

correlations but for the same conditions: ds ¼ 6mm, Vp ¼ 25m/s,Ts ¼ 300K. Fig. 1 shows that all dependences of the heat flux in argonplasma on the temperature have a monotonic character. In the case of airplasma, the character of those dependences is more complex. The maindifference between argon and air plasma is due to the dependence on tem-perature of the plasma with its heat conductivity (see Fig. 3).

If we use the temperature of the plasma flow to calculate the heat con-ductivity of an air plasma, we have to estimate the heat flux, this leads to adisturbance of dependence on temperature monotonicity for high temper-atures (higher than plasma dissociation takes place) and to an appearance ofsharp decreasing of heat fluxes. However an experimental confirmation ofthat has not been obtained up to now. Dependences on temperature of theheat flux have a smooth increasing character when we use the average of the

FIG.1. Experimental data of a heat transfer research in argon plasma jets for copper target

probes.


heat conductivity through the boundary layer:

�lp ¼ 1=Tp � T s

Z Tp

T s

lpdt.

A comparison of different criterial dependences shows a considerablevariation of heat flux values for argon plasma or for air one. For example, atthe temperature of 8000K, the heat flux ranges from 0.7 to 2MW/m2 forargon plasma, and at the same conditions for air plasma it ranges from 2 to14MW/m2. Therefore, a recommendation to use one of these formula canbe made only as a result of a comparison between specific criteria andexperimental data.

However, the direct comparison of experimental data with calculatedcurves is not possible because the data are coming for different target modelspheres (fixed copper water-cooled models or ceramic particles moving in aplasma flow) and different experimental conditions such as the velocity andthe temperature of plasma flows.

FIG.2. Experimental data of a heat transfer research in air plasma jets for different probes.


If we replace in the expression of heat flux the Reynolds and the Prandtlnumbers by the real parameters, we obtain:

qp ¼ A

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirpVpds

mp

s ffiffiffiffiffiffiffiffiffimpcplp

3

rlpds

ðTp � T sÞ

Let the equation be rearranged in the following way: the left side consistsof items that were measured during our experiments, and the right sideterms that are dependent on the plasma temperature only:

qp

ffiffiffiffiffiffids

Vp

s|fflfflfflffl{zfflfflfflffl}

Experimental data

¼ A

ffiffiffiffiffirpmp


3

rlpðTp � T sÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

Dfunction

Then the right side of the equation which depends only on the temper-ature can be denoted as D-function:

DðTÞ ¼ A

ffiffiffiffiffirpmp


3

rlpðTp � T sÞ

FIG.3. Temperature dependence of the heat conductivity for air and argon plasma.


Thus, the D-function connects a value of the heat flux qp to the sphericaltarget with the values of the sphere diameter ds, the plasma temperature Tp

and velocity Vp by the following way:

qp

ffiffiffiffiffiffids

Vp

s¼ DðTÞ

Using the D-function is very convenient to make a criterial qualifi-cation of the results of different experiments as we do on the same graphin Figs. 4 and 5. Figures 4 and 5 present dependences on temperature of theD-function for argon and air plasma that had been created for differentvalues of the semi-empirical coefficient A, if we use an average heat plasma

FIG.4. Temperature dependence of the D-function and experimental data for argon

plasma.

FIG.5. Temperature dependence of the D-function and experimental data for air plasma.


conductivity through the boundary layer. Experimental data of differentauthors expressed by a universal complex qp

ffiffiffiffiffiffiffiffiffiffiffiffiffids=Vp

pare shown in the same

figures.The D-function comparison of different experimental data with the con-

vective part of the heat transfer has shown a good agreement for the bothargon and air plasma when the coefficient A is in the range of 0.5–0.6 – formetal particles, and 0.4–0.5 – for ceramic particles.

This is why from a lot of comparisons of different experimental data ofheat transfer between plasma flow and spherical target model as well as aquantity of calculations of heat transfer between particles of different pow-dered materials and jets of RF plasma torches we have proposed the fol-lowing conclusions: (1) When the plasma flow velocity is much higher thanthe particle velocity – Vp4Vs, the conductive part does not play a noticeablerole in the heat transfer; (2) When a particle is accelerated and its velocitybecomes comparable with a plasma jet velocity – VpEVs, that is typical forsmall particles (less than 50mm) and especially for fine-dispersed ones, theconvective part of the heat transfer becomes equal to zero 0:6 Re0:5 Pr0:33 !0 because the Reynolds number becomes equal zero to Re ¼ rp ~Vp � ~V s

�� ds=mp ! 0, and the conductive part becomes the main part of the heat transfer.

1. Correction Proposal

If we use the correlation that takes into account both the conductive andconvective part of the heat transfer under the condition Vp4Vs we obtain a2–3 times overestimation of the heat flux value and considerable errors in theresults due to the presence of the conductive part because Nu ¼ 2. That factis confirmed by authors as well as calculations that had been carried out.

Thus, the criterial formulas of heat transfer between a particle and aplasma for different velocities rates:

Nu ¼ A Re0:5Pr0:33; if Vp4V s

Nu ¼ 2lpslp

� �; if Vp � V s

The goal is to find a universal correlation which satisfies a degree ofaccuracy with experimental data of heat fluxes from plasma to particles(Figs. 1 and 2) as well as takes into account the feature of a calculation ofdynamics and heat transfer of different particles in plasma jets when the heattransfer may be changed from the convective nature to the conductive one.

As shown above, a dominance of the conductive part (Nu ¼ 2) or theconvective one (Nu ¼ A Re0.5 Pr0.33) of the heat transfer is determined bythe rates between the particle velocity and the plasma one. This is why we


propose a correction to the conductive part of the heat transfer (Nu ¼ 2) ifthe ratio Vs/Vp of the particle velocity to the plasma one is close to 1; and forheat flux calculations, we recommend the following correlation that takesinto account the features of the heating of different particles in plasma:

Nu ¼ 2lpslp

� �Vs

Vp

� �þ 0:6Re0:5Pr0:33

In that case, the classical formula without any other corrections is chosenbecause different correction factors of other authors result in a correction ofthe heat flux of no more than 15%. The simplest expression is the mostreasonable for the heat transfer analysis, especially because an investigationof the convective part of that expression by using the D-function and takinginto account the heat conductivity averaged through the boundary layer,has shown a good agreement with experimental data (see Figs. 4 and 5). Theformula for an estimation of the heat flux from plasma to a particle, has thefollowing form:

qp ¼ Nu�lpds

ðTp � T sÞ

For the plasma heat conductivity �lp, we recommend to use the one averagedthrough the boundary layer.

For the other plasma properties, we recommend to use the temperature ofthe incident plasma flow (at the external border of the boundary layer).

The formula takes automatically into account the disadvantages men-tioned above, that take place when changing of the nature of the heattransfer from plasma to the particle. If the plasma velocity is higherthan those of treated particles velocities Vp4Vs then the formula takes intoaccount only convective part of the heat transfer, it is transformed into thefollowing form:

Nu ¼ 0:6 Re0:5Pr0:33 2V s

Vp

� �! 0

If treated particles velocities are comparable with the plasma velocity Vp �V s then the formula takes into account only the conductive part of the heattransfer, it is transformed into the following form:

Nu ¼ 2lpslp

� �0:6Re0:5Pr0:33 �! 0

Thus, there is the following universality of the formula that provideschanging of the nature of the heat transfer depending on the ratio of the


particle velocity Vs to the plasma one Vp:

Nu ¼ 2lpslp

� �Vs

Vp

� �þ 0:6Re0:5Pr0:33,

Nu ¼ 0:6Re0:5Pr0:33

Nu ¼ 2lpslp

� � if Vp4Vs

if Vp � Vs

8>><>>:

2. Conclusions

The study of a large number of experimental data on heat transfer be-tween particle and plasma as well as the analysis of many criterial formulaswhich describe the heat transfer let us make the following conclusions:

1. If we use the enthalpy difference DH in the formula for a calculationof the heat flux q it gives an overestimation of the last one in 3–5times. Therefore the temperature difference DT ¼ Tp � T s is recom-mended to be used for a calculation of the heat flux.

2. The calculation of the heat flux q from only the heat conductivity ofthe incident plasma flow (at the external border of the boundarylayer) leads to an overestimation of the heat flux in comparison withexperimental data in 2–3 times. Therefore the heat flux is recom-mended to be calculated from the heat conductivity averaged throughthe boundary layer. But the other plasma properties such as its spe-cific heat cp, its density rp, its viscosity mp should be calculated bytaking into account the temperature of the incident plasma flow.

3. We propose to use the correction coefficients depending on the par-ticle velocity and the plasma one in the correlation of the particle heattransfer in plasma jet. That coefficient regulates the value of a con-ductive part of the heat transfer according to the ratio of the particlevelocity to the plasma one.


