1

SCALE-UP OF LIQUID-LIQUID DISPERSIONS

IN STIRRED TANKS

A thesis submitted for the degree of

Doctor of Philosophy

in the faculty of Engineering of the

University of London

by

Zia Janjua, B.Sc. (Chem. Eng.)

Department of Chemical Engineering & Chemical Technology,

Imperial College of Science and Technology,

London S.W.7.

January, 1982.

To

Than Mohammed Janjua

and

Guizar Begum

3

ABSTRACT

A study of the drop size distributions and interfacial area of heptane/

water dispersions has been made in three geometrically similar mixing

tanks of 1 : 2 : 4 size ratio for various stirring speeds. Drop size

distributions and Sauter mean drop diameters were determined by

direct photography and a new capillary sampling technique which was

developed as part of this work. Other detection techniques also using

a capillary for drop sizing, e.g. measurement of dielectric constant

and ultraviolet absorption were investigated in detail and finally a

laser light technique was adopted. This technique gave the best

detection contrast between the aqueous and organic phases. The results

obtained from direct photography and the capillary technique showed

good agreement.

The drop size distributions of all the heptane/water dispersions

measured were normal distributions. The interfaclal areas of the

dispersions were calculated from the Sauter mean drop diameter obtained

by both techniques of drop sizing. All plots of the Sauter mean drop

diameter against stirrer speed on log-log co-ordinates gave straight

lines of negative slope which ranged from -1.15 to -1.25.

Sauter mean drop diameters were determined at one and five geometrically

similar positions in all three tanks using direct photography. Below

the level of the stirrer and near the tank wall the mean drop diameters

were lower than those for heights above the stirrer level. Above the

level of the stirrer the mean drop diameter became reasonably constant.

The capillary technique enabled the measurement of the drop size dis-

tribution and Sauter mean diameter at twenty five geometrically

similar positions in the tanks. Mean drop diameters measured at

different positions in the tanks using the capillary technique showed

4

that the drop sizes near the wall were smaller than in the bulk of the

dispersion. Mean drop sizes in the lower section of the tank below

the stirrer were smaller than those in the upper section above the

stirrer.

The large number of sampling positions provided by the capillary

technique enabled an overall interfacial area value to be computed

for each tank at constant impeller power input per unit volume. The

interfacial area of the dispersions increased with increase in tank

size for constant power input per unit volume. Plots of interfacial

area as a function of tank scale ratio yielded curves which seem to

indicate that the interfacial area of the dispersions tends to some

constant value for tank diameters greater than O.5m.

The empirical scale-up rule of constant tip speed seemed to apply

reasonably well for the range of tank sizes studied. The flow condi-

tions for the heptane/water dispersions were in the inertial subrange

and for this reason the Reynolds number cannot form a proper criterion

for scale-up. This was confirmed experimentally. Scale-up based on

constant Weber numbers similarly did not give equal interfacial area

per unit volume of dispersion for increasing tank size over the tank

sizes studied.

5

ACKNOWLEDGMENTS

The author wishes to express his sincere thanks to the following people:

Professor H. Sawistowaki and Dr E.S. Ortiz, who as personal supervisors

of the work gave constant guidance and assistance.

The Science and Engineering Research Council for financial support

covering the period of research and Mr J. Melling from Warren Spring

Laboratory for the Case Scheme.

Many members of the Technician Staff of the Department especially

Mr T. Stevenson from the workshops. Special thanks to Mr M. Dix

from electronics for his assistance In the design and construction

of the microprocessor unit.

All members of my family for their assistance.

6

CONTENTS

P age

Abstract

3

Acknowledgments

5

Contents

6

Chapter One Introduction

10

Chapter Two Literature Review

13

2.1 Introduction 13

2.2 Liquid Mixing 13

2.2.1 Dimensionless Groups

14

2.2.2 Power Curves 15

2.2.3 Scale-up of Stirred Dispersions

16

(A) Empirical Scale-up Criteria

17

(B) Theoretical Scale-up Criteria

18

2.3 Stirred Tank Turbulence

18

2.3.1 Inertial Subrange 19

2.3.2 Universal Equilibrium Range 22

2.3.3 Coalescence of Droplets

23

2.4 Drop Sizing in Dispersions

25

2.4.1 Direct Photography

25

2.4.2 Light Transmittance 27

2.4.3 Light Scattering 28

2.4.4 Conductivity

28

2.4.5 Chemical Reaction

29

2.4.6 Scintillation

30

2.4.7 Drop Stabilization

31

2.4.8 Capillary Sampling Technique

32

2.5 Drop Sizing Results

35

7

Page

Chapter Three Experimental Details 40

3.1 Description of Apparatus 41

3.1.1 Main Apparatus 41

3.1.2 Photographic Apparatus 44

3.1.3 Capillary Technique Apparatus 47

3.2 Experimental Procedures 54

3.2.1 Direct Photography 54

3.2.2 Capillary Technique 57

3.2.3 Impeller Power Measurement 63

3.3 Investigation of Alternative Detection Methods 64

3.3.1 Dielectric Constant 64

3.3.2 Ultra Violet Absorption 66

Chapter Four Results 72

4.1 Introduction 72

4.2 Stirrer Speeds for Constant Power Input/Unit Volume 72

4.3 Direct Photography 73

4.3.1 Drop Size Distributions 74

4.3.2 Cumulative Number Percentage 74

4.3.3 Equal Power Input/Unit Volume 75

4.3.4 Variation of Photographic Height 75

4.3.5 Variation of Stirrer Speed 76

4.3.6 Population Variance 76

4.3.7 Arithmetic and Sauter Mean Drop Diameters 78

4.3.8 Interfacial Areas of the Dispersions 78

4.4 Capillary Sampling Technique 79

4.4.1 Arithmetic and Sauter Mean Drop Diameters 80

4.4.2 Cumulative Number Percentage 80

8

Page

4.5 Comparison of Capillary and Photographic Technique

81

Results

4.6 Impeller Power Requirements 82

4.6.1 Power Calculation 82

4.6.2 Power Measurement

82

4.6.3 Equal Power Input/Unit Volume 82

Chapter Five Discussion of Results 118

5.1 Introduction 118

5.2 Direct Photography 118

5.2.1 Drop Size Distributions 118

(A) Variation of Photographic Height

118

(B) Variation of Stirring Speed

119

5.2.2 Population Variance 119

5.2.3 Sauter Mean Drop Diameter and Interfacial

119

Area

(A) Variation of Photographic Height

119

(B) Variation of Stirring Speed

121

5.3 Capillary Technique 123

5.3.1 Mean Drop Diameters 125

5.3.2 Cumulative Number Percentage 127

5.4 Power Measurement

127

5.5 Derived Results 127

5.5.1 Calculated Sauter Mean Drop Diameter 127

5.5.2 Calculated Clearance Between Drops 129

5.5.3 Comparison of Interfacial Area Using 132

Different Scale-up Criteria

(A) Constant Power Input/Unit Volume 132

(B) Constant Tip Speed

135

(C) Constant Reynolds Number 136

(D) Constant Weber Number 137

9

Page

Chapter Six Conclusions and Recommendations 139

6.1 Conclusions 139

6.2 Recommendations 140

Appendices

Appendix 1 Calculation of Kolmogoroff Eddy Length 142

Appendix 2 Computer Programs for Direct Photography 144and Capillary Technique Calculations

Appendix 3 Drop Size Distributions for Varying 149Heights of Photography in the 11cm,22cm and 44cm Tanks

Appendix 4 Drop Size Distributions for Varying 161Stirrer Speeds Using Direct Photographyin the 11cm, 22cm and 44cm Tanks

Appendix 5 MicroprocesBor Program 170

Appendix 6 Thickness of a Water Film Wetting 175Capillary Bore

Appendix 7 Capillary Technique Results for 11cm Tank 178

Appendix 8 Capillary Technique Results for 22cm Tank 182

Appendix 9 Capillary Technique Results for 44cm Tank 191

Appendix 10 Physical Properties of Heptane and Water 201

Appendix 11 Calculated Power Requirement for 11cm Tank 204

Appendix 12 Power Measurement Results for 22cm and 20844cm Tanks

Appendix 13 Calculation of Number and Clearance of 214Drops in Dispersion

Appendix 14 Interfacial Area Calculations Using 217Different Scale-up Criteria

Nomenclature 220

References 224

10

CHAPTER ONE

INTRODUCTION

Liquid-liquid extraction is emerging as a very important method of

separating the constituents of a homogeneous liquid mixture, a

problem frequently encountered in the chemical processing industry.

The liquid-liquid extraction operation involves the intimate contact-

ing of an extract phase which is or contains the extractant with the

raffinate solution containing the component to be extracted (the

solute). There are several methods for contacting the two phases,

e.g. mixer-settlers, spray columns and rotor-agitated columns.

Agitation subdivides one of the phases into droplets whilst the other

liquid forms the continuous phase. The large interfacial area created

between the two liquids greatly enhances the rate of solute transfer

between the phases.

Liquid-liquid dispersions are usually formed by the application of

external energy to Immisable liquids and, depending on their behaviour

on discontinuation of energy supply, they can be divided into stable

dispersions or emulsions and unstable dispersions. Only the latter,

in which the phases start separating as soon as the supply of external

energy is stopped, are considered here and given the term "dispersions".

The characteristics of a dispersion of droplets are a function of the

geometry and size of the mixing vessel, the Intensity of agitation,

the hold-up and the physical properties of the liquids forming the

dispersion. Changes in these parameters will result In different

drop size distributions and interfacial areas of the dispersion. In

this work the drop size distributions and the interfacial area of

heptane/water dispersions have been studied in three geometrically

similar mixing tanks of increasing size for various stirring speeds.

11

The flow patterns in a mixing tank are complex and influenced largely

by the geometry of the impeller and the mixing vessel. They can be

divided into primary and secondary flows. The former are responsible

primarily for liquid circulation while the latter contribute to local

velocity fluctuations. Consequently, the drop break-up and coalescence

rates, which depend on local conditions, will vary throughout the

mixing vessel resulting in different mean drop diameters at different

positions in the tank. Most workers have studied the mean drop

diameter or the interfacial area of the dispersion at a particular

position in the mixing vessel and taken that to be the overall value

for the whole of the dispersion. Alternatively, a chemical method is

employed which gives the total effective interfacial area from which

the Sauter mean drop diameter is calculated. The purpose of the

present investigation is to study the mean drop diameter by physical

means at various positions in geometrically similar tanks to provide

values of interfacial area suitable for determination of a scale-up

criterion of agitated dispersions.

The apparatus for a capillary sampling technique which enables measure-

ment of drop size at various positions in the mixing tank was developed

as part of this work. Other detection techniques also using a

capillary, e.g. measurement of dielectric constant and ultraviolet

absorption were investigated in detail but finally the laser light

technique was adopted. This technique gave the best detection con-

trast between the aqueous and organic phases.

The power consumption of an agitator in a liquid mixing system is

determined by its rotational speed and the environment in which it

operates. The most important rule to be used in the scale-up of

power data and process should be the principle of similarity, first

proposed by Newton (1). In the theoretical considerations for scale-

up of agitated tanks three types of similarity must be satisfied:

12

geometric, kinematic and dynamic. In practice this is impossible

and stirred tanks are scaled-up according to experimentally established

methods such as constant impeller power input per unit volume, constant

impeller tip speed or equal total number of impeller revolutions. The

present work compares the interfacial area of heptane/water dispersions

obtained in geometrically similar tanks of 1:2:4 size ratio using the

concepts of constant impeller power input per unit volume and constant

tip speed. The results obtained indicate how closely this system

obeys these empirical scale-up criteria in the tank size ratios chosen.

In addition, the drop sizes, interfacial area of the dispersions and

the impeller power data obtained should provide a better understanding

of the relationships between these parameters in the design and scale-

up of liquid-liquid contacting equipment.

13

CHAPTER TWO

LITERATURE REVIEW

2.1 Introduction

When two immiscible liquids are brought into contact to form a

dispersion, knowledge of the interfacial area is important. The

interfacial area must be known when considering the heat and mass

transfer between the phases to determine the corresponding area-

based transfer coefficients from their volumetric values. Knowing

the interfacial area, the former coefficient can be found, giving

information on the independent effects of area and resistance to

transfer.

Throughout the dispersion a continuous break-up and coalescence of

drops occur. Turbulent fluctuations and viscous friction produce

forces that tend to break up the droplets, whereas collisions between

two drops may result in their coalescnce into a larger drop.

Agitation maintained under constant conditions will result in a

dynamic equilibrium being established between the break-up and co-

alescence rates, and a spectrum of drop sizes results. A fairly

extensive literature exists with regard to drop sizing in liquid-

liquid dispersions. Previous workers have employed a variety of

techniques to obtain such information. Some considerations c liquid

mixing and scale-up criteria of impeller power input and dispersion

properties are followed by a review of the various techniques for

drop sizing.

2.2 Liquid Mixing

The rotation of an agitator in a confined liquid mass generates eddy

currents. These are formed as a result of velocity gradients within

the liquid. A rotating agitator produces high velocity liquid streams,

14

which move through the vessel. As the high velocity streams come into

contact with stagnant or slower moving liquid, momentum transfer occurs.

Low velocity liquid becomes entrained in faster moving liquid streams,

resulting in forced diffusion and liquid mixing (1). The degree of

mixing within a system is a function of two variables: (1) the magnitude

of eddy currents or turbulence formed and (2) the forces tending to

dampen this formation. The higher the ratio of applied to damping

forces the higher is the degree of mixing. A high degree of mixing

occurs when the entire liquid mass, confined in a vessel, is under

turbulent flow conditions. The quantity of mechanical energy required

to extend turbulence throughout a liquid mass is dependent upon

(1) vessel geometry, (2) agitator geometry, and (3) the physical

properties of the liquids being mixed. Obviously, the ideal situation

is to obtain good mixing at minimum power consumption.

2.2.1 Dimensionless Groups

Some of the most widely used and important dimensionless groups

represent the ratio of the applied to the opposing forces in a system.

In a fluid the factor resisting the applied forces may arise from

properties such as viscosity, surface tension or gravity.

In the design of liquid mixing systems, the following dimensionless

groups are of importance:

P I' - pressure forceNe = Newton Number pN3Dj' = inertia force

pNDj2Re = Reynolds Numberp

Fr = Froude Number N2Djg

We = Weber Number = PND1a

f = inertia force- viscous force

( = inertia forcegravitational force

I = inertia force- surface tension force

It should be noted that the Newton number was previously known as the

power number.

15

Dy dimensional analysis

PpN3Dj5

c1

i.e. Ne C1 ReX Fr7(2.1)

Vortexing can be suppressed by installing baffles. Since vortexing

is the only gravitational effect, the Proiade number is not required

to describe baffled systems.

For non vortexing systems, gravitational effects are negligible and

the exponent, y, of the Froude Number is zero.

Therefore, (Fr) 7 = 1 and equation 2.1 becomes

Ne = C1(Re)X (2.2)

2.2.2 Power Curves

A plot of Ne vs Re on log-log co-ordinates is commonly called a power

curve. An individual power curve is only true for a particular geo-

metrical configuration, but it is independent of vessel size.

Figure 2.1 shows the power curve for the Standard Tank Configuration (1)

which is described in section 3.1.1. It can be seen that for Reynolds

numbers < 10 the plot Is linear. In this region (AB) the viscous forces

exerted by the liquid control flow within the system. The gravitational

forces are negligible and hence the Froude number is not required to

describe the system. For the region AB the slope x has been found to

be -1.0. Thus, for this region equation 2.2 can be simplified using

Ne = P/pN3Dj 5 to read

-1.0P = C1(pN3Dj5)(pNDi2/p)

which can be rearranged to

P = C 1 (N2Dj 3 ) (2.3)

i.e. Power a viscosity at a fixed stirrer speed

From the power curve, at Re 5.0 the Newton number is 14.2. Using

this condition the constant, C 1 , can be calculated to be 71.0.

16

Viscous Trcmsition range Turbulent

range range

lOt - . U

for R.<10'

- - N1 a constant = 61 for R 1 .1O4 - - - -

10'0

Lii

100..._..__...._..J I liii I Jill I III___._..1100 101 1OL io io

REYNOLDS NUMBER

FIGURE 2.1 Power curve for Standard Tank Configuration

and a turbine impeller

As the Reynolds number increases, the flow changes from viscous to

turbulent. For the standard tank configuration the transition is

gradual, covering a range from Re = 20 to Re = 2000. The power and

flow characteristics remain dependent on the Reynolds number until

Re = 10,000. Equation 2.2 is valid over this entire range of

Reynolds numbers. When the flow becomes turbulent, the power curve

in Figure 2.1 becomes horizontal (segment DE). Here the flow is

independent of both Reynolds and Froude numbers

i.e. Ne = constant

Experiments show that Ne = 6.1 at Re > 10000.

2.2.3 Scale-up of Stirred Dispersions

In the scale-up of an agitated tank, it is generally assumed that

geometrical similarity has to be preserved. Using the terminology

of equipment and model, this means that all linear scale ratios in

17

the equipment and the model should be the same.

A. Empirical scale-up criteria

In practice, stirred tanks are scaled-up according to experimentally

established methods. These are:

(1) equal power input per unit volume

(ii) equal peripheral speed of agitators

(iii) constant total number of revolutions

Method (1) was first proposed by BUche (2) and subsequently confirmed

by Brothman and Kaplan (3), Miller and Mann (4) as well as by many

other workers. It seems to apply to a variety of mixing processes

including those involving mass transfer (dissolution) and dispersion.

Method (ii) was introduced by Hixson and Baum (5) and confirmed by

Chilton, Drew and Jebens (6) as well as by Rushton (7). It was found

to apply to dissolution of solids, heat transfer and blending.

Method (iii) states that in a batch process the same quality of mixing

will be attained in the same time with the same total number of revo-

lutions. It was proposed by Kramers (8) and confirmed by De Coursey (9).

Under fully turbulent conditions in baffled vessels, i.e. when

Ne = P/pN 3Dj 5 = constant, the experimental criteria suggest the

following ratio of power input for equipment (e) and model (m) for

a twofold increase in the linear dimension:

(1) P Ne[)2/3

= const, i.e. N 3Dj2 = const or - =Nm De)

i.e. = (}3 = 8=

= 0.63

Ne Dm(11) ND const - = - = 0.5

Nm De

Pe = 1De2

1J = 4

(iii) TN = const N = const - 1De5Pm = 32

18

Taking the empirical relation of (10) as an example

aDj a We°' 6 i.e. a = const (N2Di3pt0.6

Di 1. ° J

a = conat NL2 Dj° 8 = conat (N3D)0'

This finding supports the method of equal P/V for production of equal

interfacial area per unit volume of dispersion.

B. Theoretical scale-up criteria

Theoretically, for a complete similarity of equipment and model, they

must not only be geometrically similar but also satisfy the following

similarity states:

(a) kinematic similarity;

(b) dynamic similarity;

(c) thermal similarity (not applicable in the present case);

(d) chemical similarity.

Kinematic similarity requires that in geometrically similar systems

corresponding particles trace out geometrically similar paths in

corresponding intervals of time. This means that velocities at corres-

ponding points should have the same ratio which, in turn, implies that

flow patterns in the equipment and model should be the same. Dynamic

similarity is concerned with forces which accelerate or retard moving

masses in dynamic systems. It states that geometrically similar moving

systems are dynamically similar when the ratios of all corresponding

forces are equal, i.e. when dimensionless groups such as Re, Fr and

We are the same in the equipment and the model.

Finally, geometrically similar systems are chemically similar when

corresponding concentrations or concentration differences have the

same ratio and the systems, if moving, are kinematically similar.

2.3 Stirred Tank Turbulence

Most liquid-liquid dispersions are produced in stirred, fully baffled

19

vessels operating under turbulent conditions. Theoretical considerations

concerning the drop size in stirred tank dispersions rely to a large

extent upon Kolmogoroff's theory of local isotropy (11, 12). The

theory of local isotropy (Kolmogoroff) has been reviewed extensively

by Batchelor (13) and only a short summary will be given in what

follows.

Consider the scale of the velocity fluctuations in the turbulent flow.

Instability of the main flow amplifies existing disturbances and

produces eddies.

The primary eddies are unstable and successively decay into smaller

and smaller eddies until the energy is dissipated by viscous forces.

Kolmogoroff has put forward the hypothesis that in any turbulent flow,

at sufficiently high Reynolds numbers, the small-scale components of

the turbulent velocity fluctuations are statistically independent of

the main flow and of the turbulence-generating mechanism. The scales

of the velocity fluctuations are determined from the local rate of

energy dissipation per unit mass of fluid.

Two mechanisms of energy dissipation were considered to contribute to

drop break-up. To determine the range in which each mechanism is pre-

valent Kolmogoroff proposed an eddy length, L. Its value is given by

L = }

-1k

(2.4)

where P = power input

V = volume of system

PC = viscosity of the continuous phase

Pc = density of the continuous phase

2.3.1 Inertial Subrange

The first mechanism was considered to exist for drop diameters greater

than the eddy length. This is the so-called inertial subrange.

20

If the droplet is much larger than the microscale, L, viscous shear

forces can be neglected. In this case the droplet will oscillate about

its spherical equilibrium shape concurrently with the surrounding

fluid, provided the densities and viscosities of both liquids are

not much different. If the deformations are large, the droplets

become unstable and break up into two or more fragments. But in

order to become unstable, the kinetic energy of the oscillations must

be sufficient to provide the gain in surface energy due to the break-up.