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AUTHOR INDEX

Index Terms Links

Numerals in parentheses following the page numbers refer to reference numbers cited in the

text

A

Abbaoui, M. 397 399 400 401

403 404 447

Abou-Ghazala, A. 111 114 117 118

124 141 142

Agapakis, J. 266 336

Ageorges, H. 260 312 334

Ahmed, I. 240 333

Ahmed, S. 29 135

Akishev, Y. 74 103 138

Akiyama, H. 114 116 117 118

124 142

Al-Arainy, A. A. 111

Aldea, E. 58 59 136

Alden, R. W. 111 141

Aleinov, I. 159 160 169 170

Alexeff, I. 53 136

Alikafesh, A. 53

Allen, R. F. 288 308 311 338

Amada, S. 314 343

Amakawa, T. 431 449

Index Terms Links


Amerlinck, Y. 239 332

Amiranashvili, Sh. 91

Andersen, A. B. 109

Andreé,P. 397 399 400 401

403 404 447

Anpilov, A. M. 109 112 141

Arkhipenko, V. I. 74 138

Armster, S. Q. 286 289 306 308

311 313 338

Arundell, C. J. 374 378 379 391

446

Ashgriz, N. 160 204

Asinovsky, E. I. 51

Asisov, R. I. 103 140

Aubrecht, V. 418 448

Aubreton, J. 208 329 378 379

382 384 397 398

399 401 402 404

405 446 447

Auciello, O. 373 382

Aziz, S. D. 152 153 173 175

203 292 310 340

B

Babaeba, N. 35 135

Babayan, S. E. 60 61 137

Babicky, V. 110 111 119 141

Bach, Fr.-W. 264 267 336

Badent, A. 117 142

Index Terms Links


Baily, N. A. 50 135

Baiyer, E. 264 267 336

Baker, H. J. 63 65 67 68

70 137

Bakken, J. A. 103 140 418

Balaster, A. N. 115 117 118 124

142

Ball, L. G. 108 141

Bandyopadhyay, R. 275 337

Barénkové, H. 85 86 90 93

138

Barbezat, G. 224 231 232 233

332

Bárdos, L. 85 86 90 93

138

Bardsley, J. N. 35 135

Bark, Y. B. 109 112 141

Barkhudarov, E. M. 109 112 141

Barnes, R. M. 278 337

Baronnet, J. M. 384

Bartelheimer, D. L. 385 447

Bartnikas, R. 56 136

Baselyan, E. M. 16 43 45 51

134 135

Bauder, U. H. 385 447

Baudry, A. 419 420 448

Baudry, C. 240 244 275 321

333 337

Bayuzick, R. J. 310

Index Terms Links


Beall, L. 218 330

Becker, K. 74 93 138

Beebe, S. J. 53 111 136 141

Behnke, J. F. 58

Belashchenko, V. E. 275 337

Belov, V. A. 382 384 447

Belyaev, Y. N. 380 446

Benes, J. 234 332

Benilov, M. S. 439 440 441 442

450

Bennet, T. 154 203

Bennett, T. 310 343

Bergman, T. L. 240 333

Berndt, C. C. 187 204 284 285

286 290 296 304

306 307 313 314

323 338 339 341

342 344

Beroural, A. 117 142

Bertagnolli, M. 154 203 292 339

Bertrand, P. 266 336

Betoule, O. 220 221 330

Bewsher, A. 189 204

Bhola, R. 152 155 156 179

198 203 289 292

339

Bianchi, L. 145 202 282 288

289 290 291 294

296 300 304 307

Index Terms Links


Bianchi, L. (Cont.)

310 311 313 314

315 316 318 338

339 340 343

Birmingham, J. G. 45 46

Bisson, J. F. 265 275 276 320

336 337 344

Bisson, J.-L. 265 266 336

Blainard, J. 265 336

Blein, F. 211 220 282 290

307 310 311 313

316 329 338 339

Bödeker, H. 91

Boeuf, J. P. 80 81 91 138

Bolot, R. 241 333

Bonnefoi, C. 378 379 395 446

Bonnet, J. P. 262

Borck, V. 228 331

Borges, C. 345 444 450

Borisov, Y. 230 262 312 335

Borisova, A. 262 312 335

Boulos, M. 147 203 208 209

210 220 221 228

230 236 237 239

240 246 248 249

251 252 255 256

257 263 264 267

268 278 279 280

334 329 330 331

332 333 334 335

Index Terms Links


Boulos, M. (Cont.)

337 357 358 359

360 361 362 363

364 365 366 367

368 369 370 374

375 376 377 378

380 381 382 383

384 389 390 391

392 393 394 395

396 397 399 400

407 408 409 410

411 415 440 441

442 443 444

Bourdin, E. 249 252 256 334

Brackbill, J. U. 159 160 204

Braginsky, S. I. 46 51 135

Brand, K. P. 418 448

Brilhac, J. F. 234

Brock, J. S. 159

Brockmann, J. E. 264 267 335

Brossa, M. 211 329

Brown, C. A. 314 343

Brusasco, R. M. 28 31 44 134

135

Burgess, A. 232 233 332

Bussmann, M. 156 157 163 165

171 203 204 292

304 306 307 310

340 342

Byszewski, W. W. 85 138

Index Terms Links


C

Campbell, C. A. 125 126 127 128

129 130 131 132

Cao, Y. 161 204

Capitelli, M. 382 384 447

Capriotti, E. R. 418 448

Carpaij, M. 442 450

Catherinot, A. 355 446

Cebeci, T. 427 448

Cedelle, J. 284 294 301 302

303 307 308 309

310 314 342 309

313

Cernak, M. 110 111 119 141

Cesar, M. G. M. M. 323 344

Chadband, W. G. 117 142

Chambers, W. B. 230 331

Chandra, S. 143 144 146 152

153 154 155 156

157 163 165 167

168 170 173 175

177 179 181 186

189 196 198 202

203 204 275 289

292 293 294 296

297 304 306 307

310 320 321 337

339 340 341 342

344

Index Terms Links


Chang, C. H. 240 272 275 333

336 337 374 446

Chang, C. W. 427 449

Chang, D. 28 135

Chang, J. P. 61 137

Chang, J. S. 106 111 117 118

119 124 140

Chang, W. S. 161 204

Chapelle, J. 100 139

Chapman, S. 363 446

Charmchi, M. 143 198 204

Charuschi, M. 321 344

Chase, J. D. 236 332

Chazelas, C. 208 226 329 331

Chen, D. M. 424 429 448

Chen, J. 87 89 90 138

Chen, K. 240 333

Chen, W. L. T. 211 248 329 334

Chen, X. 241 244 333 419

448

Chen, Xi. 246 334

Chengrong, Li. 54 55 136

Chernyak, Yu. B. 275 337

Chervy, B. 355

Ching, W. K. 115 117 118 124

142

Chirokov, A. V. 36 53 57 60

61 63 67 68

69 70 71 91

135 136 137

Index Terms Links


Cho, Y. I. 1 100 101 140

Choe, W. 60 71 137

Chorin, A. J. 160 204

Chraska, P. 234 332

Chraska, T. 291 305 339

Christofi, N. 109 112 141

Chumak, A. 235

Chumak, O. 212

Chyin, V. I. 17 134

Chyou, Y. P. 246 334 428

Cielo, P. 189 195 204 264

265 266 267 335

336

Ciocca, M. 85 87 138

Cirolini, S. 198 204

Claeys, F. 239 332

Clements, J. S. 106 108 113 114

117 118 124 140

141 142

Clift, R. 247 334

Clupek, M. 110 111 119 141

Clyne, T. W. 281 282 337

Coates, D. M. 31

Coddet, C. 187 204 241 292

296 304 306 313

314 333 339 341

342

Collins, D. J. 378 379 446

Index Terms Links


Colus, A. J. 115 117 118 124

142

Colussi, A. J. 115 117 118 124

142

Copitzky, T. 264 267 336

Cormier, J. 100 139

Correa, S. M. 427

Coudert, J. F. 208 211 212 216

217 218 219 220

221 222 223 225

226 227 228 229

230 241 247 249

266 272 273 274

329 330 331 337

Cowling, T. G. 363 446

Craggs, J. D. 9 10 134

Craig, J. E. 266 268 336

Cram, L. 257 334 420 448

Croquesel, E. 48

Cross, J. D. 111

Cross, M. 163 204

Crowe, C. T. 278 337

Cunha, M. 442 450

Czeremuszkin, R. 56 136

Czernichowski, A. 100 139

D

Dabringhausen, L. 439 440 441 442

443 450

Index Terms Links


Dalaine, V. 100 139

D’Alessandro, F. 19 134

Dallaire, S. 189 204 260 262

264 266 267 335

Danikas, M. 117 142

Darken, L. S. 257 258 334

Davis, S. H. 160 204

Dawson, G. A. 14 134

Debbagh-Nour, G. 384

Deevi, S. C. 262 335

Degout, D. 355 446

Delalondre, C. 355 419 446 448

Delbos, C. 247 249

Delluc, G. 218 223 225 245

248 330 331 334

Delplanque, J.-P. 286 289 306 308

311 313 338

Dendo, T. 320 323 344

Denes, F. 115 117 118 124

142

Denoirjean, A. 145 211 212 260

262 289 290 307

310 311 313 314

315 316 317 319

320 329 335 339

340 343 344

Denoirjean, P. 260 262 314 335

343

Desai, V. 325 344

Index Terms Links


Desmaison, J. 307 315 317 319

340 344

Destaillats, H. 115 117 118 124

142

Devoto, R. S. 378 379 382 384

446 447

Dhiman, R. 177 204

Dinulescu, H. A. 431 449

Dobbs, F. C. 108 141

Doblin, M. A. 108 141

Dolatabadi, A. 275 337

Domaszewski, M. 292 339

Drabkina, S. I. 51 135

Dragsund, E. 109

Dreizin, E. L. 92

Duan, Z. 216 217 218 330

Ducos, M. 220 221 330

Dukowicz, J. K. 275 337

Dushman, S. 441 450

Dussan V, E. B. 160 204

Dussoubs, B. 223 224 243 254

257 258 259 264

265 267 268 269

270 271 272 281

290 314 316 330

334 336 339

Dyer, F. F. 53 108 136 141

Dykhnizen, R. C. 230 288 313 318

331 338 343

Index Terms Links


E

Edels, H. 75 138

Eden, J. G. 87 89 90 138

Egli, W. 31 36 135 418

448

Elchinger, M. F. 208 223 225 245

248 329 331 334

397 398 399 401

402 404 405 447

Elenbaas, W. 347

El-Habachi, A. 85 87 138

Eliasson, B. 31 36 135

Elsing, R. 198 204

Emst, F. 264 267 336

Ernst, K. A. 385 447

Escure, C. 284 285 286 308

338

Espie, G. 260 314 316 343

Essoltani, A. 246 255 256 257

279 334

Etemadi, K. 353 354 446

F

Faghri, A. 161 204

Fallon, R. J. 380 446

Fan, H. Y. 75 138

Fantassi, S. 290 304 339

Fard, M. P. 296 341

Index Terms Links


Farouk, B. 74 75 76 77

78 79 80 102

103 138

Farouk, T. 74 80 138

Fauchais, P. 145 202 205 206

208 209 210 211

212 215 216 217

218 219 220 221

222 223 224 225

226 227 228 229

230 241 243 245

246 247 248 249

251 252 254 256

257 258 259 260

262 263 264 265

266 267 268 269

270 271 272 273

274 278 279 280

281 282 284 285

286 287 288 289

290 291 293 294

296 297 298 300

301 304 305 306

307 308 309 310

311 312 313 314

315 316 317 318

319 320 329 330

331 333 334 335

336 337 338 339

Index Terms Links


Fauchais, P. (Cont.)