The kinetic energy of the oscillating droplet may be assumed as

proportional to pu2(d)d3

where u2 (d) = mean square of relative velocity

fluctuations between two diametrically

opposite points on droplet surface.

The minimum gain in surface energy is approximately proportional to ad2.

(__u2tciuiThe ratio of these two energies,

J is equivalent to the local

Weber number.

The critical value of this ratio at which break-up occurs is dependent

on the number of droplets formed as a result of the break-up. This

critical value should be constant for any given system, though it

may vary for different liquids. Such a value was defined by Hinze (14)

as

We = 2 dmaxcrit ___________a

(2.5)

Batchelor (13) derived an expression for the mean square fluctuating

velocity over the maximum drop diameter

u2 = C (E d)2/3

for S >> d >> L (2.6)2 max

where E = power dissipation per unit mass of continuous phase

C2 = Constant

S linear scale of energy containing eddies

(dependent on turbulence generating device)

21

d maximum drop diameterni ax

By considering the critical Weber number to be constant and combining

equations 2.5 and 2.6, Binze showed that if viscous forces are

neglected, 3/5

max a constant

(2.7)

Binze considers that an average maximum drop diameter may be predicted

by the above equation by using the average energy dissipation rates

if the stirred tank turbulence is not greatly inhomogeneous.

Shinnar (15) used a very similar approach to the prediction of drop

size in isotropic turbulent dispersion. He defined the critical

Weber number for drop break-up as

We _PcU2d32crit

(2.8)

substitution for the mean square fluctuating velocity in equation 2.8

yields5'3

We= C3 p E'3 d32

crita

(2.9)

Many authors have shown a linear relationship to exist between dmax

and d32 (16, 17, 18).

Rushton et al (19) found that in a stirred tank at Reynolds number

> 10000, impeller energy input was independent of the fluid properties

and dependent only on the impeller speed and impeller diameter. This

dependence may be expressed in the form

E KN3D12

where K a constant

Combining equations 2.9 and 2.10 gives

d32 Di N2 C = constant or d a32

a

Re-arrangement of equation 2.11 also gives

d 332 = C

(2.10)

(2.11)

Ipu'1 2 - 2E(prJ iSv

(2.13)

22

Chen and Middleman (16) and Sprow (17) obtained correlations of this

form when working with low dispersed phase fractions,

2.3.2 Universal Equilibrium Range

In contrast to the above, if a is very small or the velocity fluctuations

are rather large, the maximum stable droplet diameter will be smaller

than the microscale, L. In this case the viscous shear forces cannot

be neglected any more, as the stresses due to viscous shear will be

much larger than those due to inertial effects. This is the so-called

universal equilibrium range.

The corresponding equation for the break-up of a droplet, due to

viscous shear only, was derived by Taylor (20).

IIc2.. (2.12)

pra

where is a certain function, and the suffices c and d refer to the

continuous and dispersed phases.

Shinnar (15) noted that for locally isotropic flow

where E = local rate of energy dissipation per unit mass

of fluid

v = kinematic viscosity

By assuming that the local rates of energy dissipation are independent

of fluid properties at Re > 10000 the local rate of energy dissipation

becomes proportional to E and equations 2.12 and 2.13 combine to give

C , 11: N12 Di d = . (2.14)

which describes the break-up of drops by viscous shear forces operating

in the universal equilibrium range. According to Shinnar most drops

in stirred tank dispersions are of a size larger than the eddy length,

L, and therefore within the inertial subrange.

23

2.3.3 Coalescence of Droplets

Local velocity fluctuations will increase the rate of collisions

between droplets and thereby increase the chance of coalescence.

However, it is well known that only a small number of collisions

actually result in coalescence (15). This is so because a thin film

of liquid, trapped between two colliding droplets, acts as an elastic

cushion and may cause the droplets to bounce off each other. If the

two droplets adhere to each other, the thickness of the film separating

then will gradually decrease due to diffusion. When the film has

thinned down sufficiently, the boundary between the two droplets may

collapse. However, there is still the chance that turbulent velocity

fluctuations may meanwhile transfer sufficient energy to the two drop-

lets to cause re-separation, before coalescence occurs.

The droplet diameter d 1 , for which the energy due to turbulent

velocity fluctuations is equal to the energy of adhesion, depends on

the intensity of agitation, E and the physical properties of the liquids.

This droplet diameter may be estimated as follows:

The force of adhesion between two droplets of diameters d 1 and d2 is

given by Shinnar (15) as

F(h0) = Trd 1 d2I f(h) dh)

(2.15)d1+d2

where h0= smallest distance between the two droplets

(h0 is actually the thickness of the separating 'films')

(b0 0 when drops touch each other)

f(h) = force of attraction/ni 2 between two infinite parallel

surfaces separated by a distance h (21)

If the two drops are of equal diameter, d, then the energy of

adhesion, Ea is given by

24

E =A(h)da o

1= -UI I fwhere A(h0)

2 h0 h(h) dh dh'

In section 2.3.1 the kinetic energy of two drops of diameter d in

movement relative to each other is proportional to pu 2 (d) d3 . This

must be larger than the energy of adhesion to prevent coalescence.

The drop diameter for which separation is still possible in a given

fluid is therefore given by

pu2 (d) d2constant

A(h0)

In locally isotropic flow u 2 (d) C2(Ed)2/

2 8therefore C5pE " d " /A(h 0) = constant

For fluid stirred in a tank at constant power number, this gives

Pc N2D/3 d32"3 -3_____________ = constant or d32 a N 1"

A(h0)

The droplets of a dispersion coalesce until the diameter of the drop

formed reaches the unstable size for break-up, and then fragmentation

into several smaller drops becomes probable. The process restarts

with coalescence. The drop size distribution is determined by the

state of dynamic equilibrium reached.

From figure 2.2. it is apparent that prevention of coalescence due to

turbulent velocity fluctuations in the bulk liquid is of importance in

the region to the left of the point of intersection of the two lines,

where drops can exist only within the shaded area, whilst being un-

important to the right of this point.

Results obtained by Vermeulen et al (10) showed the mean drop diameter

to be proportional to -6/5 power of stirrer speed and Rodger (23) et al

found the mean drop diameter to vary as -3/4 power of stirrer speed,

thus confirming Shinnar's predictions.

rn1,

0-J

25

Log Stirrer Speed

FIGURE 2.2 Dispersed drop size dependence on stirrer

speed (Shinnar 15)

2.4 Drop Sizing in Dispersions

The drop size distribution is a significant factor apart from its

influence on the average drop size and the total interfacial area of

the dispersion. With a wide range of drop sizes the mechanisms for

mass transfer to and from the drops will be different for large and

small drops.

Previous workers have employed a variety of techniques to measure drop

size and a review of these techniques follows.

2.4.1 Direct Photography

The dispersed droplets in a fluid field may be photographed using a

windowed probe, which extends into the dispersion and a short duration

light flash, which photographically 'freezes' the drops. The camera

26

lens is focused on a plane just beyond the probe window and inside the

dispersion. Photographs may therefore be taken with the least amount

of interference resulting from out of focus drops which lie between the

probe window and the focal plane. Care must also be taken to avoid

photographing drops adhering to the probe window. Kintner (24)

describes a technique which enables only freely suspended drops in

the fluid field to be photographed using collimated beam illumination.

Having photographed the dispersion, the drop diameters are then

measured individually from the photographs.

The technique of direct photography for the determination of drop size

in dispersions has been used by many workers (25-37). Kintner presents

a review of many photographic techniques used in bubble and drop research.

Large drops (diameter > 2001un) at low concentrations of dispersed

phase present no inherent photographic difficulties. Ward and Knudsen

(25) pumped the dispersion through a tube and photographed the drops

before they were passed back into the mixing vessel. They tested

their results using glass beads of a known size distribution. They

developed an apparatus which allowed photography of drops of 1 to 800im

diameter in dispersed phase concentrations up to 50% by volume. Ward

points out that the following difficulties arose when concentration

of the dispersed phase increased and drop size decreased;

1. The light transmittance decreased.

2. Magnification by the camera magnifies drop speed,

requiring shorter exposure times.

3. Drop images may be distorted by drops between lens

and plane of focus.

Precision and accuracy of the photographic technique for the measurement

of interfacial area has been shown to be better than 10% by Trice and

Rodger (26).

27

Mylnek and Resnick (27) used a specially designed trap to draw the

dispersion and immediately encapsulate the drops with a polymer film.

The whole trapped sample was then photographed on a plate to determine

the Sauter mean diameter. Karabelas (28) also used the photographic

technique on encapsulated samples of dispersion. Coulalogiou and

Tav]arides (29) have developed a flash photomicrographic technique

to measure drop size distribution in a stirred tank. A microscope

is used to photograph the dispersion with the camera using high contrast

fl lii.

Elimination of the long tedious effort needed to determine the drop

size distribution from photographs has also received some attention.

Adler et al (30) used the sweep of a narrow Light beam and a photocell

to measure the drop size from photographic negatives.

2,4.2. Light Transmittance

The light transmittance technique has been used widely in determining

the Sauter mean drop diameter in liquid-liquid dispersions. The photo-

electric equipment required for light transmittance measurements con-

sists of a light source to provide a uniform collimated beam, a light-

sensitive detector unit and an electronic circuit to measure the

amplified output of the detector unit.

The intensity of light transmitted through the continuous phase and

through the disperalon is measured. It is known (38) that the pattern

formed by parallel incident light being defracted when passing through

a single sphere is independent of the size of the sphere and is affected

only by the refractive indices of the sphere mnd surrounding phase. This

is so when the sphere diameter is large compared to the light wavelength.

Thus, since the pattern is independent of sphere size, the amount of

light scattered is proportional to the sphere size. Correlations of

surface area to light transmittance are empirical.

28

Langlois et al (10) suggested an empirical equation of the form

= l.0+A

a constant which is a function of the ratio of refractive

indices of the dispersed and continuous phase.

Similar empirical relationships have been proposed by other workers

(23, 39, 40).

The light transmittance method is a quick and simple method of measur-

ing the interfacial area of a dispersion of drops, but it does not

give the size distribution of the droplets.

2.4.3. Light Scattering

When light passes through a dispersion a relationship exists between

the intensity of light scattered at any angle from the incident beam

and the size of particles present in the dispersion. The average size

of the particles may therefore be determined from measurements of the

intensity peaks at different scattering angles (41). The technique

has been fully described by Sloan (42) and the principles are that

1. There is no angular dependent absorption of the

incident beam.

2. The transmittance of the incident beam is between

40 and 80% of the incident beam.

3. The radius of the particles is in the range of

0.1 to l00im.

A plot of the scattering angle versus the product of the scattered

light Intensity and scattering angle squared gives a peaked curve.

The location of the peak of the curve along the abscissa corresponds

to the size of the particles.

2.4.4. Conductivity

A complete drop size distribution may be obtained by using a Coulter

counter which determineB both the number and size of the dispersion

droplets suspended in an electrically conductive continuous phase.

29

The dispersion is forced through a small aperture between two elec-

trodes. The resistance between the electrodes changes as a particle

goes through the aperture and this change is converted into a voltage

pulse in the instrument. The pulses are approximately proportional

to the particle volume and therefore the diameter corresponding to

a particular particle counter can be determined.

The principles of operation and analysis of the data obtained have

been discussed by Sprow (17), Princen and Kwolek (43) and Wachtel

and La Mer (44). Sprow used apertures of 200 and 560pm diameter;

this combination allowing distribution analysis on particles from

10 to 250pm diameter.

The counting of particles by making the continuum electro-conductive

would necessitate the addition of undesirable conductive materials

to the dispersion. It is difficult to predict how the addition of

these materials would affect the mean drop diameter and the break-up

and coalescence mechanisms tn the dispersion, although it has been

established recently in gas-liquid systems that the presence of salts

reduces the amount of coalescence.

2.4,5 Chemical Reaction

The chemical reaction method for the measurement of the effective

interfacial area in liquid-liquid contactors was first suggested by

Westerterp (45). This method has been subsequently adopted by many

workers (46-51) to obtain values of the effective interfacial area

in various types of liquid-liquid contactors. Interfacial areas may

be determined by measuring the absorption rates where an absorbed

gas undergoes chemical reaction with precisely known kinetics.

For absorption accompanied by pseudo-first order reaction, the rate

of absorption for the Danckwerts (52) surface renewal model is given

by the expression,

30

W = aC + 1C)

)'DK Caprovided 1 < -

zC*

where a effective interfacial area/unit volume dispersion (car')

W = rate of absorption/unit volume dispersion (mol/cm3a)

C* = solubility of solute in liquid (aol/cm3)

D = diffusivity of solute in solution (cm2/s)

pseudo-first order rate constant (1)

= liquid side mass transfer coefficient (cm/s)

Ca = concentration of absorbent (aol/cm3)

Z number of moles of absorbent reacting with one

mole of solute

If (W/C*) 2 is plotted against K' (the Danckwerts plot) a straight

line should be obtained with a slope equal to Da2 and an intercept

of (KLa)2. If the value of D is known or can be predicted, the values

of KL and a can be calculated. For a fast reaction DK' >> K and a

can be obtained directly from the measured value of W and known values

of C*, K and D.

Sridhar and Potter (53) have compared the chemical method of measuring

interfacial areas in agitated vessels with the light transmittance

method and found that the chemical method yielded consistently higher

values of interfacial area. Figure 2.3 given by Hofer and Mersmann (54)

shows how all other authors claim that the chemical method gives con-

sistently lower values of interfacial area.

2.4.6 Scintillation

The possibility of using short range radioactive particles for measur-

ing interfacial area was first investigated at the Oak Ridge National

Laboratory (55). Here a radioisotope emitting short range particles

6OO

raVa-t QI

C

02 0L 06 1 2mJpIffICId s vs4ocsty v -

31

I Cob4i 19512 Andr, 1%)

3 Coi.coni I92Nugl.nork 1965

S 0. Go.d.v.ø 196S

$ Fi1.r ii 1967 Sliotwsa M si 1969• $Quao,w 19699 Rodo,iov 1970

McN,sl 1970II Z,.g.i 19fl

Pciiov.cii, 197113 Slschlo., '975

1iIS Biho1omo. 1972$ Cold.'bonk 1971

FIGURE 2.3 Comparison of interfacial area results

using chemical and physical methods of

measurement

was contacted with an immiscible phase capable of interacting with

the particles. Because of the short range of the particles, inter-

action was restricted to the region close to the interface. Thus,

the product of the interaction (such as new chemical species or

radiation) will be approximately proportional to the Interfacial area.

2.4.7 Drop Stabilisation

This method relies on the immediate encapsulation of the drops with

a thin polymer film. A component is added to the continuous phase

which will react quickly with a second component (contained in the

dispersed droplets) to form the encapsulating polymeric film around

each drop. Upon terminating the agitation the encapsulated drops

settle as discrete drops and can be examined for size distribution.

32

Mylnek and Resnick (27) used this technique and designed a trap which

enables sampling almost anywhere in the stirred vessel. Shinnar (15)

studied a stirred dispersion of molten wax in hot water, stabilised

by the addition of a protective col].oid. Small samples of the dis-

persion were siphoned of f, cooled rapidly to solidify the wax droplets

and the drop size distribution was obtained by microscopic examination.

Church and Shinnar (56) point out that such a sampling procedure is

restricted to rather stable dispersions which would not tend to co-

alesce in the sampling process. High surface tensions and high vis-

cosities of the continuous phase usually increase the stability of

the dispersion.

Brooks (57) also used the solidification of the dispersed phase

(carnauba wax) by a small decrease in temperature. Drop size distri-

butions were then obtained by sieving.

2.4.8 Capillary Sampling Technique

This method involves the use of a fine bore capillary for the measure-

ment of droplet size in liquid-liquid and gas-liquid dispersions. A

sample stream of the dispersion is drawn from the mixing vessel and

the drops convert to cylindrical slugs as they pass through the

capillary. Light scattering is used to distinguish between the slugs

of dispersed and continuous phases as the sample stream passes the

detection point.

Using a series of lenses and slits, a light beam is focused on the

capillary bore and the light emerging from the other side of the

capillary Is brought to a focus on a photosensitive detector. Figure 2.4

shows a ray diagram for a section through the capillary. Careful adjust-

ments of the optical components enables the light detector to register

a contrast between the light intensities emerging from the dispersed

and continuous phase slugs as they pass the detection point.

Lj

mV

mV

33

Dispersed Phase Ray Path

Continuous Phase Ray Path

FIGURE 2.4 Refraction of light beam on passage through

dispersed and continuous phase slugs in

capillary.

The velocity of the flow in the capillary can be determined by using

two detectors and timing a slug to pass between them.

I.,

FIGURE 2.5 Signals and principle of photoelectric method

Duration of the dispersed phase slugs in front of the detector can be

recorded and using the velocity of flow the volume of the slugs can be

calculated.

34

Velocity of flow, v =

Length of slug =

Using the capillary bore diameter the liquid slug volume may be

calculated and an equivalent spherical drop diameter can be computed.

Using a data logger to record the times of all dispersed phase slugs

the drop size distribtuion and the Sauter mean drop diameter can be

determined for a particular position in the mixing vessel.

Weiland et al (58) used this technique to determine the bubble size

distribution and interfacial area for oxygen transfer in an aerobic

airlift loop fermenter.

Wiffels et al (59) used the capillary sampling technique on a 6m long

5cm diameter column for a liquid-liquid dispersion. The column pressure

was sufficient to start the flow of the dispersion in the capillary.

They noticed that hardly any interaction took place between neigh-

bouring slugs in the capillary and only a small percentage were

coalesced before the capillary measurement of slug length.

Veroff et al (60) designed a special sampling probe which was used to

extract a sample of the dispersion from the mixing vessel and protect

the sampled drops with a surfactant. The stabilised droplets were

then pumped through the capillary to determine the drop size distri-

bution. A dye was added to the continuous phase to improve the con-

trast between the dispersed and continuous phase slug light signals.

Veroff et al found very good reproducibility of the measured drop size

distribution and Sauter mean drop diameter.

Rartland (61) made measurements of drop size with a commercially

available capillary sampling apparatus but found that the photocell

used failed to distinguish drops which were close together. This resulted

in a 50% overestimate of the drop size.

35

2.5 Drop Sizing Results

Drop size and interfacial area in stirred liquid-liquid dispersions

have been studied by many workers for various liquid properties,

mixer configurations and agitation speeds.

Most of the workers have related the interfacial area or the Sauter

mean drop diameter to variables such as stirring speed, liquid physical

properties, stirrer diameter and dispersed phase fraction. Rodger et

al (23) made some of the earliest investigations of the interfacial

area in stirred dispersions. They related the interfacial area to

the stirrer speed and liquid properties for constant volume fraction

dispersed by the equation,

A = K {DI3N2Pc}° 36 (D 1k1 }u/5 __lf5exp (3.6) (2.16)

Dj D.r \c to Pc

where N = stirrer speed

Di = impeller diameter

DT = tank diameter

a = interfacial tension

p = density

v = kinematic viscosity

t settling time of dispersion

to = reference settling time

K, k = constants

c, d = subscripts for continuous and dispersed phases

Equation 2.16 may be simplified into an expression involving the Sauter

mean drop diameter

= C We°36 IDTkD 1IDT)

where We = Weber number

36

Luhning (62) simplified the interfacial area correlations obtained by

a number of workers, see Table 2.1. The results given in Table 2.1

may be summarized as

A a N072 to 15

A a D107 to 2.0

A a DT(05) to (-1.2)

A a •d032 to 1•0

Luhning's own results were correlated by

A a We0 55 to 0.65

A a N075 to 1.2

Clarke's results (63) were correlated by

A a N0"7 to 1•011

A a WeO2 1 t0 051

Thornton and Bouyatiotis (31) related the volume fraction dispersed

with the Sauter mean drop diameter by the equation

a2 ) f__a 31° 62 f.]O.O51D32 = D3 + l.18X

LI 1u J lpcJ J

where D3 = droplet size as XV tends to zero

= volume fraction of dispersed phase

D3 = f (power dissipation, physical properties)

(Dp g) - 29 0

f(P/v)3g'032 fPca3l°11'

I.. - . I 1pg )

Vermeulen (10), Calderbank (39) and Brown and Pitt (18) have also

shown that the dispersed phase fraction is an important parameter

and their results may be summarized by the expression

32 = C6(1 + C7) We 6

Dj

37

TABLE 2.1

Interfacial Area Results Summarized by Luhning (62)

Measurement Simplified relation for Relation to volumeAuthor

method constant volume fraction fraction dispersed

Rodger et al LightA = K Di 'DT'2N°72(23) Transmission

Vermeulen et LightA = K2Df •8N1•2 A -

al (10) Transmission

Calderbank LightA = K3D' 8N12A •10

(39) Transmission

Kafarov andPhotography A = KkD lN 1A •081.

Babanov (66) d

Paviushenko &Yanishevskii Photography A = K SD 7D;1•2N1• ? A(67)

Rodriguez LightA = K6D°DT'2N'2et al (40) Transmission

Nagata and LightA = K7N1•35

Yamaguchi (70) Transmission

Chen andMiddleman (16)

ONlIkPhotography A = K8D

Shinnar (15) Stabilization A = K9N075

A = K10N12

Sprow (17) Conductivity A - N 075 A -

A - N15

Fernandes and Chemical A - N0729Sharma (48) Reaction

A-

Bouyatiotis &Photography A - N° 96A +1.0

Thornton (31) d

H-

I

I

- 1:

I Ji1Jj J.i

i1i

i1i

38

4

V.