340 341 342 343

344 357 358 359

360 361 362 363

364 365 366 367

368 369 370 374

375 376 377 378

380 381 382 383

384 389 390 391

392 393 394 395

396 397 398 399

400 401 402 404

405 407 408 409

410 411 415 427

440 441 442 443

444 446 447 449

Fazilleau, J. 247 249

Feng, Z. G. 292 339

Feng, Z. Q. 292 339

Fernsler, R. F. 15 134

Filugin, I. V. 51 135

Fincke, J. 212 214 218 222

239 240 241 263

264 266 267 272

330 333 335 336

Fincke, R. 241

Finkelnburg, W. 348 352

Firsov, O. B. 10 15 134

Fischer, A. 264 267 336

Index Terms Links


Flamm, D. L. 373 382

Foest, R. 74 93 138

Ford, K. G. 230

Franck, H. 264

Freeman, M. P. 236 332

Freton, P. 240 332 419 448

Fridman, A. 1 29 36 47

53 57 63 74

75 76 77 78

79 80 83 88

91 92 96 97

98 99 100 101

102 103 134 135

136 137 138 139

140 142

Fu, A.-J. 296 341

Fujiwara, J. Y. 296 304 342

Fukai, J. 153 160 203 204

FukaiIbid, J. 153 203

Fukanuma, H. 155 296 303 304

306 313 342

Fukomoto, M. 143 145 167 180

181 186 202 203

281 283 284 287

289 295 296 297

298 299 300 301

309 310 312 314

315 337 338 339

341 342 343

Fukumoto, F. 294 295 298 310

Index Terms Links


G

Gabbay, E. 316 320 344

Gahl, T. 106 107 140

Gallimberti, I. 14 17 134

Gambling, W. A. 75 138

Gardi, B. R. 56 136

Garrison, R. L. 386 387 388

Gauthier, B. 275 276 337

Gauvin, W. H. 252 334

Gawne, D. T. 240 241 333

Ghafouri-Azar, R. 198 204 275 292

294 320 321 337

340 344

Gherardi, N. 48

Ghorui, S. 401 402 403 405

406 408 409 411

Gill, G. C. 281 337

Gitzhofer, F. 237 239

Gleizes, A. 240 246 255 256

257 279 332 334

355 390 392 418

419 447 448

Gobin, D. 288 290 304 338

339

Goldman, M. 17

Goldman, N. 17

Golubev, V. S. 103 140

Golubovskii Yu, B. 58

Index Terms Links


Gonzalez, J. J. 240 332 355 390

392 418 419 447

448

Gorse, C. 382 384 447

Goryunov, A. Yu. 16 134

Goswami, R. 296 342

Gouda, G. 48 135

Gougeon, P. 189 193 204 232

233 265 284 285

286 290 304 305

306 332 336 338

339

Grace, J. M. 36 53 57 91

135 136

Grace, J. R. 247 334

Gravelle, D. 237 239

Griem, H. 382 447

Grieven, P. 257 258 334

Grimaud, A. 245 262 282 307

311 316 317 319

320 334 338 340

343 344

Gross, K. 265 279 336 337

Grushin, M. 74 103 138

Gu, L. 418

Guessasma, S. 296 304 314 342

Guest, C. J. S. 230

Guilemany, J. M. 246 252 288 296

303 306 311 334

338 342

Index Terms Links


Gunther, K. 442 450

Gutsol, A. 1 36 53 57

63 74 75 76

77 78 79 80

91 97 98 100

101 102 103 135

136 137 138 139

140

H

Hackett, C. 345 444 450

Haddadi, A. 311 316 320 343

344

Hadfield, M. G. 308 342

Haggard, D. C. 222 272 330 336

Haggard, D. D. 263 264 266 267

335

Haidar, J. 420 435 448 449

Haji, H. 289 339

Hall, D. R. 63 65 67 68

70 137

Haller, B. 262

Ham, M. 115 117 118 124

142

Hämäläinen, E. 266 336

Hamidi, L. E. 355

Hanneforth, P. 205

Hannoyer, B. 145 314 315 316

317 343

Index Terms Links


Hansbo, A. 321 344

Harding, J. H. 198 204

Harpee, J. F. 260 334

Hartmann, T. 442 450

Haslbeck, P. 224 231 232

Haslinger, S. 60 66 137

Haure, T. 314 315 316 344

Hayashi, H. 295

Heath, W. O. 45 46

Heberlein, J. 211 215 216 217

218 223 239 241

246 248 329 330

333 334 345 419

420 421 431

432 433 435 440

441 442 443 444

448 449 450

Heesch, E. J. M. 112 141

Hell, J. 60 66 137

Heller, G. 347 412 446

Henins, I. 60 61 71 137

Henne, R. 228 230 239 331

Herman, H. 61 137 145 187

195 203 204 241

284 285 286 290

296 297 306 310

313 322 333 338

339 341 342 344

Index Terms Links


Hernberg, R. 266 336

Herrmann, H. W. 60 71 137 385

447

Hicks, R. F. 60 61 71 137

Hidalgo, H. 315 344

Hinazumi, H. 50 135

Hinterberger, H. 31 135

Hirt, C. W. 157 204

Hlina, J. 234 332

Hochstein, J. I. 159

Hofer, H. 31 135

Hoffman, T. 266 336

Hoffmann, M. R. 106 111 115 117

118 119 124 140

142

Hofmeister, W. 310

Hollis, K. 263 265 267 335

Honda, T. 155 203

Honda, Y. 49

Hood, J. L. 30

Hopwood, J. 95 96 139

Horiike, Y. 94 139

Hosoya, M. 50 135

Houben, J. M. 230 294

Hrabovsky, M. 212 234 235 332

Hsu, K. C. 353 354 406 407

424 429 446 448

Hu, Q. 111 141

Huang, P. C. 241 333 419 448

Index Terms Links


Huang, Y. 145 167 180 181

203 283 296 298

299 306 310 338

341 342

Huddlestone, R. H. 382 447

Hühle, H. M. 224 231 232

Huijbrechts, A. H. J. 112 141

Hurst, C. J. 108 141

I

Ichiki, T. 94 139

Ignatiev, M. 266 336

Ilavsky, J. 323 344

Imbert, M. 241 333

Inada, S. 155 203 296 310

341

Incropera, F. P. 425 426 448

Inoue, T. 231 331

Ishigaki, T. 239

Iskenderova, K. 62

Ito, S. 113 117 118 124

142

Iwamoto, N. 296 298 341

Iza, F. 84 88 95 96

139

Index Terms Links


J

Jaccuci, G. 154 198 203 204

292 339

Jaeyoung, P. 60 71 137

Jä ger, D. A. 231 331

Janisson, S. 272 337

Jayaraj, B. 325 344

Jayaram, S. 111

Jeffery, C. L. 264 266 267 335

Jenista, J. 431 432 433 449

Jeong, J. Y. 60 61 137

Jiang, X. 145 195 203 296

297 342

Johannessen, B. O. 109

Jones, H. M. 117 142

de Jong, P. 112 141

Jorba, J. 314 343

Joshi, R. P. 111 141

Jüttner, B. 439 449

K

Kaddani, A. 355 419 446 448

Kalashnikov, N. Y. 97 98 139

Kalra, C. S. 97 98 100 101

103 139 140

Kanazawa, S. 49 135

Kang, B. K. 60 71 137 154

203

Index Terms Links


Kang, W. 53

Kanouff, M. P. 198 204 306 307

313 342

Kanzawa, A. 155 203

Karal’nik, V. 155 203

Karthikeyan, J. 323 344

Katoh, S. 186 284 300

Katsuki, S. 111 114 117 118

124 141 142

Kavka, T. 212 235

Kennedy, L. 1 29 47 75

77 79 83 88

92 96 97 98

99 100 134 135

139 140 142

Keskinen, J. 279 337

Khvesyuk, V. I. 378 379 446

Kieft, I. E. 93 94

Kim, G. J. 84 88

King, T. G. 296 300 342

Kinh, A. H. 291 305 339

Kirillov, A. A. 74 138

Kishimoto, Y. 92 93 139

Kist, K. 117 142

Kitahara, S. 320 323 344

Klemenc, A. 31 135

Klingbeil, R. D. 15 134

Knotek, O. 198 204

Knowlton, M. 115 117 118 124

142

Index Terms Links


Kochetov, I. 74 103 138

Kogelschatz, U. 31 36 53 135

Kogoma, M. 49 93 135 139

Koidesawa, T. 139

Kolman, D. 241 333

Kong, M. G. 60 64 137

Konrad, M. 212 234 332

Kopainsky, J. 385 447

Kopecky, V. 212 234 235 332

Kopiev, V. A. 109 112 141

Korobtsev, S. 28 134

Kossyi, I. A. 109 112 141

Kostuchenko, S. V. 51 135

Kothe, D. B. 156 159 160 204

Kovitya, P. 382 384 418 447

448

Kowalsky, K. A. 264 267 335

Kozlov, Y. N. 109 112 141

Krause, T. 29 135

Krey, R. U. 386 387 388

Krikka, K. 266 336

Kroesen, G. M. W. 402 404 405 447

Kulik, P. P. 378 379 446

Kulikovsky, A. A. 35 135

Kumar, S. 427 449

Kunchardt, E. E. 35 135

Kung, H. H. 28 44 134 135

Kung, M. C. 28 44 134 135

Kunhardt, E. E. 75 117 138 142

Index Terms Links


Kurdyavtsev, N. N. 51 135

Kuribayashi, I. 155 203

Kuroda, S. 296 304 320 323

342 344

Kushner, M. J. 35 73 83 84

87 88 90 135

137 138

Kusz, J. 50

Kuznetsova, I. V. 97 98 139

L

Labbe, J. C. 260 262 314 316

335 343

Lacasse, V. 189 204 265 336

Lacour, B. 49 135

Lagnoux, O. 226 228 230 314

315 316 317 331

343

Laimer, J. 60 66 137