U

9

0

un

Hi hi }I I I

Ig.8

0 0

'.4

1 . -

!C d

I,

4

1

0

VI

I-

U

0

0

I I I

.. .. .

. C .4

•

N

'-5

• C U C 1:C)

0Cl)

- - -' C

wIs-

--5

C,

U)-1

U)8-

V

U)

C-)

o'-5

0'-5U)-1

0C-)

C.')

CU)

I-')

&'-! e -.

'' .4.4-.' Z

.4 .4- r

- I - •?- S • • V. - -

JC -; H

'.4-.' - .-J I-,• 4 - 1' i! - - •3 '

9I !.IsirI- !

- IT- II 0 0 - 0 0 3

-tJ -

j4II-'

39

Coulaloglou and Taviaridea (29) give a table summarizing the

relationships obtained for the Sauter mean drop diameter by many

workers, see Table 2.2.

40

CHAPTER THREE

EXPERIMENTAL DETAILS

This section gives a description of the apparatus used for drop size

determination by direct photography and the capillary technique, as

well as of stirrer power measurement. The description of the apparatus

is followed by the experimental procedures employed.

The laser light technique used in the capillary method for detection

between the organic and aqueous phases was chosen after the dielectric

constant and ultra violet detection techniques had been investigated

in detail and discarded. Details on the work done on the dielectric

constant and ultra violet techniques are given in section 3.3.

3.1 Description of Apparatus

The description of the main apparatus is followed by a description of

the apparatus used for direct photography of the dispersion, capillary

technique drop sizing and stirrer torque measurement.

3.1.1 Main Apparatus

The three mixing vessels used were stainless steel tanks of 11cm, 22cm

and 44cm inside diameter. The design of the vessels was based on the

Standard Tank Configuration described by Holland (64). Use of this

configuration provides adequate mixing for most processing require-

ments found in industry and also enables the results to be compared

to those of other workers. Figure 3.1 shows the standard tank con-

figuration. Figure 3.2 gives the general design of the tanks and

Table 3.1 the dimensions for all three tanks.

Four baffles were spaced equally around the tank, their width being

equal to 1/10 of the tank diameter.

The stirrers used for the tanks were six-blade flat blade turbines

located at the centre of the vessel and cleared the bottom of the

41

= ImpelLer diameter = i/3D

H1 = ImpeLler height from tank bottom = DL

HL = Liquid height = 1),.

WL= Impeller blade width = i/S D1

L. = Impeller binde length = 1/4 D

5L= Length of impeller blade mounted on

cenfrat disc = LIZ

Wb= Baffle width = i/b T

lgure 3.1 Standard Tank Configuration.

42

.fjgure 3.2 GeneraL Design of Mixing Vessels.

43

i0.rl N N

0d '-I

N N•rI C')C') N

0 0

Cv) N C')r4 C') Cv)

N C)

d C..'

N C') Nr1 C') CDC)

o - c')

N C') N.rl C') CD

Cv) Np-I

N C') NCD. Cr) ID

C') Np-I

o o 0

cq

o 0 0a,

0) CD CDp-I C')

o 0 0

N CDC.'

o 0 0C)

It) 0 0p-I

o 0 0.0

C') CD C.''-I

0•0 0C.'

0 0 0

'-I

U

•1•1

0

a,B

p-IrI.11:

44

tank by one third of the tank diameter. The dimensions of the impeller

blades were related to the impeller diameter; impeller blade width was

1/5 impeller diameter, D, impeller blade length was 1/4 Dj and the

length of the blade mounted on the central disc was 1/8 Di. The

stirrer shafts were connected directly to the motor.

For the 11cm and 22cm diameter tanks the stirrer was driven by a

1/6 HP 5000 rpm shunt wound D.C. electric motor, The speed control

unit operated from 220 volts A.C. mains current. Any variation in

the mains supply voltage was checked by the smooth speed regulator.

For the 44cm diameter tank a Lightnin 1/3 HP motor was used. The

stirrer rotation speed was measured with a stroboscope.

The five photographic ports were positioned in one vertical plane

and between baffles. The distances of the photographic port centres

from the bottom of the tanks are given in Table 3.1. A brass window

piece was secured into the port being used for photography while the

remaining ports were sealed with brass blanks. Rubber 0-rings were

used to seal the brass window fittings by tightening brass rings on

the outside of the tank.

The five capillary ports were again positioned in one vertical plane,

0but had their centres at 180 to the photographic ports. The dis-

tances of the capillary ports from the bottom of the tanks are given

in Table 3.1.

3.1.2 Photographic Apparatus

Photographs of the heptane/water dispersions were taken using a

Fujica 35mm SLR camera (model FX2) fitted with a bellows attachment

and a 42mm Summar lens manufactured by Ernst Leitz Ltd Company. A

Clive Courtenay Micro Flash Unit, specification 1020, was used to

provide a light flash of sufficiently short duration (approx. 2 micro-

seconds) to freeze' the motion of the dispersed droplets. The energy

output of the flash unit could be varied between 25 and 50 joules.

45

1-'

!

-I:i

II

:_

--

-1I1

FIGURE 3.3. Direct Photography Apparatus

Rubber •O•

inside dia.

thickness

Brasswindow —25•

disc

75—

d. copper tube

disc

de

pho

jcine mirror

46

32 ALL dimensions in mm.

-HH

bt.ci 25.4-f-. .1-31.75

Figure 3.4 Window attachments for direct photography.

Figure 3.5 Periscope arrangement for fI.ash light.

47

The apparatus with the camera and flash unit in position on the 44cm

diameter tank is shown photographically in Figure 3.3. The dimensions

of the brass window pieces are given in Figure 3.4. Light was con-

veyed into the dispersion through a periscopic arrangement shown in

Figure 3.5. The flash gun was mounted above the tank facing down

so that the flash light travelled down the tube of the periscope,

passed through the dispersion and caine horizontally out of the photo-

graphic window. The camera lens was always on the outside of the tank.

In order to photograph the dispersion at one geometrically similar

point, three windows were used which protruded 0.5cm, 1.0cm and 2.0cm

into the 11cm, 22cm and 44cm diameter tanks respectively. The gap

between the photographic and the periscope windows was always 0.5cm.

3.1.3 Capillary Technique Apparatus

Figure 3.6 shows a photograph of the capillary sampling apparatus set

up on the 44cm diameter tank.

The capillary tubing used for the drop diameter measurement were

supplied by Chance Brothers, Pilkington Pressed Glass Division. The

capillary was Veridia precision bore tubing with a bore diameter of

0.2mm and an outside diameter of 5.0mm. The end of the capillary was

blown into a small funnel shape with an 0.8cm circular entrance. The

capillary tubing used was 20.0cm long for the 11cm and 22cm diameter

tanks and 30.0cm long for the 44cm diameter tank.

In order to reduce the capillary vibrations the capillary was sealed

at the tank holder using a soft Bilicone rubber ring which was " thick.

The silicone ring was tightened onto the capillary by screwing a brass

ring onto the threads of the tank capillary holder. The soft silicon

ring sealed the capillary but still allowed some movement of the

capillary in the clearance hole of the capillary holder. This flexi-

bility made it possible for the capillary to be secured firmly onto the

- -

.1-I

r-1

0'-I

".4

0()

0

hi

1z4

48

--1

49

.

V I

—i— .#

__ If(IIIIIII1!!I ____ (rir

FIGURE 3.7 Close-up of the Lens Arrangement

and Capillary Supports

Syringe

50

perspex supports attached to the optical bench without the danger of

breaking it. Figure 3.7 shows a photograph of the capillary support

and lens arrangement.

The pump used to draw the dispersion out of the tank and through the

capillary was a Speedivac ES35 high vacuum pump provided by Edwards

High Vacuum Ltd. The suction of the pump could be adjusted by an air

bleed nozzle on the pump housing. The capillary was connected to the

pump with an 1/8" i.d. PVC tubing which also had an air bleed valve

for fine adjustment of the velocity of flow in the capillary. There

was also a facility of drawing the dispersion through the capillary

with a syringe, so that individual slugs of dispersed phase could be

stopped at the detection points for fine adjustment of the optical

components. Figure 3.8 shows a simple flow diagram for the capillary

sampling technique.

The optical system used for the measurement of the lengths of the

dispersed phase liquid slugs passing through the capillary is shown

photographically in Figure 3.9.

Punp

FIGURE 3.8 Flow Diagram for Capillary Sampling Apparatus

51

\(</f __

.___ -a

,.\

-- ___

F 0- r = -

-_a________I7J!=- wJ ,- -

_t

L C

C)

0

52

C0LI-iC)C)

a,U)

-JC.)

1)-cF-

0

C)

LL

53

Figure 3.10 shows a light ray diagram of the optical system. The light

source for the detection purposes was a Spectra Physics Stabilite

Helium/Neon laser (model l24A) which gave a beam intensity of 15 mw.

This light source produces a light beam which has the properties of

being almost totally coherent and gave sufficient intensity for the

detection required.

The light beam from the laser was collected and brought to a sharp

focus at the centre of the bore of the capillary by a Planochromat

x 50/0.80 microscope objective lens. The emergent beam from the

capillary bore was then collected by a Watson Para x 10/0.28 micro-

scope objective lens and brought to a focus on the sensitive area of

a photodlode. Slits were placed in front of the photodiodes to exclude

any light other than that coming from the bore of the capillary.

The laser beam gave a good contrast between the light signals given by

the dispersed phase slugs of heptane and the slugs of aqueous phase as

they passed the detection point.

The detection relies on the difference in refractive indices of heptane

and water and careful adjustment of the optical components ensured that

good peak signals were obtained for the heptane slugs as they passed

through the capillary. Figure 3.1] shows a polaroid photograph obtained

from the oscilloscope camera showing typical signals of light intensity.

The peaks are the heptane slug light signals and the width of the peaks

is the time duration of the slug in front of the detection point.

The light intensity signals from the photodiodes then passed through

the microprocessor unit and were traced on an oscilloscope. The M6800

microprocessor unit gave the facility of signal amplification and also

a variable threshold control which could be used to smooth the signals

into very clear step signals. The microprocessor records a preset

number of slug time lengths and categorizes these into a slug time

54

FZGURE 3.11 Oscilloscope Light Intensity Signals

duration distribution. The two detection points were exactly 25mm

apart and timing slugs of heptane between these points gave the velocity

of flow in the capillary bore. Using the slug times and the velocity

measurements a drop size distribution may be plotted. A graphical

screen (Airmec oscilloscope type 383) was connected to the microprocessor

to display drop size distributions. Figure 3.12 shows a block diagram

of the electronic system used.

The microprocessor was programmed using the MOTOROLA microsystems M6800

program manual. The program required to record slug time data and the

plotting subroutines were stored on magnetic tape (see appendix 5)

3.2 Experimental Procedures

3.2.1 Direct Photography

Before making each experimental run the tank was cleaned thoroughly.

The photographic window attachment shown in Figure 3.4 was secured

into the port required for the particular height of photography in the

tank. The remaining ports in the tank were sealed using brass blanks

55

'C

.I-J

EI-

Inci

-c4-I

ca.'-j

(n

-o

0

04-

Eci

cib

-,C.)0

c-.J

C,-,

L

56

also shown in Figure 3.4. The tank was placed on its supports under

the stirrer motor. The vessel was centered around the impeller,

levelled and the height of the impeller from the tank bottom was

adjusted to be one impeller diameter.

The flash unit was secured above the tank facing down as shown by

Figure 3.3. The periscope tube, shown in Figure 3.5, was used to

guide the light from the flash unit above the tank, down through the

dispersion and out through the photographic window to the camera lens

positioned outside the tank. The gap between the periscope and the

photographic windows was always 5mm.

The appropriate volumes of the continuous phase (water) and the dis-

persal phase (heptane) were put into the tank and the tank lid was

secured. The camera focus was arranged so that the plane of focus

of the photograph was just outside the glass window at the submerged

end of the photographic window. The magnification provided by the

photographic arrangement was determined by photographing a millimeter

scale which was carefully placed inside the tank and near to the photo-

graphic window. Photographs of the scale were taken before each run.

Agitation was started and the smooth speed regulator on the stirrer

motor was used to reach the desired stirring speed. A stroboscope

was used to check the stirring speed. The stirring was continued for

15 minutes before photographs of the dispersion were taken. The flash

unit was discharged and the film in the camera was wound on. The

photographs were taken on 35mm 125 ASA black and white roll film. The

exposure time used was 1/60 second and the camera apertures used were

f 8, f 11, and f 16. The film was developed in ICodak D19-B developer.

The film was washed and dried.

Drop sizing was carried out by projecting the negatives onto the screen

of a cin film analyser, The vertical diameter of each drop was traced

on the screen. The x-y co-ordinates at the bottom and top of each drop

57

were recorded on punched paper tape. The paper tape was read in and

stored as a data file on the College computer system. A program was

written (see appendix 2) to use the data file and produce the drop

size distribution and give the Sauter mean drop diameter for each run.

Between 200 and 300 drops were sized for each run and drop diameters

were measured down to 0.003cm. Some typical photographs of the dis-

persions can be seen in Chapter 4.

3.2.2 Capillary Technique

The tank was cleaned thoroughly before each run. The capillary and

a soft silicon rubber ring were secured into the chosen port of the

tank by screwing a brass cap onto the threads of the tank capillary

holder. The silicon rubber ring sealed the capillary port by tightening

onto the capillary, but it still allowed some movement of the capillary

in the clearance hole of the capillary holder. The remaining capillary

ports were sealed using pieces of glass rod and rubber 0-rings as

shown by Figure 3.3. The capillary was connected to the vacuum pump

by PVC tubing. To ensure reliable drop sampling using the capillary

technique the following conditions must be satiaf led

(I) the sampling must be a representative sample from the chosen

position.

(ii) there must be no interaction (break-up or coalescence) between

slugs of the aqueous and organic phases passing in the capillary

bore.

Various shapes of capillary entrance were studied and a 0.8cm funnel-

shaped inlet facing the flow in the tank gave the most consistent

results for the drop size distributions.

The tank was placed on its supports. The vessel was centered around

the impeller, levelled and the height of the impeller from the tank

bottom was adjusted to be one impeller diameter.

58

The capillary was secured onto the perspex supports and levelled (Bee

Figure 3.7). The perspex supports were attached to optical holders

which were mounted onto the optical bench. The capillary was now

connected to the tank and the optical bench by the soft silicon rubber

ring and any vibrations passing through the capillary from the stirrer

motor and liquid flow in the tank were reduced considerably. The

appropriate volumes of the continuous and dispersed phases were put

into the tank and the tank lid was secured.

The laser mounted on the optical bench (see Figure 3. 9 ) was switched

on levelled and split into two beams which passed directly through the

centre of the capillary without any lenses. The laser light beams were

adjusted using mirrors so that they passed through the capillary 2.5cm

apart. The beams leaving the capillary were directed onto the centre-

lines of the photosensitive areas of the photodiodes which were about

O.75m from the capillary along the optical bench.

The x45 objective lenses were then positioned before the capillary to

receive the split beams. Fine adjustment of the lenses in their holders

was made so that the beams were focused on the capillary bore. Correct

focusing of the beams on the capillary bore will give an image similar

to the diagram given by figure 3.13.

FIGURE 3.j Capillary bore image from x45 lenses

59

The x45 lenses were about 4mm from the capillary wall. The xlO

objective lenses were then placed on the other aide of the capillary

(about 2mm from the capillary wall) to collect the image of the capillary

bore coming from the x45 lenses. At a distance of about O.75m from

the xlO lenses the image of the capillary bore looked like the diagram

shown below as figure 3.14.

FIGURE 3.14 Capillary bore image from xlO lenses

The positions of the centres of the photodiode holders were adjusted

so that the image of the capillary bore, shown In Figure 3.14, fell

across the photosensitive area of the photodiodes.

Agitation was started and the desired stirring speed was set using the

smooth speed regulator and the stroboscope. Sampling of the dispersion

through the capillary for drop size measurement was started after 15

minutes, but in the meantime the optical system was adjusted to enable

the detection between the organic and aqueous phases by the following

procedure.

The appropriate valves were opened (see Figure 3.8) to allow a sample

of the dispersion to be drawn through the capillary by the syringe.

Careful suction using the syringe allowed single slugs of heptane to

be stopped at the detection points and the xlO lenses were carefully

adjusted to give the images shown by Figure 3.15.

a,

0>

Threshc

60

FIGURE 3.15 Image of heptane slugs in capillary

The height of the photodiodes was adjusted so that the high light

intensity centre lines of the heptane slugs were on the photosensitive

areas of the photodiodes. The light intensity readings were then

traced on an oscilloscope screen and the appropriated amplification

of the signal was set to give a high contrast of peak signal for the

heptane and a low baseline signal for the water phase. After 15 minutes

of agitation the suction pump was switched on and the appropriate

valves were opened (see Figure 3.8) to allow a continuous suction of

the dispersion through the capillary. The signals of the light intensity

were traced on the oscilloscope screen and a typical photograph of the

oscilloscope signals can be seen in Figure 3 • l1. The light intensity

signals passed through the microprocessor unit and this gave the

facility of setting a signal threshold which normalised the signal

into perfect step traces as shown by Figure 3.16.

SignaLs from photododes

Signals from microprocessor

Tima

FIGURE 3.16 Light intensity signals

61

The velocity of flow in the capillary was carefully adjusted by varying

the air-b1eed on the pump whilst the step pulses (representing the

times of heptane slug passage) were observed on the oscilloscope screen.

It was ensured that the velocity in the capillary was adjusted finely

for each capillary position to give a reasonable distribution of slug

time pulses on the oscilloscope screen. If the velocity was too high,

extremely short pulses of the same width were observed indicating

possible drop break-up on entrance into the capillary inlet. If the

suction was too low, very long pulses of the same width were observed

indicating a possibility of drop coalescence on entrance into the capillary

inlet. The velocity was adjusted to ensure a steady flow of the dis-

persion in the capillary giving a good spread of pulse lengths.

Measurement of the velocity of flow in the capillary is described towards

the end of this section.

The program written for the microprocessor can be seen in appendix 5

and this was supplied from magnetic tape. It enabled the recording

of the time duration of the peak signals (heptane slugs) and plotting

of the slug time distribution. The program was loaded into the micro-

processor before any experimental runs.

When the dispersion had been agitated for 15 minutes and continuous

sampling had started, the first subroutine of the microprocessor program

was prompted (see programming manual for M6800 microprocessor systems

for operating instructions). The times of peak signal were recorded

for a preset number of heptane slugs (normally _600), categorised

and plotted as the slug time distribution. The number of slugs in

each time category could then be recovered from the microprocessor

memory and recorded for use in the program which computes the drop

size distribution. This program (see appendix 2) uses the velocity of

flow in the capillary to convert all the slug times into lengths, uses

62

the capillary diameter* to calculate the volumes of the slugs and

hence equivalent spherical drop diameters. The equivalent spherical

drop diameters were then categorised into the same drop diameter

ranges as for drop size distributions from the direct photography

technique.

Two or three slug time distributions were recorded for each capillary

position. After this the agitation was stopped and the dispersion

allowed to settle out. The suction pump was left on for velocity

measurement.

The microprocessor was switched into the mode to record the time of

passage of one slug of heptane between the two detection points. The

heptane separated to the top of the tank and only water was passing

through the capillary when the stirrer had been stopped. The low

light intensity signals indicating passage of water showed on the

oscilloscope screen. The stirrer was switched on and the time required

for the first slug of heptane to pass between the detection points was

recorded by the microprocessor. This was recovered from the micro-

processor memory as a number of counts of the microprocessor clock

(operating at 1O5 Hz) and converted to real time. The stirrer was

stopped, the dispersion allowed to separate out and the procedure of

first drop time measurement was repeated. This was done several times

to get the average time of passage of a slug of heptane between 2.5cm

to calculate the velocity of flow for the particular run. The velocity

of flow in the capillary ranged between 50 cm/s and 120cm/s depending

* Water preferentially wets the capillary bore and a correction factor

for the wetting film thickness must be used in the calculations for

drop sizing using the capillary technique. Appendix 6 shows how the

wetting film thickness was determined.

63

on the position of the capillary in the three tanks. Higher velocities

of suction were required near the impeller regions compared with those

near the walls. Reproduction of the velocity measurement was within

10% for any particular run. The velocity was also checked by timing

the passage of 0.5cm 3 of heptane through the capillary past one

detection point and calculating the velocity using the capillary

diameter (corrected for wetting film thickness).

The dispersion was allowed to settle out. The capillary was moved to

another position (normally pushed further into the tank for a particular

capillary height) and the procedure repeated to determine the drop size

distribution.

3.2.3 Impeller Power Measurement

The torque measurement equipment used was supplied by the Warren Spring

Laboratory. The entire drive unit was mounted on a thrust bearing and

supported above the agitated liquid in the mixing tanks. The rotating

agitator imparts a mechanical force which is opposed by the liquid.

The liquid in turn imparts a torque on the agitator which is tz-ans-

mitted through the drive shaft to the motor. This reactive torque

tends to cause the drive unit to rotate on the thrust bearing in the

opposite direction to the agitator rotation. This enables the torque

to be measured by transmitting the force through a mechanical linkage

to a platform scale.