Lamontagne, M. 189 193 195 204

264 265 266 267

290 335 336 339

Lan Y, Y. C. 246

van der Laan, E. P. 93 94

van der Laan, P. C. T. 112 141

Landes, K. 224 231 232 264

267 336

Langenscheidt, O. 439 440 441 442

443 450

Index Terms Links


Largo, J. 266 336

Laroussi, M. 53 108 136 141

Latrè che, V. 56 136

Launder, B. E. 427 448

Lavernia, E. J. 154 203 286 289

292 306 308 311

313 338 339

Leblanc, L. 218 320 330 344

Lee, C. K. 205 325 344

Lee, D. Y. 266 268 336

Lee, J. F. 361 362 373

Lee, J. K. 84 88

Lee, S. 28 135

Lee, Y. C. 147 203 240 246

332 334 428

Lefaucheux, P. 100 139

Lefort, A. 397 399 400 401

403 404 447

Lefort, P. 260 314 316 317

320 335 343 344

Leger, A. 145 202 264 267

274 282 284 285

286 288 289 290

291 293 294 296

297 300 304 305

306 310 311 315

316 318 335 337

338 339

Legros, E. 242 245 277 321

322

Index Terms Links


Leigh, S. H. 307 342

Leniniven, C. 315 344

Leonard, S. L. 382 447

Leonas, V. B. 380 446

Lesinski, J. 384

Lesko, T. M. 115 117 118 124

142

Lesueur, H. 100 139

Leveillé, V. 237 239

Leveroni, E. 429

Levitsky, S. M. 66

Lewis, J. W. 252 334

Lewis, T. F. 230 331

Li, C. J. 145 292 296 306

311 313 340 341

342 343

Li, H. P. 241 244 333 406

408 419 448

Li, J. L. 145 292 296 311

340 341 343

Li, K.-I. 258 264 265 267

268 269 270 271

272 334 336

Lichtenberg, A. J. 1 134

Lichtenberg, S. 439 440 441 442

443 450

Lieberman, M. A. 1 134

Lima, R. S. 265 266 320 336

344

Index Terms Links


Linani, B. 390 392 418 447

Lisitsyn, I. V. 114 117 118 124

142

Liu, B. 240 241 333

Liu, C. 87 89 90 138

Liu, H. 154 203 292 339

Liu, W. 155 203 310 343

Llorca-Isern, N. 314 343

Lochte-Holgreven, W. 382 447

Locke, B. R. 106 111 117 118

119 124 140

Loeb, L. B. 9 11 17 134

Lowke, J. 19 134 418 435

441 448 449

Lozansky, E. D. 10 15 134

Lucchese, P. 290 339

Luchese, P. 282 338

Lufitha, M. 144 146 168 170

202 294 296 297

340

Lugsheider, E. 264 267 336

Lukes, P. 110 111 119 141

M

Madejski, J. 152 155 203 287

338

Maecker, H. 348 351 352 446

Magesh, T. 53 136

Mailhot, K. 237 239

Index Terms Links


Maiorov, V. A. 58

Maître, A. 314 316 343

Mancini, C. 296 304 314 342

Manolache, S. 115 117 118 124

142

Mäntyla, T. 266 336

Marantz, D. R. 264 267 335

Marchese, M. 154 198 203 204

292 339

Mariaux, G. 240 241 243 244

245 275 321 333

334 337 419 420

448

Markl, H. 106 107 140

Marno, H. 230

Marotta, A. 440 441 450

Marple, B. R. 265 266 320 336

344

Marr, G. V. 382 447

Mart, A. J. 246 252 334

Martin, A. J. 296 303 342

Martin, S. 48

Mason, E. A. 380 446

Massines, F. 48 135

Mathys, E. F. 154 164 166 168

169 203

Matsubara, T. 296 297 310 312

341

Matsubara, Y. 314 343

Index Terms Links


Mattachini, F. 27 28 134

Matthäus, G. 232 233

Matthys, E. F. 155 203 288 310

338 343

Mayr, M. 228 331

McCoy, K. P. 262 335

McDonald, A. 189

McKelliget, J. 427 449

Medvedev, D. 28 134

Meek, J. M. 9 10 49 134

135

Megaridis, C. M. 160 204

Meguernes, K. 100 139

Mehdizadeh, N. Z. 146 177 179 181

186 203 320

Meillot, E. 272 337 384

Meirlaen, J. 239 332

Meissl, W. 60 66 137

Menard, W. A. 378 379 446

Menart, J. A. 372 373 386 387

388 389 390 392

437

Mentel, J. 385 435 439 440

441 442 443 447

450

Meritt, B. T. 28 31 44 134

135

Mesyats, G. A. 439 449

Metallurgical, J. 240 241 332

Index Terms Links


Mexmain, J. M. 378 379 446

Mildren, R. 108

Mingze, Lu. 54 55 136

Minoo, H. 355 446

Miralaï, S. F. 56 136

Mishin, J. 264 267 336

Mitsui, T. 50 135

Miyatake, O. 160 204

Mjolsness R. C. 156

Monette, E. 56 136

Monin, V. 241 333

Montavon, G. 187 204 205 292

296 304 306 313

314 339 341 342

Moon, S. Y. 60 71 137

Moore, D. W. 260 334

Moore, R. R. 45

Moravej, M. 61 137

Moreau, C. 189 193 195 204

218 232 233 264

265 266 267 275

276 281 284 285

286 287 289 290

304 305 306 320

330 332 335 336

337 338 339 344

Moreira, K. R. 108 111 141

Morishita, T. 224 233 234

Moriwaki, T. 49 135

Index Terms Links


Morris, J. C. 386 387 388

Morrow, R. 435 441 449

Moselhy, M. 90 91 138

Moskalev, B. I. 83

Mosso, S. J. 159

Mostaghimi, J. 143 144 146 147

152 153 154 155

156 157 163 165

167 168 170 171

177 179 181 186

196 198 202 203

204 275 278 279

289 292 293 294

296 297 304 306

307 310 320 321

337 339 340 341

342 344

Mulheran, P. A. 198 204

Müller, M. 224 231 232

Mundo, C. 308 342

Murphy, A. B. 221 330 374 375

376 378 379 382

384 391 402 404

405 446 447

Musiol, K. 100 139

Mutaf-Yardimci, O. 1 97 99 100

139 142

Index Terms Links


N

Nadeau, F. 265 336

Naidis, G. 35 135

Nam, G. 28 135

Nandelstaedt, D. 442 450

Napartovich, A. 74 103 138

Nardou, F. 311 316 320 343

344

Nealsonm, K. H. 115 117 118 124

142

Neiser, R. 239 263 264 265

267 306 307 313

318 335 342 343

Nemchinsky, V. A. 431 449

Nester, S. 100 142

Nestor, O. H. 437 449

Neumann, W. 439 449

Ng, H. W. 321 344

Nichols, B. D. 157 204

Nicoll, A. R. 232 233 332

Nieser, R. A. 198 204

Nishigana, N. E. 289 339

Nishioka, E. 296 297 300 310

312 315 341

Nishiyama, T. 296 297 300 315

341

Nogi, K. 296 298 341

Index Terms Links


Nomiyama, H. 114 117 118 124

142

Notomi, A. 294 296 340

Nowling, G. R. 61 137

Nylen, P. 275 321 337 344

O

Oberkampf, W. L. 264 267 335

Ogino, K. 296 298 341

O’ Hern, T. J. 264 267 335

Ohgitani, I. 143 296 301 309

310 314 342 343

Ohgiyama, T. 113 114 117 118

124 141

Ohmori, A. 145 155 296 311

341 343

Ohshima, T. 113 117 118 124

142

Ohwatari, M. 167 296 299 310

341

Okada, M. 230

Okane, I. 186 284 300

Okazaki, S. 49 93 135 139

Okwatari, M. 283 338

Oo, N. 296 304 342

Opalinska, T. 49 135

O’Rourke, P. J. 275 337

Otooni, M. 193 204

Index Terms Links


P

Padet, J. P. 269

Paik, S. 419 448

Panelon, J. 61 137

Panevin, I. G. 378 379 446

Parameswaran, S. 53 136

Parizet, M. J. 397 399 400 401

403 404 447

Park, J. H. 60 61 137 246

Park, M. 28 135

Park, S.-J. 87 89 90 138

Parker, R. A. 266 268 336

Pasandideh-Fard, M. 146 152 153 154

155 156 167 179

181 186 196 198

203 204 289 292

293 294 304 339

340 342

Pashkin, S. V. 103 140

Patankar, S. V. 157 203

Pateyron, B. 218 223 225 241

245 247 248 249

250 272 307 308

309 310 313 314

330 331 333 334

337 342

Paulson, R. F. 431 449

Pawlowski, L. 205 315 329

Index Terms Links


Pech, J. 145 314 315 316

317 343

Peeters, A. G. 402 404 405 447

Peeters, P. 58 59 136

Pegot, E. B. 417

Pellerin, S. 100 139

Pemen, A. J. M. 112 141

Penetrante, B. M. 28 31 35 44

134 135

Pentecost, C. G. 241

Peretts, L. N. 431 449

Pershin, L. 294 296 297 340

Pershin, V. 144 146 167 168

170 186 196 202

204 289 292 293

294 339 340

Peskin, C. S. 160 204

Peterkin, F. E. 85 111 138 141

Peters, J. 444 450

Peters, T. 349 446

Pfender, E. 147 203 208 209

210 211 212 214

218 220 240 241

244 246 248 249

251 275 329 330

332 333 334 337

345 348 353 354

357 358 359 360

361 362 363 364

365 366 367 368

Index Terms Links


Pfender, E. (Cont.)

369 370 374 375

376 377 378 380

381 382 383 384

389 390 391 392

393 394 395 396

397 399 400 406

407 408 409 410

411 415 419 420

424 429 430 431

432 433 435 437

440 441 442 443

444 446 448 449

Pitz, W. J. 28 44 134 135

Planche, M. P. 211 216 217 218

223 225 241 329

330 331

Platts, D. 31

Poirier, D. R. 153 180 181 203

Poirier, E. J. 153 180 181 203

Poirier, T. 245 334

Poladian, L. 420 448

Poo, J. Y. 160 204

Potapkin, B. V. 103 140

Poulain, M. 323

Poulikakos, D. 153 154 160 203

204 310 343

Pouliot, L. 265 336

Powell, I. 189 204

Index Terms Links


Prakash, S. 260 334

Prasad, V. 241 288 333 338

Prehm B. Droessler, J. 264 267 336

Proskurovsky, D. I. 439 449

Proulx, P. 147 203 240 246

255 256 257 278

279 280 333 334

337

Ptssinski, K. J. 112 141

Pu, Y. K. 28 134

Puckett, E. G. 159 160 169 170

Purwins, H.-G. 91

Q

Qian, J. 111 141

Qiao, Y. M. 152 153 154 181

203

R

Raessi, M. 146 171 177 179

181 186 203 204

304

Raether, H. 9 134

Ragaller, K. 418 448

Rahal, A. M. 429

Ráheĺ, J. 56 57 136

Rahmane, M. 228 230 331

Index Terms Links


Raizer, Y. P. 6 9 43 45

51 62 63 66

68 69 72 83

85 135 137

Raja, L. L. 60 137

Rakness, K. L. 31 135

Ramshaw, J. D. 240 333 374 446

Rangel, R. 154 203 292 339

Rat, V. 208 226 247 249

329 331 402 404

405 447

Raynal, G. 390 392 418 447

448

Razafinimanana, M. 355

Redwitz, M. 442 443 450

Reece, R. J. 56

Rein, M. 286 289 306 308

311 313 338

Remesh, K. 321 344

Renouard-Vallet, G. 269 271

Reusch, A. 228 331

Reynolds, W. C. 427 448

Richard, F. 100 139

Richardson, J. P. 53 108 136 141

Richely, E. 397 447

Rider, W. J. 159

Rigot, D. 208 218 226 329

330 331

Index Terms Links


Robert, C. 289 339

Roberts, K. A. 282 337

Robertson, G. D. 50 135

Robinson, J. W. 115 117 118 124

142

Robinson, K. S. 36 53 57 91

135 136

Rodi, W. 427 448

Rodriguez, R. 241

Roemer, T. J. 198 204 264 267

306 307 313 335

342

Rosocha, L. A. 31

Ross, D. 232 233 332

Roth, J. R. 22 29 52 55

56 82 83 134

Roumellotis, G. 420 448

Roumilhac, P. 216 219 221 222

227 229 234 330

Rudman, M. 157 204

Rund, J. C. 246

Rusanov, V. 28 134

S

Safai, S. 296 310 341

Sahoo, P. 230 331

Sakai, O. 92 93 139

Sakakibara, N. 294 296 340

Sakuta, T. 264 267 335

Index Terms Links


Sampath, S. 145 187 195 203

204 241 284 285

286 289 290 296

297 306 310 313

333 338 339 341

342

Sanchez, D. 314 343

Sanders, N. 353 354 437 446

449

Sani, E. 27 28 134

Saotome, Y. 314 343

Sato, M. 106 108 111 113

114 117 118 119

124 140 141 142

Saveliev, A. V. 1 29 97 99

100 135 139 140

142

Schade, E. 385 447

Schaeffer, J. F. 427 449

Schein, J. 218 330

Schlump, W. 231 331

Schmidt, H. P. 418 448

Schmidt, J. 110 111 119 141

Schmidt, M. 74 93 138

Schoenbach, K. H. 85 87 90 91

111 114 117 118

124 138 141 142

Schram, P. P. J. M. 402 404 405 447

Schütz, M. 224 231 232

Schütze, A. 60 137

Index Terms Links


Schwabe, A. J. 117 142

Seals, R. D. 262 335

Sears, F. W. 361 362 373

Seiman, K. 264 267 336

Selwyn, G. S. 60 61 71 137

Sember, V. 212 235

Sevastyanenko, V. G. 418

Seyed, A. 260 261 262 312

314 343

Shakeri, S. 175 204 292 294

340

Shamamian, V. 115 117 118 124

142

Sharma, M. P. 278 337

Shaw, K. G. 262 335

Sherman, D. M. 56 57 136

Shi, J. J. 60 64 137

Shi, W. 85 87 90 91

138

Shiba, M. 289 339

Shiiba, M. 143

Shiiba, Y. 160 204

Shiryaevsky, V. 28 134

Shneider, M. N. 62 63 66 68

69 137

Sieber, K. D. 36 53 57 91

135 136

Siebold, D. 228 331

Siegmann, S. D. 314 343

Siemens, W. P. 31 36 135

Index Terms Links


Sikka, V. K. 262 335

Silakov, V. P. 109 112 141

Simek, M. 110 111 119 141

Simonchik, L. V. 74 138

Simonin, O. 355 419 446 448

Sirignano, W. A. 260 334

Skalny, J. D. 113 117 118 124

142

Slottow, H. G. 82 83 138

Smith, J. L. 353 446

Smith, M. F. 230 264 267 313

318 331 335 343

Smurnov, I. 266 336

Snyder, F. 125 126 127 128

129 130 131 132

Snyder, H. 61 137

Sobacchi, M. 29 100 135 140

Sobolev, V. V. 246 252 288 296

303 306 311 334

338 342

Sodeoka, S. 231 331

Sohn, Y. H. 205 325 344

Somers, E. B. 115

Sommerfeld, M. 308 342

Soucy, G. 220 221 228 230

330 331

Soulestin, B. 317

Spalding, D. B. 427 448

Spence, P. D. 55

Index Terms Links


Spores, R. 212 214 218 241

330

Staack, D. 74 75 76 77

78 79 80 102

103 138

Stachowicz, M. 218 330

Stange, S. 31

Stevefelt, J. 100 139

Steven Ed, B. 60 71

Stine, H. A. 415 416

Stock, D. E. 278 337

Stoffels, E. 93 94

Stollenwerk, L. 91

Störi, H. 60 66 137

Stout, K. J. 296 300 342

Stover, D. 231 331

Stow, C. D. 308 342

Streibl, T. 264 267 336

Suganuma, K. 296 298 342

Sugiarto, A. T. 113 117 118 124

142

Sun, B. 106 108 113 117

118 124 140 141

142

Sun, D. W. 288 338

Sun, H. J. 115 117 118 124

142

Sunka, P. 106 110 111 117

118 119 124 140

141

Index Terms Links


Suzuki, M. 231 331

Swank, W. D. 222 263 264 266

267 330 335

Swank, W. P. 272 336

Swindeman, C. J. 262 335

Syed, A. A. 260 262 335

Szarko, V. 125 126 127 128

129 130 131 132

Szekely, J. 154 164 166 168

169 203 240 241

292 332 339 427

449

Szymanski, A. 49 135

T

Tachibana, K. 92 93 139

Taktakishvili, M. I. 109 112 141

Tanaka, Y. 296 298 341

Tani, K. 311 343

Taura, R. 94 139

Temchin, S. M. 109 112 141

Tessnow, T. 85 138

Themelis, N. J. 254 257 258 259

260 264 265 267

268 269 270 271

272 279 296 298

334 335 336 341

Tidman, A. 15 134

Tikkanen, J. 279 337

Index Terms Links


Tixier, C. 307 317 319 340

Tochikubo, F. 49

Tomiguchi, A. 314 343

Torrey M. D. 156

Torshin, Y. 117 142

Trapaga, G. 154 164 166 168

169 203 240 241

292 332 339

Trebbi, G. 27 28 134

Trelles, J. P. 419 420 421 448

Tristant, P. 307 315 317 319

340 344

Trogolo, J. A. 262 335

Trolliard, G. 317

Tropea, C. 308 342

Trushkin, N. 74 103 138

Tsukuda, H. 294 296 340

Tu, V. J. 61 137

Tuma, D. T. 397 447

Turcotte, D. L. 361 362 373

Turkdoyan, E. T. 257 258 334

Tzeng, Y. 35 135

U

Uehara, T. 30 135

Ueno, K. 231 331

Underwood, E. E. 323 344

Ushio, M. 427 449

Index Terms Links


V

Vakar, A. K. 103 140

Valencia, J. J. 154 164 166 168

169 203

Valette, S. 314 316 317 343

Van de Sanden, M. C. M. 58 59 136 402

404 405 447

Van der Mullen, J. A. M. 402 404 405 447

Vanderslice, J. T. 380 446

Vangheluwe, H. 239 332

Vanhooren, H. 239 332

Vannier, C. 49 135

Vanrolleghem, P. A. 239 332

Vardelle, A. 145 202 211 212

223 224 240 241

243 244 245 246

249 251 252 254

257 258 259 260

263 264 265 267

268 269 270 271

272 274 275 278

279 280 281 282

284 285 286 287

288 289 290 291

293 294 296 297

298 300 304 305

306 310 311 314

315 316 318 320

Index Terms Links


Vardelle, A. (Cont.)