The impeller power inputs to the heptane/water dispersions were measured

over a range of dispersed phase concentrations and stirring speeds for

the 22cm and 44cm tanks. The vessel was cleaned and the dispersion of

a desired concentration was created in the vessel. The torque reading

at increasing stirring speeds was recorded. Using these torque readings

the power was obtained as follows

64

P = Toq

where P = power input (Kgm2/s 3 or Nm/a)

Tq = torque (Nm)

= rate of angular displacement (radians/a)

(2wN or irrpm/30)

A correction factor was applied to the torque measurements which made

an allowance for the friction in the bearings. This correction factor

was determined by measuring the force required to overcome the frictional

bearing forces with the motor turned on and the impeller revolving in

air.

3.3 Investigation of Alternative Detection Methods

This section describes the use of variation in the dielectric constant

and ultraviolet absorption which were investigated for the purpose of

detecting the difference between heptane and water slugs passing through

the capillary. The work was conducted prior to adoption of the laser

light detection technique.

3.3.1 Dielectric Constant

The dielectric constant of a material may be defined as the following

ratio:

field strength in material fcfield strength in vacuum tCo

Consider two parallel plates each of area A (cm 2 ), at a distance r (cm)

apart. The capacity of this electric condenser is given by

c electrostatic units4lTr

cAalso C = 0.08854 - pF

4irr

where c = Dielectric constant (8.854 x l042farad/m for free space)

The following table gives the dielectric constants for glass, heptane

and water,

rnn;Ilary bore

Gtuss woll.

Thin copperstrip

65

Dielectric constant

glass I 5 - 8 (depending on glass composition)

heptane I 1.97

water I 81.0

This large difference in the dielectric constants for heptane and water

was to be used as the contrast for detection between these two liquid

phases as they passed through the capillary. The following model was

considered for calculating the capacitance of heptane and water in the

capillary for a detection contrast. Consider a cross-section across

the capillary,

Copper strip__C' 02 mm

i'5 mm

on of ccipiltnry

bore

If the capacitance between the copper strip on either side of the

capillary can be measured then It may be possible to get a good contrast

between the heptane and water slugs. The copper strip is the same

width as the capillary bore and has the same length as the capillary

outside diameter, The effective area of the strip for detection will

be 0.2mm x 0.2mm.

If glass, heptane or water completely filled the space between the

copper strips then the capacity of the condensers would be

66

glass 1.127 x l0 pP

heptane 2.776 x 10' pF

water 1.141 x 1Q' 2 pP

These capacities are calculated using a distance of 0.2mm between

the copper strips. This assumes that the capillary walls can be

machined so that the glass between the strips was very thin compared

to the bore size. This would have required special machining of the

capillary and the thin glass walls needed at the detection points

would make the sampling probe very fragile.

To measure these values of capacitance and also detect a difference

between heptane and water would be very difficult. After consulting

the electronics department it was decided to find another means of

detection.

3.3.2 Ultra Violet Absorption

This method considered the use of an ultra violet light source for the

detection of heptane and water slugs in the capillary bore. A photo-

multiplier tube was used to measure light intensity readings coming

from the bore of the capillary when heptane and water were passing

through.

Ultra violet was chosen as the light source because, on comparing the

spectra of heptane and water, the cut-off point (wavelength at which

absorption of light is - 100%) for heptane was achieved at a wavelength

of 0.208 jim. At this wavelength the transmission of light through

water is calculated below

Transmission, t = = e4(al(1O)"

where 10 and lo are light intensities entering and leaving

the liquid through a path length, 1 (mm)

Ka absorption coefficient (=9.0 for water at 0.208 jim wavelength)

n = constant (= -2 for water at 0.208 pm wavelength)

w'-IC

4-

ELIQuJ u.%

LI

- 0)4-.

c

0C

cI- ,

LI

67

values for çand n were taken from International Critical Tables (69)

.. t e9 X Q 2 (10)2

... Transmission of water at 0.208 im wavelength = 98.2%

The transmissions at wavelength 0.208 m for water is almost 100% and

zero for heptane. This was the ideal contrast required and the next

step was to find a light source which would emit light of this wave-

length. ?igure 3.17 shows the typical output spectra for various

lamps.

200 4.00 600 800

WAVELENGTH (nanometers)

FIGURE 3.17 Output spectra for various light sources

A deuterium lamp gives the required wavelength of 0.208 pm and, because

one was available, this was used as the light source. A monochromator

was employed to give the required wavelength of the ultra violet light.

The apparatus which was set-up for the ultra violet tests is shown

diagramatically in Figure 3.18.

68

QuarPz SampteCe LI.

I v" DigitaL

0-Deuterium LSLits

VoLtmeter

LampMonochromator PhotomuLtipLier

Tube

FIGURE 3.18 Diagram for Ultra Violet Detection Apparatus

Ordinary glass absorbs all ultraviolet light and therefore quartz plates

were used for the sample cell. Heptane and water were placed between

the quartz plates which were placed in the light beam coming from the

monochromator. The monochromator was adjusted to give the 0.208 pm

wavelength of ultra violet light. The light iltensity readings given

by the photomultiplier tube were shown on a digital voltmeter and they

were as follows:

Digital Voltmeter Reading

mV

main beam 49.36

heptane 1.84

water 36.20

A good contrast was recorded for heptane and water light intensity

readings. However, a problem arose when the choice of a sample cell

which could be practically adopted for dispersion sampling from the

mixing tank had to be made. The dispersion sample would have to pass

continuously through the sample cell and the obvious choice was a quartz

capillary of a known bore size. Capillary made of Vitreosil (pure

silica) were considered and as Figure 3.19 shows this material gives

69

good transmission for the wavelengths to be used.

100

8O

Vitreosil 066LR. Vitreosil

2O

015 020 025 030

WQveength (microns)

FIGURE 3.j9 Light transmittance of Vitreosil

Many manufacturers were contacted for quartz capillaries of bore

diameter 0.15 or 0.2mm but the lowest bore size available was 1.0mm.

Attention had to be turned to another part of the heptane spectra which

would allow ordinary glass capillary to be used. In the infra-red

wavelength range heptane gives over 90% transmission compared to almost

zero for water at a wavelength of 2 pm. Using infra-red as a source

would not require quartz capillaries, but it was found that a very

complicated and expensive means of concentrating and directing the

source onto the capillary bore was required. Very expensive mirror

arrangements were needed and the infra-red source detection method

was also discarded.

Finally it was found that working in the visible light range, on the

wavelength of a helium/neon laser light source, a very good light

70

E• z -I

___ ___ ___ ___ 'HI

C -0

Ii Ij

II

I

I

III

UO!$$,W$UCJj 1U3Jd

71

intensity contrast between heptane and water could be achieved using

ordinary glass capillaries of 0.2 ma bore. This helium/neon laser

light of 0.6328 jim wavelength was adopted for detection purposes.

72

CHAPTER FOUR

RESULTS

4.1 Introduction

The field of study in this investigation was limited to the system of

solute-free heptane/water dispersions with heptane as the dispersed

phase. Measurements of the size distribution of dispersed phase drop-

lets were made using the methods of direct photography and the capillary

sampling technique. Measurements of drop size distribution were con-

ducted over a range of stirring speeds by direct photography and at

various positions in the tank using the capillary technique.

Impeller power input measurements to the heptane/water dispersions were

made for the 22cm and 44cm diameter tanks over a range of stirring

speeds and various dispersed phase concentrations,

4.2 Stirrer Speeds for Constant Power Input/Unit Volume

For constant power input/unit volume a N3D12

Let stirrer speed in 11cm tank = N1

22cm tank = N2

44cm tank = N3

then N1 3Dj = N23D122 = N33D132

!.L. 22/3 N2 - 2and - 213

N2 N3 -(4.1)

Using equation 4.1 the stirrer speeds required in the 11cm, 22cm and

44cm tanks to give equal power input/unit volume were calculated and

are given in Table 4.1. Over this range of stirrer speeds in the three

tanks all the heptane became dispersed in the water phase.

73

N1600 700 800 900 1000 1100

N2378 443. 504 567 630 693

N3239 278 317 357 397 436

TABLE 4.1

4.3 Direct Photography

Drop size distributions of the dispersion were measured by direct photo-

graphy at various heights near the tank wall. The heights of photography

from the bottom of the tank are given in Table 4.2.

DepthTank Heights of Stirrer

of DispersedDiameter Photography Speed

Focus Phase(cm) (cm) (rpm)

(cm) Bold-up

11.0 0.5 20 2.0, 3.0, 5.0, 7.0, 9.0 800

22.0 1.0 20 2.0, 6.0, 10.0, 14.0, 18.0 504

44.0 2.0 20 4.0, 12,0, 20.0, 28.0, 36.0 317

TABLE 4.2

For the photography tests at different heights, only one stirrer speed

was used for each tank. The stirrer speeds given in Table 4.2 gave

constant impeller power input per unit volume in the three tanks.

Drop size distributions were also measured using direct photography over

a range of stirring speeds. In these tests the dispersion was photo-

graphed at the same geometrically similar point in the three tanks.

Table 4.3 gives the stirring speeds used and the positions of the geo-

metrically similar points in the tanks.

74

Height DepthTank

of of Dispersed

Diameter Photography Focus Phase(cm)

(cm) (cm) Hold-up

5.0 0,5 10

11.0

Stirrer Speeds(rpm)

600, 700, 800, 900, 1000

5,0 0,5

20

600, 700, 800, 900, 1000, 1100

22.0

10.0 1,0

20

378, 441, 504, 567, 630

44.0

20.0 2.0

20

238, 265, 280, 300, 317

TABLE 4.3

The drop size distributions, arithmetic and Sauter mean drop diameters,

population variances, cumulative number percentages, and the interfacial

area of the dispersions per unit volume are reported in this section.

4.3.1 Drop Size Distributions

Drop size distributions of 20% vol. fraction heptane dispersed in water

were measured in the 11cm, 22cm and 44cm tanks. Drop size distributions

of 10% vol. fraction heptane dispersed in water were determined in only

the 11cm tank over a range of stirring speeds.

Figures 4.la and b show typical photographs of the heptane/water dis-

persion. A computer result printout for the calculation of the drop

size distribution can be seen on page 85.

Plots of the drop size distributions on a number percent and volume

percent basis can be seen in figures 4.2, 4.3 and 4.4 for the three

tanks. As expected, the volume percent frequency distribution is

shifted towards the larger drop size range when compared to the number

percent plot.

4.3.2 Cumulative Number Percentage

Figure 4.5 shows the cumulative population distribution in normal co-

ordinates on the number and volume basis. The plot on number basis is

75

also shown in Figure 4.6 which is used to compare normal and log-normal

distributions. The log-normal plot gives a curve whereas the normal

probability plot gives a straight line. All other plots of cumulative

number percentage of drops versus drop diameter on normal probability

paper yielded straight lines indicating that the dispersed phase drop-

lets have a Gaussian or normal size distribution. At small drop dia-

meters the results tend to fall below the straight line drawn through

the points at larger drop diameters. The drop size distribution is

therefore normal over most of the size range.

4.3.3 Equal Power Input/unit volume

Figure 4.7 shows a plot of the number precent drop size distributions

for equal power input per unit volume at one geometrically similar

point in the 11cm, 22cm and 44cm tanks. It can be seen that as the

tank size increases the drop size distribution shifts towards the

smaller drop size range and the Sauter mean drop diameter decreases

for equal power input per unit volume.

4,3.4 Variation of Photographic Height

Plots of the drop size distributions of the heptane/water dispersions

in the 11cm, 22cm and 44cm tanks can be seen in Appendix 3. In all

three tanks there is no great change in the shape of the drop size distri-

butions with increasing height from the tank bottom, and only the lowest

heights show a slight shift of distribution to the smaller drop size

range.

Figures 4.8, 4.9 and 4.10 show plots of the cumulative number percentage

of drops versus drop diameter for variation of photographic height in

the 11cm, 22cm and 44cm tanks respectively. A straight line is drawn

through the points on figures 4.8, 4.9 and 4.10 and taking this to be

the mean of the points Figure 4.11 was drawn. Figure 4.11 shows how

the drop size distribution, averaged over five heights in each tank,

76

shifts towards the smaller drop size range with increasing tank size

for constant power input per unit volume. The shift of the drop size

distribution for the 22cm to 44cm tank diameter increase is not as

large as the shift for the 11cm to 22cm tank diameter increase. It

seems as if the drop size distribution is tending towards some fixed

distribution and constant power input per unit volume may give the

same drop size distribution for tanks larger than O.5m diameter.

4.3.5 Variation of Stirring Speed

Figure 4.12 shows the variation of drop size distribution with stirring

speed in the 11cm tank. Plots of drop size distributions for variation

of the stirring speed in the 11cm, 22cm and 44cm tanks can be seen in

Appendix 4. Figure 4.12 shows how the drop size distribution becomes

narrower and shifted towards the smaller drop size range with an increase

in stirring speed.

Figures 4.13 to 4.16 show plots of the cumulative number percentage of

drops versus drop diameter for the variation of stirring speed in the

11cm, 22cm and 44cm tanks. Although straight lines were drawn through

the points for all stirring speeds, this was not justified at low

speeds for the 11cm and 44cm tanks. In general, however, the plots

indicate again the shift of the drop size distribution towards smaller

drop size ranges as the stirring speed increases.

4.36 Population Variance

Figure 4.17 shows a plot of the population variance vs stirrer speed

for the 11cm, 22cm and 44cm tanks. The variance of the dispersed

heptane drop diameter decreases continuously as the stirrer speed in-

creases in all of the tanks in the range of stirrer speeds investigated.

The variance falls as the tank diameter increases for a constant power

per unit volume input from stirring. This is shown in Table 4.4.

77

Tank StirringVariance

Diameter Speed(j2y

(cm) (rpm)

11.0 800 0.0081

22.0 504 0.0033

44.0 317 0.0017

TABLE 4.4

The variances from Table 4.4 suggest that as the tank diameter increases

and the impeller power input per unit volume remains constant, the drop

size tends towards a more narrow size distribution and hence a more

uniform drop size. Figure 4.17 shows that the variance falls sharply

for the 44cm tank compared to the 11cm and 22cm tanks. If the decrease

in variance is compared for the 11cm and 44cm tanks, Table 4.5 shows

that the fall in variance is of the same order when the increase in

stirrer speeds is taken into account.

Tank StirrerVariance A Variance

Diameter Speed (2) A rpm A Variance A rpm(cm) (rpm)

11.0 600 0.025 500 0.022 4,4 x l0

1100 0.0031

44.0 238 0.0061 79 0.0044 5.5 x l0

317 0.0017

TABLE 4.5

The variances for the drop size distributions for the 11cm tank with

dispersions of 10% volume fraction heptane dispersed were lower than

the variances for 20% volume fraction dispersed for the same stirrer

speeds.

78

4.3.7 Arithmetic and Sauter Mean Drop Diameters

For direct photography at the geometrically similar points of 5.0cm,

10.0cm and 20.0cm heights in the 11cm, 22cm and 44cm tanks respectively

Table 4.6 shows the drop diameters obtained for constant impeller power

input per unit volume.

Tank StirrerDiameter

d d32Speed

Sauter Mean Diameter vs.(mm) (mm) Stirrer Speed Relationship

(cm) (rpm)

11.0 0.205 0.279 800 d32 = 1132 N2'

22.0 0.170 0.204 504 d32 217 N15

44.0 0.144 0,164 317 d32 = 22]. N125

TABLE 4.6

The Sauter mean drop diameter decreases as the tank size increases for

constant power input per unit volume. Figure 4,1.8 shows a plot of the

Sauter mean drop diameter versus photographic height from the tank

bottom for the 11cm, 22cm and 44cm tanks for constant power input per

unit volume. The Sauter mean drop diameter is almost constant at positions

above the impeller height but lower values of the Sauter mean diameter

were recorded below the impeller height.

Figure 4.19 shows plots of the Sauter mean drop diameter versus stirrer

speed in log-log co-ordinates for the 11cm, 22cm and 44cm tanks.

Straight lines which gave the best visual fit were drawn through the

points and, as expected, the Sauter mean drop diameter decreases as the

stirrer speed increases. An arbitrary line of slope -1.2 was drawn in

for reference purposes.

4.3.8 Interfacial Area of the Dispersions

Using the Sauter -mean drop diameter the interfacial area of the dispersion

per unit volume was calculated using

79

d32

A plot of the interfacial area versus stirring speed on log-log co-

ordinates would yield a straight line having the same slope as the

corresponding d 32 versus stirring speed plot but opposite iii sign.

The interfacial area versus stirring speed relationships for the 11cm,

22cm and 44cm tanks are given in Table 4.7.

As shown in Table 4.6 the mean drop diameters obtained in the three

tanks at constant power input per unit volume were not the same.

Consequently, the interfaclal areas produced were not the same.

Table 4.7 shows the interfacial areas of the dispersion for constant

power input/unit volume for the three tanks.

Tank Stirrer InterfacialDiameter Speed Area

Interfacial Area vs.

(cm) (rpm) (cm2/cm3) Stirring Speed Relationship

11.0 800 42.92 a = 0.0106

22.0 504 58.88 a 0.053 N 1.15

44.0 317 73.08 a = 0.054 N 1.25

TABLE 4.7

The Interfacial areas of the dispersion for 10% volume fraction heptane

dispersed were higher than those for 20% volume fraction heptane dis-

persed at the same stirring speeds in the 11cm tank.

4.4 Capillary Sampling Technique

This part of the investigation concentrated on the 'mapping' of one

vertical plane in the three tanks for the arithmetic and Sauter mean

drop diameters. Capillary sampling was conducted at 180° to the photo-

graphic windows, at five heights all in one vertical plane and at

several radial distances Into the tank. A typical computer print-out

is shown on page 103.

80

The mean drop diameters obtained at various heights and radial positions

in one vertical plane of the mixer can provide useful information about

the behaviour of drops in the turbulent flow regime. If drop circulation

patterns are known thi8 'map' of mean drop diameters for each tank can

be used to derive local probability functions for drop break-up and

coalescence.

Using all the points of measurement from the capillary technique at

constant power input/unit volume an overall average of the Sauter mean

drop diameter and hence the overall interfacial area can be obtained

for each tank. The overall value of the interfacial area of the dis-

persions calculated from the Sauter mean drop diameter assumes that

the dispersed phase fraction is constant throughout the tank.

4.4.1 Arithmetic and Sauter Mean Drop Diameters

Plots of the arithmetic and Sauter mean drop diameters for five height

and increasing radial distances for the 11cm tank may be seen in

Figures 4.20 to 4.24. Table 4.8 gives the dimensions of the sampling

positions in the 11cm, 22cm and 44cm tanks.

Plots of Sauter mean drop diameter versus radial distance for five

heights in the 22cm and 44cm tanks can be seen in Appendices 8 and 9.

Figures 4.25, 4.26 and 4.27 show the arithmetic and Sauter mean drop

diameters obtained in the 11cm, 22cm and 44cm tanks respectively.

4.4.2 Cumulative Number Percentage

Plots of the cumulative number percentage of drops versus drop diameter

on normal probability co-ordinates for the 11cm tank can be seen in

Figures 4.28 to 4.31. All the plots yield straight lines indicating

that the dispersed drops are of a Gaussian or normal size distribution.

Plots of the cumulative number percentage versus drop diameter for the

22cm and 44cm tanks can be seen in Appendices 8 and 9.

81

Tank Stirrer Capillary Capillary Radial DistanceDiameter Speed Reight From Tank Wall

(cm) (rpm) (cm) (cm)

1.0 0.5, 2.0, 30, 4.0, 5.0

3.0 0.5, 2.0, 3.0, 4.0, 5.0

11.0 800 5.0 0.5, 1.0, 2.0, 3.0

7.0 0.5, 1.0, 2.0, 3.0, 4.0

9.0 0.5, 1.0, 2.0, 4.0

2.0 2.0, 4.0, 6.0, 8.0, 10.0

6,0 2.0, 4.0, 6.0, 8.0, 10.0

22.0 504 10.0 1.0, 2.0, 4.0, 6.0, 7.0

14.0 1.0, 2.0, 4.0, 6.0, 8.0

18.0 1.0, 2.0, 4.0, 6.0, 8.0

4.0 2.0, 4.0, 8.0, 12.0

12.0 2.0, 4.0, 8.0, 12.0, 16.0

44.0 317 20.0 2.0, 4.0, 8.0, 12.0

28.0 2.0, 4.0, 8.0, 12.0, 16.0

36.0 2.0, 4.0, 8.0, 12.0, 16.0

TABLE 4.8 Capillary Sampling Positions

4.5 ComparisOn of Capillary and Photographic Technique Results

Figures, 4.32, 4.33, 4,34 and 4.35 show a comparison of the drop size

distributions obtained by direct photography and capillary sampling at

geometrically similar positions in the 11cm, 22cm and 44cm tanks. Good

agrenent of the drop size distributions and Sauter mean drop diameters

was found, Figure 4.34 gIves the best agreement of Sauter mean drop

diameters. The Sauter mean drop diameter from the capillary technique

is 3% higher than that for direct photography. The agreement in Figure 4.35

82

is around 18% for the Sauter mean drop diameters using the two techniques.

4.6 Impeller Power Requirements

4.6.1 Power Calculation

The stirrer speeds required for constant power input per unit volume

in the 11cm, 22cm and 44cm tanks are shown in Table 4.1. Appendix 11

shows the impeller power requirement calculations and computer result

outputs for the heptane/water dispersions over a range of stirring speeds

and dispersed phase concentrations for the 11 cm tank. A plot of the

calculated impeller power requirement against dispersed phase fraction

for increasing stirring speeds is also shown in Appendix 11.

4.6,2 Power Measurement

Impeller power input was measured for the 22cm and 44cm tanks for a

range of stirring speeds and increasing dispersed phase fractions.

Appendix 12 gives tables of the torque measurements and the calculated

Reynolds and Newton numbers. Figures 4.36 and 4.37 show plots of the

Newton number versus Reynolds number in log-log co-ordinates for the

22cm and 44cm tanks respectively. The Newton number for the 22cm tank

was 6.25 and for the 44cm tank it was 6.4 over the range of Reynolds

numbers tested.

4.6.3 Equal Power Input/Unit volume

The following calculations show that impeller power input per unit

volume was achieved within 2% in the 11cm, 22cm and 44cm tanks.

(A) 44cm Tank

at 317 rpm 20% volume heptane dispersed in water

Measured power input = 58.1 W

.'. power/unit volume = 868.4 W/in3

(B) 22cm Tank

at 504 rpm 20% volume heptane dispersed in water

Measured power input = 7.33 W

power/unit volume = 876.5 W/m3

83

(C) 11cm Tank

at 800 rpm 20% vo1iime heptane dispersed in water

Calculated power input = 0.8987 W

.. power /unit volume = 859,7 W/m3

I-

(

,., 'o

tS4

mm I

Fgure 4.1 a Photograph of a heptane/waterdispersion. (N = 600 rpm, c = 0.2)

j

I

1 mmI

Hgure 4.1 b Photograph of a heptane/water -

dsperson.(N=900rpm,ø=02) -

RUN 1.3 11 CM.DIAMET(R TArJK

20 VoL,pTANE DISPERSED IN WATERSTIRRER SPEED 800 RPMPHOTOGRAPHIC HEIGHT 5.0 CM.PHOTOGRAPHIC LPTH OF FOCUS 0.5 CM.

SIZE MM. NO.OF DROPS TOTAL DROP DIA. OI**2 DI**3*********** ***********************************************************0 - .05 2 8.96287E-2 2.00833E-3 9.00018E-5

.05 - .1 36 2.91933 6,57601E-3 b.33266E-4

.1 - .15 47 5.86611 1.55777E-2 1.94Le27E_3

.15 - .2 66 11.6554 3.11864C-2 b.5Q742E-3

.2 - .25 66 14.7704 .050084 1,121385(-2

.25 - .3 37 1.0.0567 7.38768E-2 2.0Q799E-2

3 - •35 19 6.17157 .105508 .034271

35 - •4 13 4.79788 .136211 .050271- 6 2.55899 .181901 ?.758OeE-2

.45 - .5 1.40296 .218701 .102276

5 - •55 1 .506676 .256721. .130074

uuunnnunuuunnnunnstnununns#uuus*uunARITHMETIC MEAN DROP nIAMETER = .205391 MM.

SAUTER MEAN DROP OIAMrTER , 032 = .280409 MM.

NUMBER OF DROPS SIZED = 296nunu nuts nun nu tin ussnhl#*$ñut$tS#sl sill

is si ** nuts is ii is is is sin s isis t nun nun nun nun unitSTANDARD DEVIATION = 9.05367E-2 MM.

VARIANCE = 8.19689E-3 MM**2n#u#uuntsnuNnnunuuuuuuunnunnssunss

SIZE MM, PERCENTAGE OF DROPS CUMULITIVE NO, PERCENTAGE********$ $ * *********************************************************

0 - .05 .L75676 .675676

.05 - .1 12.1c22 12.8378

.1 - .15 15.8784 28.7162

.15 - .2 2.2q73 51.0135

.2 - .2! 2^.2973 73.310d

.25 - .. 12.5 85.8108

.3 - .3! .4ia92 92.229735 q.,39i89 96.6216

. - .4! 2.U2703 98.64d6

.! i.0i51 99.6622

.5 - .5! .337r38 100.

0

0

0

0

LU

0c-j LU

C)

z .

L

*

0U)0

aoaa 0lbaLIU •10

(Ca 00 lb ID 041a0 •a) -- 0 040 1.4 00aS

aa z aa Li- Ii, -0 Lia Li LI aaLA (0 0 ala- a tLA Iii Dl.ia 0. L.0a lb ela0a- - I- r.40o 0 a-ao0 (-(CO- Li -.0. 0.t Z lalaWZOu a

l... 0 ClaD-- l.Jl&i."O S

z0.zS Ija(00. & L - Li- aao.-t- _iaaa Li• OlaOOara- >Xoolatla-

S flOCt-a o.zav,

*

0

E20z >0—.

o I(I1UJo

Lu

a:

o C)c.J

C)

C)

0

0

-3-

a.'S..

uI

86

a aa •a.aaa IoO,

(.1 .00 (CD

004' 04• 0aa

z Z aa - Li0- (C 0-

0 Li

Li LI aa

Li (C 0 UJ

- a L -0-.

Li Li DIa

a . io a

a W 0Li&a- - - (400 0 EX0

Dl- lb 0

• Li bZ LILiWZD

LI a zo&aa0 . 0 OLiD04 LiLILI04 LiLi...D Z

(C 0.. 0. L - Lilb - aao.-a- ..iaaa Li• oLiODaaa- >a00LiLLi

a I-0 I-Za

0"JO

011 • 0 o-o oo 01-0

A3NflOJJ

0\jo

000 S30 030

S10 010

S0 0AJNJflOJeLJ

87

0.10 0.20 0.30OROP DI1RMETEF (MM

>-C)

LU

uJ

IL

'-4

0

0

00

.

0.40 0.50

Figure 4.4

88

RUN 1.1 11cm DIAMETER TANK

ød 02 N=800rpm

PHOTOGRAPHIC HEIGHT 2-0cm

99.9

99-8

99.5

99O

9 8O

95-0

90-0

80-0LU

70-0

600

500LU> 40-0

30-0

E200

10-0

5•0

2-0

1-0

0-5

02

01

0-0 0-1 0-2 0-3 04

DROP DIAMETER (mm)

Figure 4.5

99.9

996

99.5

99O

9843

950

90•O

800

700wU

600w

50uJ

400

LJ

=

200LU

>

I.- •

50

2•0

1•0

0-5

02

0-1

89

RUN 1.3 11cm DIAMETER TANK

04 = 0. 2 N=800rpm

PHOTOGRAPHIC HEIGHT SOrin

10

10—I

icr

0-0 0-1 0-2 03 04

DROP DIAMETER (mm)

Fgure 4.6 Drop Size Distribution of Heptcine/ Water

DisDersion.

0.10 0.20 0.30 0.40 0.50DROP DIAMETER (MM.)

CD>(Y)c-i.

Lu::

LLJc3

1LCD

0

CD

CD

CD

CD

CDCD

00

90

TankDiameter

(cm)

—*—*— 11•0

—EJ------c3-- 22•0

—O----O— 44.0

Heightof

Photography

(cm)

50

100

200

Depthof

Focus

(cm)

05

1•0

20

Numberof

Drops

Sized

296

200

204

N

(mm) (rpm)

0280 800

0202 504

0164 317

F]gure 4.7 Drop Size Distrbutions for ConstantImpeller Power/unit volume.

91

11 CII. DIF1IIETER TANS

207. VOL. IIEPTANE DISPERSED IN WF1TERSTIRRER SPEED 800 RPM

PKOTODRRPIIIC HEIWIT RUN

-O-W- 2.0 1.1-ø-- 3.0 1.2-A-A- 5.0 1.3-+-+- 7.0 1.4-X-X- 9.0 1.6

9 .99

9 .90B9 .80

B9 .509 .00

B8 .00

5 .00

90.00

80.00

7Q .00

50.0050.0040.00

30.00

20.00

10.00-

5.00-

2.00- 0

1.00-

0.50-cii

0.20-

0.10-

0.05-

0.01-

0.0 0.1 0.2 0.3

DROP DIAMETER0.4 0.5 0.6

(MM.)

x

Figure L.8

92

22 CM. DIRMETER TRNP

207. VOL. HEPTRNE DISPERSED IN WRTERSTIRRER SPEED 504 RPM

PHOTOORAPHIC HEIGhT RUN

-0-0- 2.0 1.12-0-0- 6.0 1.13--- 10.0 1.14-+----+- 14.0 1.15-X---X- 18.0 1.16

099.99

99 .9099 .80

99 .5099.00

a 98.00

95.00

90.00

uJa 50.00

'70.00

LU 60.00cD 50.00

40.00

30.00

u_i 20.00>'-' 10.00

cz 5.00-J

2 001.00

Li 0.50

0 .200.100 .05

0.01 --

0.0

0.1 0.2 0.3 0.4 0.6

DROP DIAMETER (MM.)

Figure 4.9

99.99

99 .9099 .80

99 .5099.00

98.00

95.00

90.00

80 .00

•70 .00

60 .0050.0040 .00

30 .00

20 .00

10 .00

5 .00

2.00

1 .000 .50

0.200.100 .05

0.01

93

44 CM. DIAMETER TANK

20Z VOL. HEPTANE DISPERSEt IN MATER

STIRRER SPEED 317 RPM

PHOTOGRAPHIC HEIGHT RUN

-W-9-- 4.0 1.22

-O-&- 12.0 1.23

----- 20.0 1.24-+-+-- 28.0 1.25-X-)4--- 36.0 1.26

*

C .0

0.1 0.2

0.3

0.4

DROP DIAMETER

(MM.)

Agure 4.10

94

99.9998

99.5

990

980

95•O

90-0LU

B0O

700

- 600

500LU

300LU>20I-

10•0zLi

IT

(cm)

A 110

B 22•O

C 44•O

20

1•0

05

020•1

00 01 02 0-3 04 0-S 06

DROP DIAMETER (mm)

jgure 4.11 Drop Size Distributions of Heptane

Water Dispersions Averaged Over FiveHeights For Constant Power / Volume.

Cr)

>-.(JD

zLU

ci

LLcJ

00

00 0.10 0.20 0.30 0.40 0.50DFOP DIRMETER (MM)

Li)

D

D

0

0

95

11cm DIAMETER TANK

PHOTOGRAPHIC HEIGHT 5-0 cm0-2

N Numb of d33,

(rpm) Drops Sized (mm)

—Q------O-- 1100 202 0189

- - 700 200 0-332

Fgure 412 Drop Size Distribution Variation With

Stirrer Speed.

/

96

11 CM. DIAMETER TANK

lox VOL. JIEPTAME OI6PERSED IN RATERPHOTOGRAPHIC HEIGHT 5.0 CM.PHOTOGRAPHIC DEPTH OF FOCUS 0.5 CM.

6TIRRER SPEED RPM RUN

-1-W- 600 1.32

-0-0- 700 1.33

-*-&- 800 1.34

-+-+- 900 1.35

-X-X- 1000 1.36

99.99

99.9099.80

99 .5099.0098.00

95.00

90 .00

80.00

70.00

60.0050 .0040 .0030 .00

20.00

10.00-

6.00-

2.00- +1.00-0 .50 -

0.20-0.10-0.05-

0.01-

0.0 0.1 0.2 0.3

DROP DIAMETER

0.4 0.5 0.6

(MM.)

jgure 4.13

0

97

II CII. DIAMETER TANK

20Z VOL. HEPTANE DISPERSED IN IfflTERPHOTOGRAPHIC HEIGHT 5.0 CM.PHOTOGRAPHIC DEPTH OF FOCU6 0.5 CM.

STIRRER SPEED RPM RUN

-0-0- 600 1.6

-0-0- 700 1.7

-A-a- 600 1.8

-+-+- 900 1.9

-X-X- 1000 1.10

-G-- 1100 1.11

99 .99

99 .9099.80

LU 99.5099.00

a: 98.00

95.00

90.00

c_ 50.00

70.00

LU 60.0050.0040.00

Z 30.00

LU 20.00>'•-' 10.00

a: 5.00-J

2 00= 1.00C-) 0.50

0.200.100 .05

£

0.01 -1-

0 .0 n I A AU1

DROP DIAMETER0.4 0.5 0.6

(MM.)

Figure 4.14

99 .99

99.9099.80

99.5099 .0098.00

96.00

90.00

80 .00

'70 .00

ij 60.00n so.00

40.00

a 30.00

.LJ 20.00

10.00

5.00 /

2.00 'I

j 1.00Li 0.50

0.200.100.05

0.01

98

22 CM. DIAMETER TANK

20X VOL. HEPTANE DISPERSED IN WATER

PHOTOGRAPHIC HEIGHT 10.0 CM.PHOTOGRAPHIC DEPTH OF FOCUS 1.0 CM.

STIRRER SPEED RPM RUN

-0-0- 378 1.17

-0-0- 441 1.18

--- 504 1.19

-+-+- 567 1.20

-X-X- 630 1.21

*

0

0.0

0.1 0.2

0.3

0.4

DROP DIAMETER

(MM.)

Figure 4.15

99

44 CII. DIAMETER TANK

20X VOL. IIEPTANE DISPERSED IN WATERPHOTOGRAPHIC HEIGHT 20.0 CM.PHOTOGRAPHIC OEPTH OF FOCUS 2.0 CM.

STIRRER SPEEC RPM RUN

-W-- 238 1.27

----O- 266 1.28

--A- 280 1.29

-+-+- 300 1.30

-X-X- 317 1.31

99.99

9g.9c99.80

gg .5099.0098.00

95.00

90.00

60.00

70 .00

50 .0050.0040.00

30 .00

20.00

10 .00

5.00

2.001 .000 .511

0.200.100.05

/

7

0.01 -i---0.0

0.1 0.2 0.3

0.4 0.5 0.6

DFOF DIAMETER

(MM.)

Agure 4.16

100

C.,.

04. (mm)

00 02 11.0

-9-X- 0.1 11.0

-A-A--- 0-2 22•0

-fJ---O- 02 44-0

003

f 002E

wL)

I-,

0-1I--I

3-000•01

?UU 40U 6(K) UU 1UOU

STIRRER SPEED (rpm)

Figure 4.17 PopuLation Variance vs. 5tirrer Speed.

0

0

0

a

101

*

0

0

aII

w1ø

V)

ELC cD ç'L Q -

9-a

QcDQ

43k.

*

co2L/,

-

E

u,c,cD

E

I.-±co'O

- 1Zw

L)

0

0=

-C

•a;

t- 0

Eco oi51?i

c0

(-)0

0

a)

cn

-,-c

a)

0)

ILl

0

U.'cJ0

(ww) Ep

(cm)

04

11•0

0•2

—-.---*- 11 0

01

-0-0-- 22•O

02

44.0

02

10_2.

N•g

-o

102

Ptiotogi-ciiic Depth ofHeight Focus

(cm) (cm)

50 05

5-0 0.5

10•0 to

20•0 20

0

i0- ' IlOt

iü

STIRRER SPEED (rpm)

...flqure 4.19 Sauter Mean Drop Diameter vs

Stirrer Speed.

103

RUN 2.2 11 CPt. DI,METER TANK

20 VOL. 1EPTA1L OISP(SEO Iii WATERSTIRRER S pEED 800 RPMCAPILLARY hEIbHT 1.0 CM.

RADIAL DiSTANCE 0.5 CM.

SIZE MM, N0.OF DROPS TOTAL DROP UIA. nI**2 UI**3*********$ $ ******************************************* ***** **********0 - .05 Ii.0 - .1 39 3.16619 6.59092E-3 5.35080E-4•1 - .15 126 17.046 183022E-2 2.L7603(_3.15 - .2 188 31.5679 2,R1955C-2 4.7344fl..3.2 - .25 78 2.7.6587 5.12538E-2 l.16035E-2.25 - .3 58 15,8799 7.49621E-2 •u2052L,

- •35 8Q 25.879 .104644 3.48509E-2•35 - .4 2L 8.66015 .130205 4.69833E-2.4 - . 45 U

ARITHMETIC MEAN DROP nIAMETER = .202121 MM.

SAUTEK PEAN DROP OIAMFTER , 032 = .245168 MM.

NUMBER OF CROPS SIZED = 593#flflflflflftflUflfl4UtflP#fl*flflflUUfltt

SHISfl1n#UUnflUflflflt*at*fltSt*ufl#U#*ft$flSTANDARO DEVIATION = 7.78713E-2 MM.

VARIANCE 6.06394E-3 MM**2t4flUnuflfl#S1n*4

SIZE MM. NUMBEtC PEHCENTiGE CUMULATIVE NO. PERCENTAGE* ******** * * $ * ******$4 *** ** ** *** ********* *****$******** **0 - .05 0 0 0.05 - .1 59 6.57673 6.57675.1 - .15 12i 21.2479 27.8246.15 .2 188 31.7032 59.527ts.2 - .25 78 13.1535 72.6815.25 - .3 8 9.78078 82.4621

- .35 80 13.4907 95.9528•35 - 24 4.04722 100.

* 0

104

LtDS

LtD

0S

LtD

LtDS

DEe

a:

LU

Lira:

2:

r.

LUI-LU2:a:- I-

LU2:

a: a.. a:e,

IDID

-z c

ID a:Lii LI ID(0 2:

zLU (.3 a:

LiiHo 2:

4- LUID 2:

] LiLi- - I-

-4a: ID CrI-ID- Cr COQLU LULU1U

I I0

ID LU_i. c ic-

N a

CO C.)

UJLiJL)

cna:H-

DUD• I-4

• I-I

CJDcE

D•>-

cc

-JLIJJ

-

a:C.-)

0

-I

0NJ

3

LL1

LID

0

I ic

D

LO

D Lf)D

D

D D

11ftJIU dOJU Nd4

105

LI)S

LI)

D0 a

LI)

U)

-ci

Li

Li

a: Li- -I b-

UJG Li

a: a. a:•

zcn-I

D a:Li Li

Li L)a. LiCo

Lia:

LiLi b- I.- I-

'-ILi a: c £ a:I- I-DI- a: U3Li a. Li Li

a: Li Li I I•U3;; S )IE

LLJ_c

L)

o-

CJCD(J

LOLLJ-ci

DUJ• b—I

CflD

-JLDQ

•C'JD

a:

•>-

a:-J

U)J• b—f

a:C-)

D

-

N

LI)

D

D U) D UJD

Cr) C\J

D

D D D

IW3IU cIDIU NU[4

106

L)

*1* ole

U)

D*

0 .Cr)

Id1-Iii

. — ,-.wa a

00 0

0 • a0

—0

oIa t&I 0to

zUi

s-I (Iito I-- 'Uo

I- IaIii I- I- -

—1,- a'- Co

'U a. Ui

0 •toe

0w-J

-e *a- I I

LU(j

Dcc

• I-.-

jU)'-4D

-Ja:'-4

>-

-JD-J

• I—.

ccL)

C4c.%J

LID* 0

U) DO

Cr) C'J CJ

• • .

0 0 0

(WW) dILJWUIO dOO NUJW

D

w

LO

(1

LD

Cr)LLJ

c-i

F-(flu)

>-,,-LJJ

-J

0I-IL-)

D

jcD uJCr)

D D

D

107

(WJ) di4UIU dOiO Nd4

D

LO

IDS

108

* oil

S

Li

Li

a: Li.-.

LIJ.a..r D Li

a: a:DD '-4

•

za:

Li Li

U) Ez

Li a:

a. '-' w(0 I-

•-. Licz DI-

Z LiLi I- f- I-

Li Cr t C CrI- #- '-. Cr 03Li

a:a. I I

a:

S *-. o p-a: I 1•-' CJU)L)

Li

Lo '-

0LLjLi

CaF-U):1

LOD

—JCJcE

DD

>-,,LJJ

—J

I;

0

-4.

-1

30)

LLj

ID

jcLO cj

(0

C\J

Q

D

•I4l1)

fl14UIO dDO NUL4

9•0

70

F-

Li=

>-

a-Li

3•0

10

109

Fgure 4.25 Capillary Technique Resul.ts

for 11cm Tank.

N= 800 rpm

1 80

14•0

I-=LJ

LiJ

>-

-J-Ji-I3-

Li

6•0

20

110

jgure 4.26 Capillary Techrique ResuLts

for 22cm Tank.

N = 504 rpm

2 6 6 8 10 12 14

111

Figure 4.27 Capillary Technique Results

for 44cm Tank.