321 329 330 333

334 335 336 337

338 339 340 341

343

Vardelle, C. 419 420 448

Vardelle, M. 145 189 202 204

211 212 220 221

243 245 252 254

257 258 259 263

264 265 266 267

268 269 270 271

272 273 274 278

279 280 281 282

284 285 286 287

288 289 290 291

293 294 296 297

298 300 301 304

305 306 307 308

309 310 311 313

314 315 316 318

320 329 330 334

335 336 337 338

339 340 341 342

344 427 449

Varisto, P. 266 336

Vasconcelos, D. C. L. 323 344

Vasconcelos, W. L. 323 344

Vasilyak, L. M. 51 135

Index Terms Links


Vattulainen, J. 266 336

Vaudreuil, G. 265 336

Velikhov, E. P. 103 140

Vergne, P. J. 418 448

Verhappen, R. 85 138

Vesely, E. 234 332

Vesteghem, H. 245 334

Vitello, P. A. 35 135

Vitruk, P. P. 63 65 67 68

70 137

Vogtlin, G. E. 28 31 44 134

135

Voller, V. 163 204

Voss, K. E. 28 44 134 135

de Vries, H. 58 59 136

W

Wallac, H. 115 117 118 124

142

Wan, C. Z. 28 44 134 135

Wan, Y. 145 195 203 241

288 296 297 333

338 342

Wang, G. X. 155 203 288 289

310 338 339 343

Wang, H. P. 246

Wang, S. P. 288 338

Wang, W. B. 145 296 311 341

343

Index Terms Links


Wang, X. 54 55 136 145

203 296 342

Ward, B. 108

Watanabe, T. 49 155 203

Watson, V. R. 415 416 417

Weber, J. E. 247 334

Wei, Z. 108 141

Weissman, M. 230 331

Weissman, S. 380 446

Wertheimer, M. R. 56 136

Wester, R. 67 137

Westhoff, R. 240 241 332

White, A. D. 83 84 85 87

89 138

Wigren, J. 218 330

Wilden, J. 264

Williamson, R. L. 240 333

Winn, W. 14 134

Wittmann, K. 211 220 226 228

230 329 331

Wolfe, R. L. 107 108 141

Wong, A. C. L. 115

Woo, M. 28 135

Worthington, A. M. 156 203

Woskov, P. P. 28 134

Wu Xin-Can, 246 334

X

Xiaohui, Y. 60 137

Xie, R. 296 304 342

Index Terms Links


Xu Dong-Yan 246 334

Xu, J. 288 338

Xu, X. P. 35 135

Xue, M. 321

Xue, S. 240 333

Y

Yamada, H. 314 343

Yamamoto, T. 160 204

Yamashita, H. 117 142

Yamazawa, K. 117 142

Yang, W. J. 155 203 296 310

341

Yang, X. 61 137

Yasui, T. 143 289 296 301

310 314 339 342

343

Yatsenko, N. A. 62 63 66 68

69 137

Yelk, E. 125 126 127 128

129 130 131 132

Yematsu, S. 314 343

Yikang, Pu. 54 55 136

Yin, F. 444 450

Yokoyama, T. 295

Yoshida T. T. 239

Young, R. 241 333 430 449

Youngs, D. L. 157 204

Yu, S. C. M. 321 344

Index Terms Links


Z

Zaat, J. H. 230

Zadiraka, Yu. 112 141

Zadiraka, Y. V. 109 112 141

Zahn, M. 117 142

Zahrai, S. 419 448

Zanchetta, A. 316 320 344

Zang, H. 288 292 338 340

Zanolini, J. 125 126 127 128

129 130 131 132

Zanstra, G. J. 112 141

Zemach, C. 159 160 204

Zgirouski, S. M. 74 138

Zhang, H. 145 203 260 265

279 296 335 336

342

Zhang, J. 325 344

Zhang, T. 240 241 333

Zhao, Z. 153 154 160 203

204

Zheng, L. L. 145 203

Zhivotov, V. K. 103 140

Zhou, X. 223 330 440 441

442 443 444 450

Zhukov, M. F. 219 330

Zimmerman, S. 264 267 336


SUBJECT INDEX

Index Terms Links

Note: Page numbers in italic type indicate figures and tables

A

active corona volume 20

adhesion of coatings, in plasma spraying 315

chemical reaction 315

diffusion 316

mechanical interlocking 316

AJD (anode jet dominated) region, of thermal

arcs 354

α and γ discharges, RF 66

α–γ transition, RF discharges 69

amorphous steel splats 195

anode erosion 217

anode heat transfer, in thermal arcs 431

constricted attachment 434 438

diffuse attachment 434 438

diffusion fluxes 432

electron density derivation 432

electron temperature and heavy-particle

temperature distribution in 433 434

models 431

potential distribution in 435

streamlines in 434

Index Terms Links

his page has been reformatted by Knovel to provide easier navigation.

anode region, of thermal arcs 352

charge carrier generation in 353

by field ionization (F-ionization) 353

by thermal ionization (T-ionization) 353

APG (atmospheric pressure glow discharges) 47 52

in argon 80

atmospheric pressure plasma jet (APPJ) 60

see also separate entry

electronically stabilized APG 58

noble gases in atmospheric glows 72

one atmosphere uniform glow discharge

plasma (OAUGDP) 55


resistive barrier discharge (RBD) 53

APPJ (atmospheric pressure plasma jet) 60

discharge conditions 70

nature of 60

stability 61

APS (atmospheric pressure spray) 148

arc column 349

ionization in 349

arc discharges modeling

see also thermal arcs

early models 347

heat transfer processes and 345

in water 117

arc root instabilities 213

arc fluctuation modes 215

engulfment process in 214

mixed arc fluctuation modes 215

Index Terms Links


arc root instabilities (Cont.)

restrike arc fluctuation mode 215 216

steady arc fluctuation mode 215

takeover arc fluctuation mode 215 216

atmospheric and higher pressure, in plasma

spray torches 231

axial III plasma-spray torch 233

AXI-symmetric impact 151

B

ballast water treatment 109

Barré de Saint Venant-type equation 226

Biot number 248 255

Boltzmann equation 69 356

Born-Oppenheimer approximation 360

boundary layer 457

boundary layer thickness evaluation 459

dynamic boundary layer 458

equations 468

thermal boundary layer 458

bubble process, of plasma discharge in water 117

C

CA (cellular automata) scheme 37

capillary jet mode 93

cathode heat transfer, in thermal arcs 439

2D and 3D models of 442

emission mechanism 439

energy fluxes in 440

Index Terms Links


cathode heat transfer, in thermal arcs (Cont.)

in free-burning argon arc 443

modeling 439

thermionic cathode modeling 439

cathode region, of thermal arcs 349

cathode jets, sources 350

CCP (capacityvely coupled plasma) discharges 62

chemical reaction, in adhesion of coatings 315

chemical reactions, in plasma spraying modeling 257

SHS reaction 262

with the particle 258

convection-controlled reactions 260

diffusion-controlled reactions 258

reactions occurring between condensed

phases 262

with the vapor surrounding a particle 257

chlorination, in water treatment 105

circuit breakers 346

CJD(cathode jet dominated) region, of

thermal arcs 353 354

CM-DBDs (coaxial-hollow microw dielectric

barrier discharges) 92

coating formation, in plasma spraying 279

adhesion of coatings 315


characteristic times 281

coating architecture 321

crystalline structures adaptation 317

deposition process, stages 281

diagnostics 282

Index Terms Links


coating formation, in plasma spraying (Cont.)

electrochemical methods 325

impacting particles 282

inclined substrates, impacts on 305

layer formation stage 281

millimeter-sized particles 283

particle flattening 311


pore network in 321

see also pore network

rough orthogonal substrates 303


single particle, experimental set-up 284

single particle, imaging 285

single splat formation stage 281

smooth substrates normal to impact

direction 286

splashing 307

splat collection 282

splat layering and coating construction 320

substrate oxidation 316

techniques in 324

transition temperature when preheating the

substrate 294

see also transition temperature

condensed phases, reactions occurring 262

continuity equation 466 468

convection-controlled reactions 260

Index Terms Links


convective heat transfer

see also laminar boundary layer

boundary layer 457


convective heat transfer coefficient as

function of medium and flow parameters 470

definition 452

energy conservation law at the solid wall

interface 453

equations for 464

full energy of the oncoming flow 461

see also general concepts of 451

heat transfer coefficient calculation 472

heat transfer coefficient 453

Newton’s formula 451

similarity criteria (numbers) 454

see also Nusselt numbers; Peklet numbers;

Prandtl numbers; Reynolds numbers

similarity theory 457

sphere, cylinder and plate, heat transfer

formulas for 476

temperature and enthalpy heat concepts 482

thermal boundary layer thickness 469

cooling velocity 288

corona/corona discharge 17

active corona volume 20

corona in air, ignition criterion for 19

current-voltage characteristics 22

electric field in, space charge influence 21

negative and positive coronas 18

Index Terms Links


corona/corona discharge (Cont.)

packed-bed corona discharge 45

power released in 23

pulsed corona discharge 24


spray corona discharges 30

wet corona discharges 29

CPE (capillary plasma electrode) discharge 93

critical electric field, of Townsend breakdown 6

crystalline structures adaptation, in plasma spraying 317

CSF (continuum surface force ) model 159

CTE (coefficient of thermal expansion) 260

current-voltage characteristics of corona discharge 22

cylinder, heat transfer formulas for 478

correlations for 479

cylinder target in cross flow 478

D

Delton’s law 356

Damkler number Dk or the inverse quantity 487

DBD (dielectric barrier dicharge) 2 30

atmospheric pressure glow DBD 47

DBD microdischarges 32

see also microdischarge

interaction characteristics 33

properties 34

ferroelectric discharges 49

filamentary mode discharge 47

filaments in 34

Index Terms Links


DBD (dielectric barrier dicharge) (Cont.)