N= 317 rpm

ç4 = 0-2

360k 0 00-203 0-206

0-242 0-247

0

d(mm)d (mm)

o 0 0

0-226 0-227 0-235

0252 0-250 0254

2&0 0 0- 0-195 0206

0-215 0-225

w

-J-J-I

Li 200 0 00-195 01880226 0-214

o 0 0

0-228 0221 0225

0-236 0-255 0-251

o 0

0-183 0-179

0-208 0-199

12-0 I- 0 0

0 0 0

0-187 0-206

0-20 8 0-214 0-218

0211 0-221

0-229 0-227 0-228

4-0k 0 0

0 0 00189 0196

0-204 0-208 t}2 3

0- 13 0-213

0-227 0-231 0-223

4 8 12 16

L1C11)

a z -aZO C4NCI-aI.J h

'a- -

C) Illz - -

Ia O- JUDOODz

'a OC'€fl10- D-' a'a

IaI.Jr II I. eo4^X

.-

o eoi+x-. I I— NWO 0

0 —

o

LuI-Lu

C)

a-C)

0

cr,

'a- 0I 0 Z)IDIC0 . -.-ata 'a10 0La -U) U)

a - -a aLI - ..JI00000aU.S 0 - e e In. in

- '-a- aIa QI.JUJ

ILJUJz- III

; .U) ee4+x• Oia.J J

_,5j BO4+X-- CUICLJ

0

C')° (4

Lu

Lu ci,

3

C)

0C)

-'DC)

112

Il)C)

IC)I I I I I I I I I I? I

a) DC) DOD C) C) C) C) C)C)0 C) C) C) C) C) DC) DOLl) .C) 0' C) 11) 00 0 C) C) C) C) C) C) 0 C) C) C) C) C) U) — C) 0C) 0)0) 0)0) C) Lr) CD C) C) C) C) 0 0 C) C) U) C..J — C) ODD C)a, 0)0) 0)0) 0) 0) C) r- CD U) C C'4 -'

9L.JflN AI1U1flL1flJ

U)0

10II I I I I I I 1 I I I I I I I I Ill I

0) DC) C) 00 0 C) C) C) C) C) C) C) C) C) C) C) C) C) —C)C)tflDC) C) 0 0000000 C) 0 0DU)—. D C)

C, 0)0) 0)0)0) U) C) C) 0 DC) C) C) 0 C) ID C.J — 0 000 0a) 0)0) 0)0) 0) 0) 0) 0) C COlD C') CI —

JU1N3Jd J@WflN :jAIIulflI.JflJ

a ua I'1WIOI1 0

0•10 1- a Ca Cl Ca-0

aiu LaCo LIa aLU a- -10 100 0Cu - _j100000I a a .....a a_0- 0acutu a

aa)- 1111Co p-

..Iaa a01CC_I _Ia_I _a

OS4+Xa-a a I I IC4WLJ LI

aaa

a"a

"a

aa

a'-C

El0

I,,

0

LuI-Lu

cict0 D

D

0

•4ja.cII-I

IL

a a"a- a LIaz 0 Z--OJo =ZDIO aaa.J

0a

Cu l.a

CO U

a a

l.a a

Q_ -

a co Ca,

a - -

a a a

IAJ I- J 10 000

a z atu a 0 ONfl- 0. 0Cu 01.al.J aa ujIur aa r

Co) ElC4+a

• OLJJ _aa a.j _C

- 0-a a I I- ClOt) U

0

1')

0

LuI-Lu

eQ0 D

U-

0

0-4-wI_0)ILl

113

U,

0

0I II I I I Ii I I r i I iii

0) 00 00 0 0 0 0 0 000 0 0 0 0 0 00 0010 -. 0a) a) 10 0 0 0 0 0 0 000 0 0 0 0 00 IS) .J -.0 00) 0)0) ala) 0) La 0 0 0 000 0 0 0 LI) C4 - . 0 000 00) 0)0) 0)0) 0) 0) 0) La La U) C'J -

OU1NJ]d 9JflN JAIIW1flI.Jfl3

LO

0

01 00000 0 0 0000000 0 0 000 00100) 0) U) 00 0 0 0 0 0000 0 0 0 00 La a,J-00) 0)0)0)0)0) U) 0 0000000 0 La C.I-00000) 0)0)0)0)0) ala) LaLaU) C-J -

JU1Nd 9WflNJ fI1I31flWfl3

114

.4I-D

0

DIn

0

0

C —.

01')

LiI-U

o a:—I

a-

o D

Cl

a0La I-

*

= F= F

Fa_FE ..

(00a (0

F 00 (010IIC -01- (0100 C CCF3

FF F FF - l.a- 10 -

0 l.aF (U LI CFl.a (0 0 FlU- F l -.(U l.a 01.1C a. la.O CF (0 0(Ua.F- - - (W0o 0 CZ-F00 l-100• l.a a.C F 11Jl.JWZ0U F ZOQFF

_O 01.10- a_IJULIFC- 111.1--C F

CaZC (.)F(CA. a. II. .-. l.a

('1 JFF (U- 0IJC0FF-

F 0IIz -0oC-

Cl-F ZFFF

iI a

**

*

*

. g

r-rI.) 101

0 (D00

I.J C lb C- C.400z

z z-

I.- lb I-C (Ul( 1.(

(U (0 0 IlJ- I_ --(U (U OIUF a. I.D C

(0 0I.Ja-- - - ,WO_O 0

Cl- 100• l.a -a. a.

C Z IaJI.JWZOF-a 0l(O

C a.(.Jl.)IJFl.Jl.a--D 2ta_CF IJF

IC a. a. Ia. - l.a- (U

-F --(0--

Z l400CF C410a.a.ZFW

I0N°

00 030 01

cFA3NflJ

s • 0 0•0

J:CIn

o

*

0 *

0cLLJC

Lu

a:

o D

0

0

0

S10 01.10 S0.0 o(PCFA3NflOJJJ

(N.4a,I-

Li!?

o

hi0g0!

0l

51(-4 I-

*

*

0

0

(4) -

0

0C')

cr

D

a-.

If)(0)

-i

*

115

r r

0.4.) 4004_I

0 .r-0. N 0 N -. -LI - 0- Ifl N N N 000.3

0.30. 0.0. IS.- (0 4-

o II)0. IS) II rtLI (0 0 0.44)

0. I --III 54 014)0. IL 14.0 0.0. (0 tLI0.0.- - - (100 0 3-0.D

o (100• (SI .0 0.0. 0. 5414)1030LI 0.1-0 014)0• @1S)LIU0.L• t1J14J0 0.rarr (.10.(0 & L Is. - IS)0.0.04-0.N .J0.0.0. IS)• 015)000.0.0.- >0.00LILI= - I- to - -0. 44-000.-fl= 00.E0.0.0. C.) 0)0.0.30.10

0vcJ

os . o o•o

0z.0

01 0A3NflCL

0.0.0.

0.1'Si

U)0.0.

C

0.LIN'

0.

0.

0.0.0. • ==(-0.

LIE 4001LI .-.00 4000. • C C.) - NLIo• •0

4- 0)0.3

0. 0.- LI(0 -O fiLI LI 0.0.41) 0 0.LI0. Is. .-(LI CLI4_ (.0 0.(0 0LI0.0.- n10.O 0.0O (-(00LI -0 0.0. LIISJ(0Z00.1-0 01540U) LI LI 0.0.1sJLI"O 0.

(.10.10 0.14. .-. Si• 0.0.01-0.J0. LI0 LI 0 s 0.0.0. 00 LI 0. IS)0.P to - I.-

44 00 0. .-0.0. 0.0.N (00. 0.. Z 0. (1)

0

0

*(0)

0*

Lu

* DICJLLJ

I_-I•:ct4-)D

*

I I I0I0 0E0 030 010 ood

A3NflOJJ

43.-

*

10'

100

116

% HeptoneDispersed n water

01

02

0•3

0-4

0-5

-

-/ -k--

-+ +-

+

u-I

0I-LiJ

REYNOLDS NUMBER

(mean phicot properties)

Rgure 43G

ios

10'

100

ii'

% HeptaneDspersed in water

0•1

- 02

0.3

0•6

05

+

I-LU

z

1

REYNOLDS NUMBER

I mean physical propei-ties)

Figure 4.37

118

CHAPTER FIVE

DISCUSSION OF RESULTS

5.1 Introduction

The results are discussed in a similar order of presentation as in

Chapter 4. References to literature are made wherever possible to

compare the results obtained with the findings of other workers.

5.2 Direct Photography

5.2.1 Drop Size Distributions

The most frequently reported drop size distributions are the normal

and log-normal. For the drop size distributions obtained from direct

photography of the heptane/water dispersions the number frequency was

examined to check if the drops were distributed according to a normal

or log-normal distribution. It was convenient to plot the cumulative

number frequency versus drop diameter on normal probability paper

(see Fig. 4.6). For any single run a straight line (or nearly straight)

resulted from the plot, indicating normality of the drop size distribution.

Most drop sizing techniques provide only a mean drop diameter and few

authors have reported drop size distributions in liquid-liquid dis-

persions. Bouyatiotis and Thornton (31), Chen and Middleman (16),

Luhning (62) and Sprow (17) reported normal drop size distributions.

The distributions obtained by Brown and Pitt (18) and Clarke (63) were

log-normal.

Log-normal drop size distributions have usually been found in dispersions

with high dispersed phase fractions, or when chemical reaction or mass

transfer occurs (65).

(A) Variation of Photographic Height

Drop size distributions of beptane/water dispersions were determined

at increasing heights from the tank bottom in the three tanks with con-

119 -

stant impeller power input/unit volume and 20% volume fraction heptane

dispersed (see Figs. 4.8 to 4.10). The drop size distributions were

very similar in shape for each of the three tanks and only near the

tank bottom was the distribution narrower and shifted towards the

smaller size range. As the tank size increases the drop size distri-

bution becomes narrower for the geometrically similar heights.

(B) Variation of Stirring Speed

Drop size distributions of the heptane/water dispersions were determined

at one geometrically similar point in the three tanks for increasing

stirring speeds. As expected, the drop size distributions become

narrower and shifted towards the smaller size range as the stirring

speed increases. The plots of cumulative number frequency versus drop

diameter on normal probability paper give lines of increasing slope

showing the gradual shift of the drop size distribution towards the

smaller size range as stirring speed Increases (See Figs. 4.12 to 4.16).

5.2.2 Population Variance

The variance of the dispersed heptane drop diameter decreases continuously

as the stirring speed Increases in all of the three tanks. For a con-

stant power input per unit volume the variance falls as the tank diameter

increases. This suggests that the drop size tends towards a more narrow

size distribution and a more uniform drop size as the tank diameter

increases for constant power input per unit volume.

Dispersions of 10% volume heptane dispersed in water were only observed

In the 11cm tank and the variances for these dispersions were lower

than the variances for 20% volume heptane dispersed for the same stirring

speeds.

5.2.3 Sauter Mean Drop Diameter and Interfacial Area

(A) Variation of Photographic Height

A plot of the arithmetic and Sauter mean drop diameters versus the

height of photography near the tank wall shows that above the level of

120

the stirrer in the three tanks the mean drop diameter becomes reason-

ably constant. A straight line may be drawn through these points

(see Fig. 4.18).

Below the level of the stirrer and near the wall the mean drop diameters

were lover than those for heights above the stirrer level. A possible

explanation may be given with the aid of the fluid flow pattern diagram

for the Standard Tank Configuration shown by Figure 5.1

FIGURE 5.1 Standard Tank Configuration Radial Flow Pattern

The flat-blade impeller in the Standard Tank Configuration induced a

radial flow. The region of greatest fluid shear is near the impeller

and as the drops break-up and move away from the impeller, they are

thrown into another shear region at the baffles and the tank wall.

As the dispersion flows radially from the impeller region towards the

baffles and wall, the larger drops will be more bouyant than the smaller

drops and hence it is possible that a larger portion of the smaller

drops take the flow path below the stirrer. Drops striking the baffles

121

and changing direction quickly at the wall will also result in drop

break-up. Also, the volume of the fluid in the sections above and

below the stirrer are divided unequally into 2/3 and 1/3 of the total

volume respectively. Therefore more of the agitation energy is exerted

on the volume of fluid below the stirrer resulting in a higher degree

of mixing of fluid entering the volume below the stirrer and its shorter

circulation time.

Reference will be made to the fluid flow diagram shown in Figure 5.1

and the break-up and coalescence mechanisms possible in different regions

of the tank when the mean drop diameters obtained by capillary technictue

are discussed.

(B) Variation of Stirrer Speed

In order to avoid the complications of interpreting geometrical variations

of the mean drop diameter, photography at a single geometrically similar

point in all three tanks was used to observe the effect of stirring

speed on the mean drop diameter and the interfacial area of the dis-

persion.

Hinze (14) defined a critical Weber number for a drop to break up in

isotropic turbulent dispersion which was an average maximum drop diameter.

Ideally an average maximum drop diameter should be used in the plot of

drop diameter versus stirring speed, but many research workers (16, 17, 18)

have shown a linear relationship between the maximum drop diameter and

the Sauter mean drop diameter. Hence, assuming this linearity, the

Sauter mean drop diameter was plotted against the stirring speeds on

log-log co-ordinates. All the plots resulted in straight lines of a

negative slope and may be expressed by the equation

Cd32 = C6N

where C5 ranged from 217 to 1132 (for N in rpm and d 32 in aim)

C7 ranged from -1.15 to -1.25

122

A plot of the interfacial area of the dispersions against the stirring

speed gave straight lines of positive slope which can be expressed by

the equation

Ca = C8N 9

where C8 ranged from 0.0091 to 0.054 (for N in rpm and a in cm2/cm3)

C9 ranged from 1.15 to 1.25

This was to be expected as a and d 32 are related by the expression

a = 6+/d32

Results obtained by authors using direct photography to determine the

relationship between the interfacial area of the dispersion and the

stirring speed are as follows:

Chen and Middleinann (16) A a

Kafarov and Babanov (66) A a N1

Paviushenko (67) A a N

Bouyatoitis and Thornton (31) A a N 096

Shlnnar (15) predicted a similar relationship with C9 equal to 0.75

to 1.20. He suggested that the interfaciai. area for dispersions con-

taining smaller drops is related to the 1.20 power of the stirring

speed and for larger drops the interfacial area is related to the 0.75

power of the stirrer speed. Luhning (62) found that the interfaclal

area for solute free dispersions which contained large drops was pro-

portional mostly to 0.75 power of the stirring speed. Similarly,

Clarke (63) found that with the water phase continuous in xylene /water

dispersions the interfaclal area was related to the stirrer speed to the

power 0.5 to 0.7 and for xylene continuous the exponent was around 1.0.

123

Less dense dispersions of 10% volume heptane dispersed in water studied

in the 11cm tank gave lower interfacial areas per unit volume than for

the 20% volume beptane dispersions at the same stirring speeds.

5.3 Capillary Technique

The capillary technique has proved to be a satisfactory, quick and

continuous technique for drop sizing and some points about the technique

are discussed here.

The size of the capillary bore restricts the measurement of the lower

range of the size distribution. It is difficult to say how accurately

drops smaller than the capillary bore diameter can be measured. If

drops smaller than the bore diameter travelled along the centre line

of the bore, they could be detected. Consider the three cases of drop

size possible in the capillary shown by the diagram below,

wettino fi'm

(a) (b) Ic)

For case (a) the slug is easily detected and sized. Case (b) where

the drop diameter equals the effective capillary bore diameter the

drop is also detected and the computer program does not convert drops

in this case to an equivalent spherical drop diameter. In case (C),

the drops smaller than the capillary bore will travel along the centre

line of the bore if the drop bouyancy is Just overcome by the velocity

of suction. In practice, there must be a drop size distribution of

droplets having diameters smaller than the capillary bore diameter,

U

C,

U-

124

and the capillary technique ay or may not give accurate information

on the portion of the overall drop size distribution given by the

dotted line in the diagram shown below,

Drop Diameter

ccpUtory

wettedbore

Very small drops can become quickly exhausted in chemical reactions

and mass transfer and it is the larger drops which give the most sig-

nificant contribution to chemical reaction and mass transfer. For the

consideration of mass transfer, the interfacial area calculated from

the mean drop diameters in the macrorange is more meaningful. In fact,

from the material balance point of view, it is the mass, and hence

volume, distribution which is important. Only 3.5% of the drops on a

volume percent basis fell below the 0.15mm drop diameter category.

There is a limit on the lowest size of the bore diameter of capillary.

Many manufacturers were contacted and the smallest capillary bore

diameter available was 0.15mm ± 0.01mm. Capillaries may be manufactured

with smaller bore diameters, but then the pressure drop across the

capillary would become quite large and only very high velocities of flow

in the capillary would ensure a continuous stream of dispersion passing

through the capillary.

The liquid film formed in the bore by the liquid preferentially wetting

the glass will reduce the bore diameter and this must be taken into

consideration. The capillary wetting film in the bore was calculated,

125

see Appendix (6). The filii* thickness was estimated to be 0,03mm which

reduced the capillary bore diameter from 0.2nim unwetted to 0.14mm wetted.

The velocity of flow in the capillary could be measured very accurately

by using the microprocessor to time a slug of heptane to pass between

the two detection points. The capillary technique relies on the fact

that little interaction takes place between the drops as they enter the

capillary inlet and between slugs of dispersed and continuous phases as

they pass along the capillary bore. Wijffels (59) observed that hardly

any interaction took place between neighbouring slugs in the capillary.

If accurate sampling is to be achieved then isokinetics have to be

achieved at the capillary inlet. In this study the velocity of suction

ranged between 50 cm/s and 120cm/s depending on the capillary position

in the tank. It Is difficult to predict the exact velocity of suction

required for each capillary position to give isokinetic sampling.

Therefore, the velocity of suction was carefully adjusted whilst the

step pulses (representing the times of heptane slug passage) were

observed on the oscilloscope screen. It was ensured that the velocity

was adjusted finely for each capillary position to give a reasonable

distribution of slug time pulses on the oscilloscope screen. If the

velocity was too high, extremely short pulses were observed indicating

pssible drop break-up on entrance. If the velocity was too slow very

long pulses were observed indicating possible coalescence of droplets

at inlet to the capillary. Reproduction of the velocity measurement

was within 10% for any particular run.

5.3.1 Mean Drop Diameters

The following general trends can be listed by observing the mean drop

diameters measured in the different positions in the tanks using the

capillary technique.

(I) The drop sizes near the wall of the tank were smaller than

in the bulk of the dispersion.

(iv)

(1

126

(ii) Mean drop sizes in the lower section of the tank below the

stirrer were smaller than those in the upper section above

the stirrer.

(iii)

Drops taking this path initially break up as they hit the

stirrer. Smaller drops near the walls and baffles join the

flow from the stirrer and as the flow goes towards the bottom

corner of the tank, the smallest drop sizes in the tank were

observed. As the drops travel along the bottom of the tank

they grow in size before being drawn into the impeller region

again.

Drops taking this path are smallest near the impeller, and

as they move towards the wall and upwards their size increases.

As the drops move towards the the top of the liquid and back

downwards towards the impeller, the largest drop diameters

were recorded in the region just above the stirrer. The drops

are then drawn into the impeller region. Some of the dispersion

127

may bypass the impeller region on its way down and some smaller

drops resulted in the central regions of the upper section of

the tank.

5.3,2 Cumulative Number Percentage

Plots of the cumulative number percentage versus the drop size all

yielded reasonably straight lines on normal probability paper. This

confirmed normality of the drop size distributions.

5.4 Power Measurement

The experiments were carried out at 25°C and 19°C. Dispersions in the

11cm and 22cm tanks were at 25°C and dispersions in the 44cm tank were

at 19°C. The impeller power input requirements for the 11cm, 22cm and

44cm tanks were calculated at 25°C and 19°C. The mean density for the

dispersion was involved in the calculation of the power and only a small

variation in the power requirement between these temperatures was observed.

0 0The 19 C dispersions required at the most 0.4% more power than the 25 C

dispersions. Power curves plotted from the calculated results for the

11cm tank are shown in Appendix (11).

The measured Newton number was 6.25 for the 22cm tank and 6.4 for the

44cm tank over the range of Reynolds numbers tested. Rushton etal (19)

reported the power number for a six blade flat blade turbines in the

Standard Tank Configuration tanks to be 6.0 at Reynolds numbers of 106.

Laity and Treybal (68) obtained similar results with power number

measurements for dispersions.

5.5 Derived Results

5.5.1 Calculated Sauter Mean Drop Diameter

Comparision can be made between the measured Sauter mean drop diameter

(d32 ) and its calculated value using correlations obtained by other

02

015

128

workers such as Bouyatiotis and Thornton and Coulaloglou and Tavlarides.

Figure 5.2 shows a plot of the calculated and measured Sauter mean drop

diameters against stirring speeds.

O30

035

025

06

600 700 800 900 1000 1100STIRRER SPEED (rpm)

8000 10000 12000 14000

REYNOLDS NUMBER

FIGURE 5.2

At the stirring speed of 700 rpm the d 32 calculated using Bouyatiotis

and Thornton's correlation differs from the measured value by +4%, whereas

at higher stirring speeds they differ by +22%. Using Coulaloglou and

Tavlarides' correlation the measured and calculated d 32 differ by about

129

-12% at 700 rpm and by -3% at 1000 rpm.

Although Calderbank studied a gas-liquid system the d 32 calculated from

his correlation were quite close to those measured with a difference of

about ±3% for the 600-1000 rpm range.

5.5.2 Calculated Clearance Between Drops

Appendix (13) shows the equations used to calculate the number of drops

in the dispersion based on the Sauter mean drop diameter. Assuming the

drops in the dispersion to be arranged on a cubic lattice, the equation

for the clearance between drops, c is given by

1/3

c=d32 {}

-1

at 20% hold-up c = 0.378d32

For a closely packed hexagonal lattice

( l/3C 2d3 rn -1

where dinax = 0.76

at 20% hold-up = 1.12d32

Assuming a cubic lattice arrangement of the drops throughout the dis-

persion, the clearance between the drops was calculated for increasing

stirrer speed in the 11cm, 22cm and 44cm tanks. Figure 5.3 shows a

plot of the calculated clearance between the drops against the stirrer

speed for the three tanks. Figure 5.4 shows aplotof the clearance

against the power input per unit volume for the three tanks.