for pollution control 31

homogeneous mode discharge 47

industrial applications 82

properties of 31

surface discharges 42

DC direct current) plasmas

direct current (DC) plasma gun 148

modeling 241

DC (direct current) stick-type cathode 212

anode erosion 217

arc root instabilities 213


Ar-H2 plasma gas 221

Ar-He plasma gas 221

characteristics 224

DC stick-type cathode plasma torch 213

plasma–gas mixture injection mode 219

torch characteristics 218

decontamination in water

cryptosporidium 107

E. coli 107

UV radiation treatment in 107

D-factor 492 517

diffusion coefficients

ambipolar diffusion 373

for two-temperature plasmas 402

of thermal arcs 373

self-diffusion 373

Index Terms Links


diffusion

in adhesion of coatings 316

diffusion-controlled reactions 258

direct coating model 196

discharge lamps 346

Drexel Plasma Institute, plasma water

treatment at 124

elongated spark configuration 130

magnetic gliding arc configuration 128

point-to-plane plasma discharge system 125

droplet impact on plasma spray coating

droplet impact apparatus 178

droplet impact velocity 182

laboratory experiments 173

large droplets 173

small droplets 175

substrate material effect 183

transition temperature model 179

droplet impact, spread and solidification in

plasma spray coating process 150

AXI-symmetric impact 151

molten droplets impact 155

n-cetane impact 155

n-eicosane impact 155

splashing and break-up 155

droplet solidification rate 146

droplet–substrate surface wetting 298

DS (degree of splashing) 187

dynamic boundary layer 458

Index Terms Links


E

Eckert number 312

Eggert-Saha equation 356 358

Einstein relation 11

electric arcs

applications 346

in circuit breakers 346

in discharge lamps 346

electric breakdown

of gases, Townsend mechanism of 4

in water 120

electrical conductivity

thermal arcs 375 377

of two-temperature plasmas 406

electrical discharges production in water 109

electrode geometries 110

needle-to-plane geometry 110

point-to-plane geometry 110

electrochemical method, in characterizing

coating formation 325

electron avalanches 10

avalanche-to-streamer transition 36

electronic process, of

plasma discharge in water 117

electronically stabilized APG 58

electroporation, in water treatment 106

Elenbaas–Heller model, of thermal arcs 412

elongated spark configuration 130

Index Terms Links


emission mechanism, in cathode heat transfer 439

energy conservation law at the solid wall

interface 453

engulfment process 214

ensemble measurement techniques 263

ensemble of particles, in plasma spray

modeling 267

particle injection 267

see also injection

particle distribution within plasma jet 272


enthalpy heat concept, in convective heat

transfer in plasma 482

dissociation energy 484

energy of excited atoms and excited ions 484

energy of rotational ER and oscillational

motion of molecules 484

ionization energy 484

kinetic energy 484

enthalpy, of thermal arcs 363

of argon/helium mixtures 368

of argon/hydrogen mixtures 368

of dry air 369

enthalpy, two-temperature plasmas 399

Ar/H2 mixture 400

hydrogen plasma 400

nitrogen plasma 401

Index Terms Links


entropy

of dry air 370

of thermal arcs 367

two-temperature plasmas 401

equilibrium properties, thermal arcs 355

plasma composition 356

thermodynamic properties 359


transport properties 370

F

fast-flow discharges 2

ferroelectric discharges 49

FHC (‘fused’ hollow cathode) source 90

Fick’s law 370

F-ionization (field ionization) 353

flashing corona 25

flattening

analytical models 286

flattening splashing 309

and solidification 292

and splashing phenomena 293

fluid flow

and free surface reconstruction 156

solidification effect on 162

Fourier’s law 371 458 460

friction 459

frozen boundary layer 487

Index Terms Links


G

GD (gliding dischages) and fast flow

discharges 96

in a cylindrical reactor 101

in the counter-current vortex reactor 102

GA discharge, stages 100

GD in air 98

GDT, advantages 103

gliding discharge in tornado (GDT) 103

Gibbs function 359

of thermal arcs 367

of two-temperature plasmas 401

H

HCD (hollow cathode discharge) 82

enhanced ion collection 88

HCD effects 87

metal ions influence 89

opposite cathode influence 88

pendulum motion of “beam” electrons 87

secondary electron emission coefficient γ 88

heat propagation 255

heat transfer coefficient calculation 472

boundary layer theory methods 474

boundary layer thickness concept in 473

thickness of impulse loss 474

thickness of mass extrusion 474

with flow parameters 459

Index Terms Links


heat transfer

equation 466 468

in plasma spraying 254

helium discharges 2

Helmholtz function 359

of thermal arcs 367


Hirt–Nichols algorithm 157

HVOF (high-velocity oxy-fuel) 148

hybrid plasma torch 235

I

ICP (inductively coupled plasma) discharges 62

ignition criteria, for corona in air 19

impact splashing 307

inclined substrates, impacts on 305

industrial sensors 265

ACCURASPRAY 265

DPV 2000 sensor 265

spray and deposit control (SDC) 266

spray watch commercial sensor 266

inertial force 459

in-flight particle measurement, plasma

spraying 262

industrial sensors 265

particle fluxes and trajectories 264

particle vaporization 264

transient measurements 266

velocity, diameter and temperature 263

Index Terms Links


in-flight particles interaction

heat transfers, basic equations for 247

momentum transfer, equations related to 246

with plasma jet 246

with single particle, modeling 246

injection, particle, in plasma spray modeling 267

curved injector 271

double-flow injector 271

powder particle injectors 267

see also powder injectors

injection, plasma–gas mixture 219

axial injection 219

radial injection 219

selection 219

vortex injection 219

in-line filters, in water treatment 105

internal energy, of thermal arcs 363

J

Joule heating 122

K

k-ε model 241

L

Lagrange scheme 269

lamella solidification 286

Index Terms Links


laminar boundary layer

boundary layer equations 468

continuity equation 466 468

equations 465

heat transfer equation 466 468

motion equation 468

for plane stationary motion of real

non-compressible medium 465

laminar flow in non-LTE arcs 422

Laplace equation 157

large droplets 173

large gaps, Townsend

breakdown mechanism in 7

laser directed spark discharges 51

photoionization 51

LCD (liquid crystal displays) 80

LDA (laser Dopper anemometry) 264

leader breakdown mechanism 16

LES (large-eddy simulation) prediction,

of turbulent flow 427

Lichtenberg figures 45

LTE (local thermodynamic equilibrium) 207 347

LTE thermal arcs models 412

Lorentz force 128

low discharge power 2

LPPS (low pressure plasma spray) 148

LSV (laser strobe

control vision) system 267

Index Terms Links


M

magnetic gliding arc configuration 128

mathematical model of impact 156

continuum surface force (CSF) model 159

effect of roughness 171

fluid flow and free surface reconstruction 156

Hirt–Nichols algorithm 157

numerical procedure 163

RIPPLE algorithm 156

solidification and heat transfer 161

splat formation in thermal spray,

simulation 163

thermal contact resistance 162

volume-tracking algorithm 156 159

Youngs’ equivalent 2D method 157

Maxwell equation 22

mechanical interlocking, in adhesion of coatings 316

Meek’s breakdown criterion 10 13 18 38

47

MHCD (micro hollow cathode discharge) 82

geometries 85

micro DBDS for plasma TV 80

microarc discharge 92

microdischarge interaction 35

micro-discharges 3 32

remnants 34

micrometer-sized particles, in plasma spraying 283

Index Terms Links


microplasmas 73

micro glow discharge 74

micro DBDS for plasma TV 80

microstrip resonator 95

millimeter-sized particles, in plasma spraying 283

mixing length hypothesis, of turbulent flow 427

modeling of thermal arcs 412

3D time dependant modeling approach 421

Elenbaas–Heller model 412

LTE arc models, developments of 418

non-LTE arcs models for 420


simple models based on LTE 412

Stine–Watson model 415

Two-dimensional steady state model 419

two-temperature model 424

modeling, plasma spraying 239

2-D models 245

3-D models 241

chemical reactions 257

corrections specific to plasmas 251

heat propagation 255

heat transfer 254

momentum transfer 251

radiation emitted by the metallic vapor 257

vapor buffer effect 255

DC plasmas 241

ensemble of particles 267

Index Terms Links


modeling, plasma spraying (Cont.)

in-flight particle measurement 262


in-flight particles interaction with the

plasma jet 246

see also in-flight particles interaction

RF plasma models 240

molten droplets 155 177

molybdenum splats 192 193

molybdenum, plasma sprayed 145

momentum transfer, in plasma spraying 251

Monte-Carlo simulation 37 198

motion equation 468

multiple time scale turbulence model 427

N

nano-second pulse power supplies,

pulsed corona discharges sustained by 27

Navier–Stokes equations 160 245 466

n-cetane 155

n-eicosane 155

Newton’s formula 451

nickel sprayed plasma coating 144

noble gases in atmospheric glows 72

non-equilibrium properties, of thermal arcs 391

number densities of an Ar/H2 mixture 396

number densities of Ar and Ar+ 395

plasma composition of

a two-temperature plasma 394

Index Terms Links


non-equilibrium properties,

of thermal arcs (Cont.)

two-temperature plasmas,


see also two-temperature plasmas

non-LTE arcs models for thermal arcs 420

electron energy equation 423

global momentum equation 425

heavy-particle energy equation 423

laminar flow in 422

mass conservation equation 422 425

momentum equations 422

turbulent flow in 426

see also turbulence

non-thermal atmospheric pressure plasma 1

atmospheric pressure glows (APG) 52


chemical applications 3

corona discharge 17


dielectric-barrier discharge 30


gliding discharges (GD)and fast flow

discharges 96

leader breakdown mechanism 16

microplasmas 73

non-equilibrium plasma,

approaches to overcome 2

plasma discharges in water 104


Index Terms Links


non-equilibrium plasma,

approaches to overcome (Cont.)

production 3

spark breakdown mechanism 9


spark discharges 50


stabilization at high pressures 1

streamer breakdown mechanism 14

Townsend mechanisms 4


Nusselt number 248 251 428 454

459 461 471 472

475

O

OAUGDP (one atmosphere uniform glow

discharge plasma) 55

discharge uniformity formation 58

experimental set-up for 57

initial state of 56

key feature of 56

key question about 56

OFHP (oxygen-free high purity) 212

Ohm’s law 371 431

overshooting effect 98

ozonation, in water treatment 105 108

ozone injection, in plasma water treatment 104

Index Terms Links


P

P-1 plasma torch 494


turbulence measurements at 497

packed-bed corona discharge 45

partial discharge, of plasma discharge in water 117

particle distribution within plasma jet 272

see also ensemble of particles

alumina particle distribution 273

measurements 272

modeling 275

particle-source-in-cell model (PSI-Cell) 278

zirconia particle distribution 274

particle flattening, parameters controlling 311

particle temperature 311

substrate 313

see also substrate velocity 312

particle vaporization 264

partition functions, thermal arcs 359

Paschen curve 7 120

PDA (phase Doppler anemometry) 263

PDF (probability density function) 199

PDPs (plasma display panels) 80

alternative current coplanar (ACC)

sustained structure 81

alternative current matrix (ACM) sustained

structure 81

color plasma displays 81

monochrome displays 81

Index Terms Links


Peclet number 287 310 463 470

Peek formula 19

photoionization 51

pinch effect 351

Plank’s law 264

plasma discharges in water 104

see also water treatment

approaches in mechanism of 117

different plasma discharges for water

treatment, comparison 132

electrohydraulic discharge reactor 115

mechanism 116

ozone injection 104

plasma water treatment, need for 104

point-to-plane electrode configuration 125

ultraviolet radiation 104

validation and characterization 125

plasma jets

see also convective heat transfer

assessment and generalization 560

boundary layer equation 489

boundary layer 487

correction proposal 519

in-flight particles interaction with 246

heat and mass transfer in 451

heat transfer in plasma, experimental studies 492

Nu-criterial form 505



Index Terms Links


plasma jets (Cont.)


similarity criteria in 484


theoretical formulas for 490

plasma needle 93 94

plasma particle impact, in plasma spray coating 189

plasma spray coating processes

deposition zone 147

droplet impact on 173

see also droplet impact

droplet impact, spread and solidification 150


heat transfer in 143

mathematical model of impact 156


nickel sprayed plasma coating 144 201

particle-heating zone 147

plasma spray sources 148

direct current (DC)plasma gun 148

radio-frequency inductively coupled

plasma (RF-ICP) 148

wire-arc spraying 150

plasma sprayed molybdenum 145

plasma-generation zone 147

regions/zones of 147

simulating coating formation 196


thermal spray splats 185


Index Terms Links


plasma spray torches 207

axial III plasma-spray torch 233

DC plasma-spraying process 207

direct current stick-type cathode 212


electrical conductivity and 208

hybrid plasma torch 235

nozzle geometry in 228

plasma jet characterization 211

plasma jet momentum 210

plasma jet, turbulence around 212

plazjet torch 233

rotating mini-torches 232 233

soft vacuum or controlled atmosphere 230

Triplex I and IITM systems 231

velocity and temperature distributions 223

plasma spraying 205

see also individual entries

characteristics times in 282

coating formation 279


from plasma generation to coating structure 205

modeling 239

see also modeling

RF plasma spray torches 236


sub-systems 207

plasma spray torches 207


Index Terms Links


plasma water treatment 111

at Drexel plasma institute 124

see also Drexel plasma institute

streamer discharges 114

plasma-forming gas 209

primary, argon as 209

secondary, hydrogen as 209

plasmas

non-thermal atmospheric pressure plasma 1


plasma composition, in thermal arcs 356

plasma-enhanced chemical vapor

deposition (PECAV) coating 317

plasma TV, micro DBDS for 80

temperatures and pressure describing 392

plate, heat transfer formulas for 476

flat target with gas flow or a jet 480

plazjet plasma-spray torch 233

point-to-plane plasma discharge system 125

pore network of coating 321

metallographic observations and image

analysis 323

physical methods 323

powder injectors 267

curved geometry 268

double-flow geometry 268

geometries of 268

k-ε turbulence model 269

pneumatic transport of powder 269

straight geometry 268

Index Terms Links


power released in

continuous corona discharge 23

Prandlt number 167 248 428 463

470 471 517

definition 463

pulsed arc, characteristics of 118

pulsed corona discharge 24

applications 29

characteristics of 118

configurations of 28

corona ignition delay 25

flashing corona 25

sustained by nano-second pulse power supplies 27

trichel pulses 26

in wire-cylinder configuration with preheating 29

pulsed electric field technology, in water treatment 105

pulsed spark, characteristics of 119

Pyrex ® sheets 56

Q

quasi-self-sustained streamers 14

q-value 502

R

radiation properties, thermal arcs

at high temperatures 385

of high-pressure argon arcs 384

prediction 386

temperature and 385

Index Terms Links


radiative transport

coefficients for two-temperature plasmas 408

of thermal arcs 382

Rayleigh–Taylor instabilities 165 169 292 308

RBD (resistive barrier dishcharge) 53

equivalent circuit 54

reference temperature 501

remnants 34

Re-normalization group k–ε 241

Reynolds number (Re) 70 151 175 177

247 269 287 306

310 428 454 460

461 470 471 517

RF discharges

α and γ discharges 66

key features of 62

RF CCP discharge, space-time structure of 63

typical configurations of 62

RF-ICP (radio frequency inductively

coupled plasma) 143 148

disadvantages 149

RF plasma spray torches 236

conventional torches 236

main characteristics 237

RF plasma models 240

skin depth in 236

supersonic torches 239

TEKNA ceramic-wall

induction plasma torch 236 237

Index Terms Links


Richardson–Dushman equation 441

RIPPLE algorithm 156

rotating mini plasma-spray torches 232 233

rough orthogonal substrates

models 303

measurements 304

roughness effect, in plasma

spray coating processes 171

S

Saha equations 395 420

Saint Elmo’s fire 17

Schottky effect 441

secondary electron emission coefficient γ 5

self-organization in plasma 91

short pulse discharges 2

similarity criteria in plasma 484

heat transfer coefficient α and conductivity λ 486

Nusselt number (Nu) 485 486

Prandtl number (Pr) 485

similarity theory 457

simulating coating formation, in plasma spray

coating 196

direct coating model 196

stochastic coating model 198

single-particle technique 263

single-shot photographic technique 173

skewness Sk 300

small droplets 175

Index Terms Links


smooth substrates normal to impact direction

lamella solidification 286

models and results on 286

particle flattening 286

solidification (analytical models) 288

soft vacuum, in plasma spray torches 230

solidification

analytical models 288

effect on fluid flow 162

and heat transfer 154 161

numerical models 292

splashing and 167

spark breakdown mechanism 9

streamer concept in 9

spark discharges 50

laser directed spark discharges 51

spark channel, development 50

spark gaps 113

rotating spark gap 113

triggered spark gap 113

specific heat

at constant pressure, of thermal arcs 363

for constant volume, of thermal arcs 363

specific heat flux 436


sphere, heat transfer formulas for 476 507

correlations for 477

Prandtl numbers 477

Reynolds number 476

Index Terms Links


splashing phenomena 293 307

and break-up 155

flattening splashing 309

impact splashing 307

solidification and 167

splats

see also thermal spray splats

alumina splats 170 172

amorphous steel splats 195

degree of splashing (DS) 187

formation, major parameters controlling 287

layering and coating construction 320

molybdenum splats 192 193

splat formation in thermal spray,

simulation 163

splat shape factor (S.F) 168 282

substrate temperature effect on 145

statistical analysis 145

SSD (slipping surface discharge) system 112

Stanton number 461

statistical prediction approach, of turbulent flow 427

Steenbeck’s minimum principle 244 349 419 441

Stefan number 167 181 288

Stine–Watson Model, of thermal arcs 415

stochastic coating model 198

Stoletov constant 86

streamers 13

anode-directed 13

cathode-directed 13

concept in spark breakdown 9

Index Terms Links


streamers (Cont.)

discharge system for

industrial water treatment 114

formation, Meek criterion of 13

quasi-self-sustained streamers 14

streamer breakdown mechanism 14

streamer-to-leader transition in air 17

substrate material effect

on plasma spray coating 183

substrate oxidation, in plasma spraying 316

substrate, controlling, particle flattening 313

substrate surface oxidation 314

surface topology 313

tilting 313

supersonic induction plasma torch 238 239

surface discharges 42

Lichtenberg figures 45

modes 43

T

TEKNA ceramic-wall induction plasma torch 236 237

temperature concept, in

convective heat transfer in plasma 482

temperature distribution, in plasma spray torches 223

temperature pressure 453

thermal arcs

anode region 352

arc column 349

cathode region 349

Index Terms Links


thermal arcs (Cont.)

equilibrium properties 355


general features 347

heat transfer processes in 428

see also separate entry below

high current densities feature 348

high luminosity of column feature 348

low cathode fall feature 348

modeling of 412

see also modeling of thermal arcs

non-equilibrium properties 391


thermodynamic and transport properties 355

thermal arcs, heat transfer processes in 428

anode heat transfer 431


cathode heat transfer 439


general considerations 428

thermal boundary layer 458

thickness, estimation 469

thermal conductivity of two-temperature

plasmas 406

Ar/H2 410

argon plasma 409

oxygen plasma 409

thermal conductivity, thermal arcs 376

of argon components 379

Index Terms Links


thermal contact resistance 162

thermal instabilities of plasma 67

thermal ionization (T-ionization) 353

thermal spray splats 185

plasma particle impact 189

simulation 163

three-slit mask 191

transition temperature prediction 188

wire-arc 185

thermionic cathode modeling of,

cathode heat transfer 439

thermodynamic properties, thermal arcs 359

enthalpy and specific

heat at constant pressure 363

entropy 367

Gibbs function 359 367

Helmholtz function 359 367

internal energy and specific heat for

constant volume 363

partition functions 359

3-D models, plasma spraying 241

three-slit mask 191

Townsend breakdown

critical electric field of 6

of centimeter-size gaps at atmospheric

pressure 9

electric breakdown of gases 4

mechanism in large gaps 7

mechanism 5

Index Terms Links


Townsend ionization coefficient (α and β) 5 8

calculation, numerical parameters for 6

definition 5

transient measurements, plasma spraying 266

transition temperature (Tt) 188 287

model 145 179

transition temperature in substrate preheating 294

adsorbates and condensates, desorption 296 302

droplet– substrate surface wetting 298

specific properties 297

surface roughness after treatment 300

wetting or desorption 301

transitional and specifically gliding discharges 3

transport properties of two-temperature plasmas 402

diffusion coefficients 402

transport properties, thermal arcs 370

bound–bound radiation 371

diffusion coefficients 373

electrical conductivity 375

Fick’s law 370

Fourier’s law 371

free–bound radiation 372

free–free radiation 372

Ohm’s law 371

radiation properties 384


radiative transport 382

thermal conductivity 376

viscosity 380

Index Terms Links


trichel pulses 26

Triplex I and IITM plasma-spray torch 231

turbulence/turbulent flow

characterization 427

2-D models 245

in non-LTE arcs 426

large-eddy simulation (LES) prediction of 427

mixing length hypothesis 427

models 427

multiple time scale turbulence model 427

of thermal arcs 419

prediction of 427

statistical prediction approach 427

two-equation k–ε turbulence model 427

two-equation k–ε turbulence model, of turbulent flow 427

two-temperature plasmas

electrical conductivity of 406

enthalpy 399

entropy 401

Gibbs function of two-temperature plasmas 401

Helmholtz function 401

nitrogen plasma, number densities of 398

plasma composition of 394

radiative transport coefficients 408

specific heat 399

thermal conductivity of 406


transport properties of 402


viscosity 407

Index Terms Links


U

UV (ultraviolet) radiation treatment of water 104

V

vapor buffer effect 255

velocity distribution, in plasma spray torches 223

viscosity of two-temperature plasmas 407

Ar/H2 411

argon plasma 410

oxygen plasma 411

viscosity, thermal arcs 380

of an Ar/H2 383

of dry air 383

of hydrogen 384

VOC (voltaic organic cinpound ) emissions 28

volume-tracking algorithm 156

Voronoi polyhedra analysis 40 41

VPS (vacuum plasma spray) 148

W

water treatment 105

see also plasma discharges in water

chlorination 105

conventional methods for 105

electrical discharges production in water 109

in-line filters 105

ozonation 105 108

Index Terms Links


water treatment (Cont.)

pulsed electric fields 105

using plasma discharge 106

UV lamps 105 107

Weber number 151 175 287

White-Allis similarity 85

wire-arc 185

wire-arc spraying 150

Y

Youngs’ algorithm 158

equivalent 2D method 157

Transport Phenomena in Plasma

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