As the tank size increases and the drop size distribution becomes

narrower and shifted towards the lower drop size range, the number of

drops in the dispersion increases leaving smaller clearances between

the drops. From Figure 5.4 it seems as if the clearance tends towards

a constant value as the tank size increases for a constant power input

C-C-

QC-

cD0'

0

aCr)

0LU

:3

00

0

130

00c'.J

0

0 a

wuJ SdOdO N3]M13 3JNVdV31)

0 —o_____

131

0-20

015

D

LULU

I-LU

LU

Lx

0-10U

0-05200 400 600 800 1000

STIRRER POWER/ VOLUME (W/rr?)

Figure 5.4

132

per unit volume. Tanks larger than O.5m diameter may give more uniform

Sauter mean drop diameters and hence constant clearances for equal power

input per unit volume.

In practice, the arrangement of drops in the dispersion may alternate

between the cubic, hexagonal and other lattice arrangements in the

turbulent flow regime; only the simplified model of the cubic lattice

arrangement has been calculated for comparison in the three tanks.

5.5.3 Comparison of Interfacial Area Using Different Scale-up Criteria

Comparison of the interfacial area of the dispersions of heptane/water

obtained in the geometrically similar tanks of increasing size can be

made on the basis of different scale-up criteria, I.e. kinematic and

dynamic similarity and constant impeller power input per unit volume.

Appendix (14) shows calculations based on

(I) Constant Tip Speed 11 = ND1 = constant

(ii) Constant Reynolds number, Re a ND j2 a uDj

(iii) Constant Weber number, We a ND1 3 u2D

(A) Constant Power Input per Unit Volume

FIgure 5.5. shows a plot of the Interfacial area of the dispersion

against the tank scale ratio for three values of constant impeller

power input per unit volume. The plot gives curves which show an

increase In the interfacial area of the dispersion as the tank size

Increases for each constant power input per unit volume value.

The interfacial area plot in Figure 5.5 was calculated from Sauter mean

drop diameter values obtained by direct photography at one geometrically

similar point in all three tanks. This one point was near the tank wall

and hence a better estimate of the interfacial area was made by averaging

Sauter mean drop diameters over about 25 points using the data obtained

80

70

U

U

u-i< 50

-j

-IL)

LL

LUI-z

30

20

133

I LI.

TANK SCALE RATIO

FIGURE 5.5 Interfacial area vs tank size for constant

power input per unit volume

from the capillary technique. Figure 5.6 shows a plot of the inter-

facial area against the tank scale ratio for one constant power input

per unit volume value with values of interfacial area averaged over

25 geometrically similar points (canillary technique) and 5 geometri-

cally similar points (direct photography).

134

60

70

6O

:°- 40

30

Number of geometricalLy

simikir points used

for averaging d3.

—O-----O— I photography

—*--E— 5 photograp-iy

—O-----E1-- 25 rapiltary

1 2 4

TANK SCALE RATIO

FIGURE 5.6 Interfacial area vs tank scale ratio

(interfacial area averaged over 25 & 5

geometrically similar points)

All the plots of interfacial area vs tank scale ratio for constant

power input per unit volume yield curves which seem to indicate that

the interfacial area of the dispersion tends towards a constant value

for tank diameters greater than O.5m. A possible explanation is that

Hinze (6) based the concept of constant power input per unit volume

(described in section 2.3.1) for flow in stirred tanks upon Kolmogoroff's

theory of local isotronric turbulence. The theories of drop break-up

and coalescence are derived on a single drop model In an infinitely

- 60

LJ

t 60U-

UJ

100

Constant Tip Speed

(U const)cm/s

80 -o----o.--

-*-4- 172•9

-O----O- 192.2

—E-----&.— 2114

20

1 2

6

135

large continuous fluid, The drops in the dispersion are in comparison

very closely packed and there are also boundary effects, i.e. the

presence of tank wall and baffles. It seems that the power losses in

the friction at the walls and baffles and the cushioning effect of the

closely packed drops becomes more important in the case of the smaller

tank which produced lower interfacial areas. For tanks of diameter

greater than O.5m the curve for interfacial area vs tank size may

become horizontal and the concept of equal interfacial area for con-

stant power input per unit volume may well apply.

(B) Constant Tip Speed

Figure 5.7 shows a plot of the interfacial area of the dispersion against

the tank scale ratio for four values of tb speed.

TANK SCALE RATIO

FIGURE 5.7 Interfacial area vs tank scale ratio for equal tip speed

136

The empirical rule of constant tip speed, which is equivalent to

kinematic similarity, satisfied also one aspect of dynamic similarity, i.e.

we u2Dj viscous forcesRe uDj

U surface tension forces

It seems to apply reasonably well to the tanks in question. This may

be explained in terms of the small size of the tanks. On account Of

kinematic similarity the velocity at the tip of the impeller and at

the wall is the same for all of the tanks. In small tanks, say less

than O.5m, the velocity variation between the impeller tip and the

wall may not be considerable and the flow throughout the tank may be

more uniform compared with larger tanks.

(C) Constant Reynolds Number

Figure 5.8 shows a plot of the interfacial area of the dispersion vs

tank scale ratio for constant Reynolds numbers (i.e. uDI = constant)

60

Constun Reyno'ds Number

(uaL = const.)

60

--O----'— 563-6

—*-- 633-9—O------D— 704-9

w

—E1------i— 775-1

40-J

L)

LL

Lu

20

1 2

4-

TANK SCALE RATIO

FIGURE 5.8 Interfacial area vs tank scale ratio for uD4 = constant

E

LiiLX

• 40

'-4Li

LLLX

20

Constunt Weber Number

( u2 O = const)

7x1j

.9x1cP

-610

4x1fj'

137

The drop size in the heptane/water dispersions indicate that the flow

conditions are within the inertial subrange (see Appendix 1). In this

range viscous forces are not important whereas the interial forces

govern the drop break-up and coalescence mechanisms. Since the

Reynolds number is a ratio of the applied to the viscous forces it

follows that scale-up in the inertial subrange cannot really be based

on constant Reynolds numbers. Figure 5 • 8 shows that the interfacial

area falls as the tank size increases for constant Reynolds numbers

so that Re = constant cannot be used as the scale-up criterion.

(D) Constant Weber Number

Figure 5.9 shows a plot of the interfacial area of the dispersion vs

tank scale ratio for constant Weber numbers (i.e. u2Dj = constant).

60

1 2 4

TANK SCALE RATIO

FIGURE 5.9 Interfacial area vs tank scale ratio for u 2D1 = constant

138

As can be seen from Figure 5.9, the scale-up criterion based on a constant

Weber number does not give equal interfacial area for increasing tank

size over the range of tank sizes studied. This shows that dynamic

similarity expressed solely as the ratio of inertia to surface tension

forces does not hold over this range of tank size. A possible reason may

be that the Weber number, as used in dispersion studies, is based on two

different linear dimensions, i.e. the critical drop diameter for drop

break-up or the impeller diameter for scale-up. The Weber number

calculated using different linear dimensions will give different scale-

up of the interfacial area.

139

CHAPTER SIX

CONCLUSIONS AND RECOMMENDATIONS

6.1 Conclusions

1. The concept of constant power input per unit volume as a scale-up

criterion does not give equal interfacial areas in the range of tank

size studied. However, the results seem to indicate that it could be

applicable to large tanks with the model larger than O.5m diameter.

2. Of the other scale-up criteria considered, constant tip speed in

the three tanks seems to give almost constant interfacial areas for

the investigated tank size range but its application to larger sizes

is doubtful. Partial dynamic similarity, as expressed by the Reynolds

and Weber numbers does not give equal interfacial areas for the range

of tank sizes. In the case of the Weber number this may be due to the

use of the impeller diameter as the characteristic linear dimension

rather than of the variable mean drop diameter.

3. Drop size distributions of the heptane/water dispersions studied

using direct photography and capillary sampling were normal size distri-

butions both on number and volume basis. As expected volume percentage

size distributions showed a shift of the distribution plot to the larger

drop size range compared with the plot of number percentage distributions.

The variance of the drop size distributions decreased with increasing

stirrer speed.

4. The interfacial area of the dispersions increased with increasing

stirring speed. Relationships in the form A = C8NC 9 were found with

C9 ranging from 1.15 to 1.25. The latter is in agreement with theoretical

considerations based on drop break-up in the inertial subrange of a

turbulent flow field.

140

5. Sauter mean drop diameters determined using the capillary sampling

technique were on average 16% larger than those obtained by direct

photography of the dispersion.

6. With direct photography of the dispersion near to the tank wall

smaller mean drop diameters were found near the tank bottom compared

with those obtained higher up the tank wall.

7. With the capillary sampling technique smaller drop diameters were

found in the impeller region and near the tank wall compared with other

radial and vertical positions in the tank. It is difficult to say how

accurately drop diameters smaller than the wetted capillary bore dia-

meter were recorded but, as shown by the plot of volume percentage

drop size distributions, only about 4% of the drops fall into size

categories in this range.

8. The stirrer power requirement decreased with increasing dispersed

phase hold-up for a constant stirring speed. The measured Newton

numbers for the 22cm and 44cm tanks were 6.25 and 6.4 respectively.

9. The calculated clearance between the drops in the dispersion

decreases as stirring speed increases. For a constant power input per

unit volume the clearance falls with increasing tank size but seems to

tend towards some constant value. This indicates that the Sauter mean

drop diameter also tends towards a constant value for tanks larger than

O.5m diameter since the clearance/Sauter mean drop diameter ratio is a

constant for a fixed dispersed phase hold-up.

10. Sauter mean drop diameters calculated from correlations obtained

by other authors gave good agreement with those measured in this work.

6.2 Recommendations

1. This study was limited to the study of heptane/water dispersions

and an advisable extension of this work would be to test the applicability

141

of the above conclusions to a much wider range of systems.

2. Only one dispersed phase hold-up was studied and it would be very

interesting to see how the scale-up criteria for drop size are affected

by the variation of hold-up.

3. Tank diameters larger than O.5m must be tested with the liquid-

liquid dispersions to check if the power input per unit volume concept

or other scale-up criteria hold for tanks larger than those used in

this study.

4. The capillary sampling technique can be developed further to find

some means of sampling the range of drop sizes smaller than the wetted

capillary bore diameter.

5. The camera lens extension tube was placed outside the tank for

this study and direct photography could only be used to size the drops

near to the tank wall. An extension tube holding the camera lens can

be designed so that the tube diameter is small enough not to interfere

too much with the hydrodynamics in the tank. The lens extension tube

may then enter the tank and the drop size distribution can be determined

very accurately at various radial and vertical distance in the tank.

6. The present work was restricted to the study of dispersions in the

absence of mass transfer. It has to be extended to cover various mass

transfer conditions with the objective scale-up function changing from

equal interfacial area per unit volume to equal rate of mass transfer

per unit volume.

7. A model of dispersion behaviour which could produce probability

functions of drop break-up and coalescence by parameter fitting should

be developed.

142

APPENDIX 1

CALCULATION OF KOLMOGOROFF EDDY LENGTh

Kolmogoroff has put forward the hypothesis that in amy turbulent flow

at sufficiently high Reynolds numbers, the small-scale components of

the turbulent velocity fluctuations are statistically independent of

the main flow and of the turbulence-generating mechanism. The scales

of the velocity fluctuations are determined from the local rate of

energy dissipation per unit mass of fluid.

Drop break-up was considered to occur in

(1) the inertial subrange - energy transmitting eddies

(ii) the universal subrange - energy dissipating eddies

Kolmogoroff proposed an eddy length, L given by

1

L _PC 1!. ,p1/2 V

where P = power input

V = volume of system

= viscosity of the continuous phase

PC = density of the continuous phase

Sample Calculation:

For the 11cm diameter tank with a 20% volume heptane in water dispersion

stirred at 800 rpm

P = 0.8987 watts

V = 1.045 x lO- in3

at 25°C j = 0.8949 x jØ-3 Kg/msC

p = 997.1 Kg/n3

0.8949(1.045 x io-3J

(0.8949 xL =

(997 1) 1/2

143

L = 3.026 x 10 m or 0.03 mm

The drop diameters measured in the heptane/water dispersions were much

larger than the eddy length calculated above and this shows that the

drop break-up is controlled by conditions in the inertial subrange.

In the inertial subrange the dynamic pressure forces of turbulent

motion, caused by the changes in the fluid velocity over the diameter

of the drop, contribute to drop break-up.

144

APPENDIX 2

COMPUTER PROGRAMS FOR DIRECT PHOTOGRAPHY AND

CAPILLARY TECHNIQUE CALCULATIONS

145

RINTRINTRINT• RI NTRINTRINTRINTRINTPRINTDIM A(2500)DIM C1(500)B=0PRINTPRINT' RUN 1.27 44 CM. DIAMETER TANK'PRINT' ********************************'PRINT' 20 VOL. HEPTANE DISPERSED IN WATER'PRINT' STIRRER SPEED 238 RPM'PRINT' PHOTOGRAPHIC HEIGHT 20,0 CM.'PRINT PHOTOGRAPHIC DEPTH OF FOCUS 2.0 CM.'0=1635FOR H=1 TO 2500INPUT *2,A(H)IF END t2 GOTO 180NEXT HF=4E=2

i DIM 11(500)

R=1D(R)=(A(F)—A(E))/0PRINT 11(R),IF D(R)=0 GOTO 260T=T+D(R)B=B+1GOTO 310PRINTPRINT60T0 480J=0.05x=1IF 1I(R)=0 6010 480IF D(R)<J 6010 380J=J+0.05x=x+1GOTO 340C1(X)=C1(X)+1DIM T(100)T(X)T(X)+1I(R)F=F+4E=E+4

i R=R+1Sc GOTO 2003C Z=0.05

J=0)C PRINT' SIZE MM. ,N0.OF DROPS',TOTAL DROP DIA.'r DI**2','t'I**3'LC PRINT •

DIM W(50)3C DIM 6(50)

FOR X=1 TO 2050 V=V+C1(X)so IF C1(X)0 GOTO 600

W(X)=((T(X)/C1(X))**2)*C1(X)

146

G(X)=((T(X)/C1(X))**3)*C1(X)PRINT;J'—;J+z;c1(X);T(x),;wcx)/c1(x),;G(x)/C1cx)6010 620PRINT;J' — ;j+z, Ci(X)IF C1(X)=0 6010 640

I GOTO 640W=W+W(X)6=6+6(X)IF V=B 6010 670J=J+0.05NEXT XPRINTPRINTPRINT't*$*ttttIt4tttt**tt*tt*tIt4*t**Ittt*t#t*t*t*t*ttt*'PRINT ARITHMETIC MEAN DROP DIAMETER =';T/B'MM.'PRINTPRINT' SAUTER MEAN DROP DIAMETER , D32 ='G/W'MM.'PRINTPRINT' NUMBER OF DROPS SIZED ='BPRINT • tttttIttt*t*t*tt#tttItt*ttt*$*ttttt*$*t$*tt***tt$$'PRINTFOR X=1 TO BE= C (DC X )—( 1/B) ) **2)S=S+E

F NEXT XS1=( S/C B— i) ) **0 .5PRINTPRINTPRINT*tt**Ittttttttt***tttt*t$ttt$$**ttt*t*'FRINT' STANDARD DEVIATION =S1MM,'PRINTPRINT' VARIANCE =S1**2'MM**2PRINT't*t*ttttttttIt*Ittttt*t*tt*4ttttt*$ttI'PRINTPRINTPRINTJ=0Z=0.05PRINT' SIZE MM.','PERCENTAGE OF DROPS CUMULATIVE NO. PERCENTAGE'

5 PRINT' *****************************************************************FOR Y=1 TO 100N=N+C1(Y)IF C1(Y)=0 6010 895P=l00*C1(Y)/BIF P=0 GOTO 900U=U+PFRINT;J'—';J+Z,' ';P,,;u

I GOTO 9005 IF N=B 6010 1000FRINT;.y—';J+z,' ';cl(y)J=J+0.05NEXT Y

)O END

147

PRINTPR I NTPR I NTF RI NTFR IN TP RI NTPRINTPRINTPRINT' RUN 2.35 11 CM. DIAMETER TANK'PRINT ********************************'PRINT 20 VOL. HEPTANE DISPERSED IN WATER'PRINT' STIRRER SPEED 800 RPM'PRINT CAPILLARY HEIGHT 9.0 CM.'PRINT' CAPILLARY RADIAL DISTANCE 4.0 CM.'0=0.14N=1.5V=1200DIM T(50)DIM 0(120)DIM A(120)DIM 11(100)DIM W(50)DIM 6(50)X= 1B=0READ A(X)IF X=100 GOTO 121D(X)=2*( (3*(tu**2)/16)**0.33333333)*( ((2**N)*X*V/100000)**0.33333333)5 S=A(X)*ti(X)6 T=T+S7 B=B+A(X)0 X=X+10 GOTO 701 X=10 Y=10 J=0.050 DIM C(50)0 X=10 IF X=101 GOTO 2400 IF D(X)<J GOTO 2101 Y=Y+12 J=J+0.050 GOTO 170o C(Y)=C(Y)+A(X)2 T1(Y)=T1(Y)+(D(X)*A(X))5 IF X=100 GOTO 2400 X=X+10 GOTO 1700 PRINT5 PRINT0 X=10 Z=0.050 J=0O PRINT SIZE MM,','NO.OF DROPS','TOTAL DROP DIA.',' DI**2','DI**3'0 PRINT' ****************************************************************I0 IF C(X)=0 GOTO 3405 W(X)=( (T1(X)/C(X) )**2)*C(X).0 G(X)=( (T1(X)/C(X) )**3)*C(X)O FRINT;J'- ;j+z, ;C(x), Tl(X), ;w(x)/c(x), ;G(X)/C(X)0 GOTO 360

148

PRINT;j'- J+Z, C(X)V1=V1+C(x)IF V1=B 6010 440J=J+0.05W=W+W(X)6=6+6(X)X=X+1GOTO 300J=J+0,05X=X+1FRINTJ'' ;j+z, ;c(X)PRINTPRINTF RI NTFOR X = 1 TO 100E=( (D(X)-(T/B) )**2)*A(X)S=S+ENEXT XS1=(S/(B-1) )**0.5PRINT' ttttt*tttI*ttttt$tttt**ttt4**ttt*4*4t$*4*4*$I*t'PRINT' ARITHMETIC MEAN DROP DIAMETER ='T/B'MM.'PRINTPRINT' SAUTER MEAN DROP DIAMETER , D32 ='G/W'MM.'PRINTPRINT' NUMBER OF DROPS SIZED ='BPRINT' $44*4I#*$**ttttttIt$ttt*ttttt*4*$*It#*tt*ttt$t$'PRINTPRINTPRINT' ttt$tttt**ttttttttttt*tttt144t14*ttt**t'PRINT' STANDARD DEVIATION =';Sl'MM.'PRINTPRINT' VARIANCE =';S1**2'MM**2'PRINT' 4*t$t*tt*t*ttttt*tt*tttttttt$t*tt**t*$t''J=0Z=0.05PRINTFR I NTPRINTPRINT' SIZE MM. PERCENTAGE CUMULATIVE NO. PERCENTAGEPRINT' ****************************************************************

I P=100*C(Y)/BU=U+PPRINT' ;j'-;j+z,' F,'IF U>99.999 GOTO 1500

I J=J+5YY+1GOTO 550DATA 28,20,21,16,14,15,13,19,21,22,27,33,35,26, 19,16,15, 13,7,5,6,8,6DATA 44v2,1r1,0,5,4,6,3,5,6,4,6,3,3,2,1 ,1,0,0,2,1,4,2,4,110,3,1,21DATA ,0,0,3,2,0DATA 1,0 END

149

APPENDIX 3

DROP SIZE DISTRIBUTIONS FOR VARYING HEIGHTS OF

PHOTOGRAPHY IN THE 11cm. 22cm AND

44cm TANKS

I)

a)

p4

C-)

r

1.-I

HC)

'-4-4

F-'

zI-4

CI)

p4CI)'-4

rx

F-'p4r

HpI,

00a)

p4CI)

F-'Cl)

'-4

C')

a).'*

150

-4

C) Ha) C') a) t -

00 C') N N N.' , ' .' '

4.) C)

'-4

o C) N a) 0)

o '-. In N C) 0)CO ' v-I u-I CO

a In a) a) 00 00

H 0 0 0 0 00 0 0 0 00 0 0 0

0

00

,04 a) N CO 00C) 41) 0) 00 0N C') N C'1 C')

0

CO - 0 '-4 41)C'1 ' t- 00 00 00

H N N C') N NV

o o o 0 0

r u t- N00 0) 0 0 0

H '-I N N N'0

o o 0 0 0

4)0 0 0 0 0

0C) c , a)

p4

v-I N C') ' It)

u-I -4 -4 1-4 v-I

S3 . O 030 S10 900 OOT

A3NJflOJi

A3NJflOJH

Li

Li

D

ci

LiI-uJ

D

D

'Si

LAj

LU

cr

D

D

152

LUI-LU

D

0

D

SZ . O OU 910 010 S00 000A3NJflJ

s . o 030 SPO OPO S00 OO

AN3f101J

RUN 1.12 22 CM. OI/METER TitN<********* , * *******************20 VOL. HEPTANE DISI'ERSED In WATERSTIRRER sPEED 504 RPMpHOTOGRApHIC HEiGHT 2.0 CM.PHOTOGRA pi-IC DEPTH OF rOCUS 1.0 CM.

SIZE MM. NO.OF DRO P S TOTAL DROP UIA. PI**2 OI**3

********* ***********,****,**************************************o - .05 17 .730527 l.84661E-3 ?.93529E-5.05 - .1 51 4.02516 b.22910E-3 '4.91630E-4.1 - .15 57 7.22109 1.60496E-2 .03322E-3.15 - .2 48 8.45767 3.10469E-2 5.47051E-3.2 - .25 17 3.90905 5.2874[-2 1.21581E-2.25 - .3 9 2.38703 7.03449E-2 1.86573E-2.3 - .35 Ii

.35 - .4 1 .377358 .142399 5.37356L-2

n fl flU Ufl PU Si U U 1* U U U U U tin U #n fi U UP U U fi ll 71 U Un U U UUU U U U 1$ H U 7111

ARITHMETIC MEAN DRO P Di AMETER .135539 MM.

SAUTER MEAN DROP DIAMETER 032 .188154 MM.

NUMBER OF DROPS SiZED 200U U U U U flU U nfl U ii n n nn U ti tt U l U U U U U U U U U if U U H 1111 P1111 U U U H U U

U flU U P PU U U 7$ ci U 74 71 Nfl U 7$ U flU U U U U Nfl N 1$ U 7$ PU HUn

STANDARD CE'JIATION 6.29298E-2 MM.

VARIANCE 3.96016E-3 M**2UUUPHUUHHUUUUHPUHUUUUUUUU74UH'IHUUflflPHUH

SIZE MM. PERCErlTAE OF DROPS CUMULATIVE NO. PERCENTAGE

0 - .05 .5.05 .1 25.5 34.1 - .15 28.5 62.5.15 - .2 24 M6.5.2 - .25 8.5 95.25 - .3 4.5 995

o.35 - .0 . 100

ru

Cl)k

ru 0

rururuCl)

0 ru

Cl)

Iru

154

C')

.- C')C)

u-I C) t

C') I) 0)D I) i Il) IC)

4) C)

I-I

CD C1 - U)

C) ' CD IC) cq CoC) Co C') CD -C') C') C') C') C')

•i.I E 0 0 0 0 00 0 0 0 0d00dd

WON0 0 0 cq 00 0 0 0 0C1 C'1 C'I C C4

zq0

- u-I C')CSI Co u-I 0 0 u-IC') u-4 C C' C1 C1

'0 •0 0 0 0 0

CD CD 0 C' IC)C') CD t- COru-I u-I p4 u-4

0 0 0 0 0

4)

0 0 0 0 0

4' u-I ,-I u-I

C C') '' U) COu-I u-I u-I u-C u-I

p4 u-I u-I u-I u-I

o . o 0E0 030 010 Oa.OAJNJfltJJJJ

s . o o•o SPO O•O SO•OA3NflDJJ

cD

ood

0

0

0C'•) -0

Lu

Ui

0—.D

D0

0

U,

0

0-'

0c'

cLu

Lu

0-

0

0

155

0

to

0

C

4°

LJI-uJ

ct

LI-

D0

C

C

C

C(CrC

0 uJI-LU

CC'

D

0D

CD

flfr . fl fl.fl fl7.fl fltfl flfl.IF

158

4:E

a.xuc

0 r-00-

lJ 0 0

z 2l.J

- €0 €-0 Ii

w €0 0 I.J- I_ --I.J t€€ 0I.J

a.c o o€€a.— — - ,w0_0 0

0 €00• €•J a.

2

- 0€UDC€ a.IuL2(.)Zc. tuI€€••0 Z

a_= t€€0 a. a. L — LU

(0 •LU

-t --(0--a noor-=

uro IJcYU (Jt1J UUA3NflJ

0U)

a.€3E •(0

C3 Ono o- 00(Si 00 • 0

xa a- LU€0 -

0 LULU (.3 EX

(Si €I 0 l€i- t•_ •--LU LU OLU

a. (S.D(0 (0LUa.- - _O-

0 00 - €00

• (U —a. a.a ULUWZOU

(-0 OLUDQO bJLU0 2

La.Z U(0 a. a. (S. — LU

• .- (Si

0ISi00- >00wLU

- - e - -a 40O

A3NflO

157

RUN 1.22 4'4 CM. DI AMET E R TANK********** $ *********$***********20 VOL. HEPIANL DISPERS LO IN WATERSTIRRER SPEEO 317 RPMPHOTOGRAPHIC HEIGHT 6.0 CM.PHOTOGRAPHIC DEPTH OF FOCUS 2.0 CM.

SIZE: MM. NU.OF DROPS TOTAL DROP DIA. PI**2 DI*w3*********$ 4

0 - .05 10 .1+35332 1.89514E-3 i3.25017E-5.05 - .1 6.614265 6.25352E-3 14.94523E-4.1 - .15 15 9.03468 1.te5ll2E_2 1.74O5E-3.15 - .2 56 6.169 2.936146E_2 b.03195E-3.2 - .25 14 3.09944 .04901 1,08509E-2.25 - .3 1+ 1.11516 7.77235E-2 2,j.6664E-2.3-.55 U.35 - .1+ 1 .372485 .13874 .16bO5E-2.1+ - .45 1 .41234 .170O2 !.01076E-2

flfl$lfl#flt1fllJ u$#flfl PflflUflUUUUHtUflfln#tU$fltH#ARITHMETIC SEAN DROP DIAMETER = .12124 MM.

SAUTER MEPN DROP DIAMETER • 032 = .178941 MM.

NUML3ER OF DROPS SIZ E D 225fllflfl$ltUffl tiflflUflflflnflflflflUHfltU1flURUflfltU

t$*lItUUUflfl RflflflflflIflflSHUSTANDARD cE\IIATION 5.69751E-2 MM.

VAR1AIICE 3.24b16E-3 Mx*2U14b*Ut*Uu iøtflPnflflftflflUUUUfU1

SIZE: MM. PERCENTAGE oF DROPS LUMULATIVE rio. PERCENTAGE* ******** *4 ** *** **$************** ***** **************** ** *** ** *******O - .05 4.44i44.05 - .1 37.3333 1+1.777b.1 - .15 3.3333 75.1111.15 - .2 lb 91.1111.2 - .25 6.22222 97.3335.25 - .3 1.77778 99.1111.3-.s5 0.35 - .4 .44444 99.555b.4 - .1+5 •41+4444 100.

U)

U)

'-4

p4U)

Up4

U),I-I

'-I

1xz

r4CI)

F-I

rxp4

U)

0 rxi

N U)

(Y)

C)

158

1-I

,l CV)o

C) ,-4 CV) ,-4 C)

C) CI) CO

wa CD CO t- CD CO4' C)'-I

0 CD CO 0 t- '-4C) CO N ' C)

cs1 N i-I t- CO

E c N v-I I-4 N-'-4 0 0 0 0 0

.-.. 0 0 0 0 0

0 0 0 0 0

k

00 It) ' ' t- CI)N 0 0 0 r-4N N N N N

Zq.40

C) CV) '

e1'' t- t- CD t- t-C,, -4 v-f r-4 i-I 14

o 0 0 0 0

I-f ' C) C)N ' 4 CV)v-f 1-4 1-4 ,-4 i-f

o 0 0 0 0

p4

. k#. 0 0 0 0 0

-,-I000 ' N 0 CD CD

0 4) i-f N N C')0

p4

N CV) 4 ) CD

Z N N Cl cl N

1-4 i-f v-I v-I i-I

N

DuJ

'I

D0.a-

0

D

C.)0

010

159

-t

aur ONU0

a o . - -Ia -0 0- ri N N N C Ca

a

a - Iiio -0 I

a IU U EI.J a 0 aaj

a i --

Ia OW

r & U.Da - - IWO-0 o zz-ao

C - I CIa -& C.z wwozO0 a ZOa.aa-0 ClaDC. Ia U 1.1 a aIalU0 Zzax c.aU a. a. 11 - Ui

N .iaaa Ui

a o C Ui r Ui0

z - C C a - aa N O a. a. Z U 10

-I

0 - 3

30

07.Q O10

oc.A3NJflJlJ

aaUiUia0

aI-,

C,,N

z=

aa. E -UE ON

U '•(flOa F-Ca - N • C- Cfl -. N N C Caz a- Cli

10 -C UiCli lJ EUCl) 0a U. - -ia 011iC_ Cl.0 C(0 Olaa.z- -O EE-UCo (00Ia -a. a.z Wla(OZOa ECa.aaClaDa. Ca U U a aUu__o r

10 a. a. U. - Ui

.JarXU CaC Ia C C a a Ua o C ii a ao - a = a aN CO a. a. r a 10

0

0N LJJ0

.Q:

'C

0S 0

Jc • 0 0.0

01 0A3Nfl3JJ

uJ

ci

D

0c

D

160

I')

0S0 030 310 OOJANflOLI

LIE IDOU W

0C- 0 C- — —

IJ — 0- III N N N 00

zJzIJ

1.- I CO -10

LI XWIlD 0 W-I IC.ICJIICJ OW

ICDJw 0IClQ

1 N0DID

• 0_COoIICi

rlz ICJCCJIOZDIo owe

ICJ C.) LIIUJ%U.0 ZI.Z U

CDI • 0E

__ C-I oor00 ICC £

zi C.-0O•11 0

NW 0.0. Z (0

os•o op•o

D

000 0Z0 010 00AJN3flOJdJ

cv,

D

LiJI-LU

c.

0

161

APPENDIX 4

DROP SIZE DISTRIBUTIONS FOR VARYING STIRRER SPEED USING

DETECT PHOTOGRAPHY IN THE 11cm, 22cm AND

44cm TANKS

CD

CD

p4

p4CD'-I

z

0

'-4

E

00p4

o

I-I

'-4

162

-I-I CVC)

C) t- C') SO ø SO-4Q -.-. . .

t.4kC'4 CD N 0 C')

< 0 ,-4 N N C')+ U

'-4

SO ø N NC) - 0 N CD i-I N

CD N C') C') IC)

0 SO ' C') ,-I

i-4 0 p-I 0 0 0 0Ii 0 0 0 0 0

0 0 0 0 0

1.40 0 ' N '

oON CD N 00 0 CDI-I

N C- O ' CDN C) C')C') N N -I r4

o 0 0 0 0

N ''IC) N CD ' NN N u-I u-I u-I

o 0 0 0 0

'4o • -OE 0 0 0 0 0

0 0 0 0 0CD C- CD 6) 0

U)

N C') ' U) CDZ C') C') C') C') C')

- u-I - rl u-I

U)

U)

p4U)

Up4 0U)'-4

F-'w

'-I

C.)

p.

0EC?

r4

c•;i

P4

163

r4

o

' '-I 1- C)

t- U) C ' r-I CV)

C1 CV) I U) CO COC)

I-'

0 C) 0 t- C')

0 C1 C.) - Vt) CV)

r-I CO ,-I U) CO 0

U) ,-4 U) ' C') CV)

C.) v-4 0 0 0 014 0 0 0 0 0 0

0 0 0 0 0 0

14

C.) 0 0 C 0 C.)ON 0 0 0 0 0 0k .r4 r C.) CV) C.) C.) C.)

z

U) CV) 0 C) C) 0C.1 CV) C') U) ,-t C) C)C', ' CV) C.) C.) ,-4 r.4

0 0 0 C 0 0

CO C.) U) u-I CD CV)

0 U) 0 CD CV)

C') CVI C u-I u-I u-I

0 0 0 0 0 0

140 V140E 0 0 0 0 0 0140 0 0 0 0 0 0

CD t- U) C) 0 u-I

u-I u-IU)

0 u-IZ CO F- U) C) u-

u-f u-I u-I u-f u-I u-I

0.10 0.20 0.30 0.40DROP DIRMETER (MM.)

>-L)Zo

uJ

IL0

0

00

0

00Gb .00

164

11cm DIAMETER TANK

Photographic height 5-0 cmcz= 0•2

Numberof

N Drops d

(rpm) Sized (mm)

—O-----O— 800 300 0-280

--.*- 900 202 0•219

—O-----O--- 1000 200 0199

U)

Cl)

z

C,0 U) E

C)0

0

U) 0I-s

F-f

C.,.4: I-I

C)

0 C,0

Cl

C.)

.4:

U).4:

165

I-s

C) a ' C') C) 10 C)• . •

Q) v-I C) U) F- ClIt) It) It) F- U)

4J C)

'-4

U) v-s Cl U) U)a) U) v-I ' U) CO

C) It) U) Cl 0U) U) Cl Cl

a o o o o orI 0 0 0 0 0

0 0 0 0 0

ka) Cl 0 0 0 CD

ON 0 0 0 r-I 0S.r4 Cl Cl Cl Cl Cl

z

C') ' tO It)C') 0 0 It) j'

C) Cl Cl Cl v-s

o 0 0 0 0

F- It) 0 C') ClCO CO F- Cl v-sv-I v-I v-I v-I v-I

V .. • .o 0 0 0 0

a

U) v-I F- 0F- 0 CO C')

4Cz C') ' It) It) COU)

U)

F- U) C) 0 i-IZ v-I v-I v-I Cl Cl

v-I r-I v-I v-I v-I

0.10 0.20 0.30 0.40DROP DIIHIETER (MM..)

C)>—.

2:ttJ

'It,

u—c,

-4

CC

93 .00

166

22cm DIAMETER TANK

Photographic height 100 cm

4- 02

Numberof

N Drops d(rçxii) Sized (mm)

—+—+— 378 202 0234

-&i-----i- 441 200 0203

—Q-----.-D-- 504 200 0204

—*----*-- 567 210 0155

—O----.O— 630 206 0145

U)

U)Iz;1

p.'

F.'C.)

14

'-4

C.)

14

z'-I

L1

p.'U)I-'

r

0

C)0

0

C.)'-4

p.'

167

14

'-I

•1•1 C')o E

N CD U) f-I

N 10 ,-I Cl U)

WØ ' It) CD CD N+' C)

b-I

W N N 10 U) 0

O. U) N 10 10

c.1 0 C') 0) U) N

a3 CD C') Cl Cl r-4

•'-I 0 0 0 0 0

14'_' 0 0 0 0 0

0 0 0 0 0

p.'

Cl I 4 l 1

Cl 0 0 0 0k . 4 cq Cq Cl Cl C.I

U)

I Cl U) U) 'i' It) v-C C) C) CD

C') Cl Cl v-I i-I f-I

0 0 0 0 0

C) Cl 0 It) l'

N 10 CD U) '

r4 v-I rC - p-I

0 0 0 0 0

IIV

U) It) 0 0 NkQ. C') CO 10 0 i-C

.,-Ig,P.' Cl Cl Cl C') C')4) U)U)

N CO 0) 0 i-I

z Cl Cl Cl U) C')

1-4 v-I l v-I i-I

If)

D

D

a(Y

>—.

(_) C

Lu

LiJ

IL. C

C

C

1.68

44cm OLAMETER TANK

Photographic height 200cm

4 02.

Numberof

N Drops d

ir Sed (mm)

—E)------EJ— 280 204 0195

—O-----o— 300 204 0193—*—*— 317 204 0164

.00

0.10 0.20 0.30 0.40DROP DIAMETER (MM.)

169

00

0.10 0.20 0.30 0.40 0.50DROP DIAMETER [MM.)

D

D

(V)

D>-C-)

LU

LUc

LL

-4

D

170

APPENDIX 5

MICROPROCESSOR PROGRAM

001020

MACHINE CODE MICROPROCESSOR PROGRAMME3040

WRITTEN FOR SIZING SLUGS OF HEPTANE60

PASSING THROUGH A CAPILLARY AND GIVING70

A PLOT OF THE DROP SIZE DISTRIBUTION.8090

WRITTEN BY H, DIX00

Z. JANJUA102030

NAM MAIN40 0080 ORG $008050

2131 SLUG EQU $213160

2005 SORT LOU $200570

202C INIT LOU $202C80

204E AXIS LOU $204E90

2081 PLOT EQU $2081;oo

*MAIN PROG10 0080 BD 2131 JSR SLUG;20 0083 BD 2005 JSR SORT

0086 Br' 202C Al JSR INIT40 0089 Br' 204E JSR AXIS5O 008C BD 2081 JSR PLOT60 008F 7E 0086 JMP Al70

END80590

NAM

COLLECT S U BR 1JT IN E100 2131

ORG

$2131110

006C

SAM

EDU

$006C120

*LAST Li A TA IN SAM(EVEN)130

*GET SLUGS SUBROUTINE140 2131 CE 2800

LOX

t$2800ISO 2134 B6 4003 I' A TA

L 0 A A $4003160 2137 2A FB

B PL

Li A TA170 2139 A7 00

STA AX180 21 3B 08

I NX190 213C B6 4002

LDA A $4002

GET LSB500 213F A? 00

STA AX510 2141 08

INX20 2142 9C 6C

C PX

SAM530 2144 26 EE

BNE

DATA540 2146 39

RTS550

END560570

NAM SORT580 2005

ORG $2005590

0067

INOB EQU $0067600

006B

TEMP1 EQU $006B610

006F

TEHP2 EQU $006F620

0070

TEMP3 EQU $0070630

006C

SAM EQU $006C640

*L1IV POWER AT $0071650

*SORT SUBROUTINE660 2005 CE 0000

LOX t$0000

SO 2008 6F 0070 2OCA 0830 2OCB BC 006410 2OCE 26 F8DO 2000 7F 006B1020 2003 CE 280030 2006 96 7140 2008 27 iF50 200A A6 0160 200C E6 0070 200F OF 6780 20E0 C4 7F90 20E2 4400 20E3 5410 20E4 24 0220 20E6 BA 8030 20E8 97 7040 2OEA 07 6F50 2OEC 7C 006B60 2OEF 96 6B70 20F1 91 7180 20F3 27 1090 20F5 96 7000 20F7 20 E910 20F9 A6 0120 2OFB E6 0030 20F0 OF 6740 20FF C4 7F50 2101 97 70'60 2103 07 6F'70 2105 BE 6F'80 2107 96 6F90 2109 26 1100 210B 96 7010 2100 81 64.20 210F 22 OB

0 2111 A6 00.40 2113 81 99.50 2115 27 05.60 2117 8B 01L70 2119 19L80 211A A? 00L90 211C BE 6700 211E 9C 6C!10 2120 27 07220 2122 08230 2123 08240 2124 7F 006B250 2127 20 AD260 2129 39270 212A 3E280 212B 3E290300 0000310 8004320 8006

CLR CLR XINXCPX *30064BNE CLRCLR $006B

*BIVISION BY 2SLOX *32800

DIV2 LDA A $0071BEQ NDIVLIlA A 1,XLIlA B XSTX INDBAND B *$7F

DIVA LSR ALSR BBCC NCORA A *380

NC STA A TEtIP3STA B TEMP2INC TEMP1LIlA A TEMP1CMP A $0071BEQ TSTXLIlA A TEMP3BRA DIVA

NBIV LDA A 1,XLIlA B XSTX INDBANtI B *$7FSTA A TEMP3STA B TEMP2

TSTX LOX TEMP2LBA A TEMP2BNE BIGiLtIA A TEMP3CMP A *362BHI BIOlLIlA A XCMP A *399BEQ BIG2AOl' A *301II A ASTA A XLOX INDBCPX SAtBEQ BONEINXI NXCLR TEMP1BRA DIV2

DONE RTSBIG1 WAIBIG2 WAI

ENDORG $0000

PRX EQU $8004PRY EQU $8006

FIRST DATA ADDGET POWERNO DIVGET LSBGET MSB

MASK FLAG

NO CARRYCARRY 1

GET LSBGET MSB

MASK FLAG

GET PRESENT VALUE

PUT VALUE BACKRECOVER POINTERLAST X?

003C PUP EQU $3C30 0034 PDN EQU $34

0 0000 0063 HYSB RMB 9950 0063 0001 NXB RMB 1f0 0064 0001 NYB RMB 170 0065 0001 OXB RMB 130 0066 0001 OYB RMB 1?0 0067 0002 INDB RMB 2DO 0069 0002 HYSP RMB 210 006B 0001 TEMP1 RMB 1

*PUT PRESENT COORIJ IN A30 *PUT NEW COORO IN B40 *LOAtI X WITH PRX PRY50 *MOVE SUBROUTINE60 2000 ORG $200070 2000 07 6B MOV STA B TEMP130 2002 91 6B TST1 ClIP A TEMP190 2004 23 12 BLS TST200 2006 Oti SEC10 2007 89 98 ABC A t$9820 2009 19 BAA30 200A A7 00 STA A X40 200C OF 67 STX INEIB50 200E CE 1000 LOX *$100060 2011 BD EOE1 JSR DLY170 2014 tuE 67 LOX INDB80 2016 20 EA BRA TST190 2018 27 11 TST2 BEG TST300 201A SB 01 ADD A t$0110 201C 19 BAA20 2010 A7 00 STA A X30 201F OF 67 STX INIIB40 2021 CE 1000 LOX $100050 2024 BD EOE1 JSR IJLY160 2027 BE 67 LOX INEIB70 2029 20 07 BRA TST180 202B 39 TST3 RTS90 EOE1 BLY1 EQU $EOE1100 *INITIALISE SUBROUTINE10 202C CE 8004 INIT LOX $PRX120 202F 6F 01 CLR 1,X130 2031 6F 03 CLR 3,X40 2033 86 FF LBA A FF150 2035 A? 00 STA A X160 2037 A7 02 STA A 2,X170 2039 86 3C LBA A *PUP80 203B A7 01 STA A 1,X90 2030 A7 03 STA A 3XO0 203F 4F CLR A1O 2040 A7 00 STA A X20 2042 A7 02 STA A 2,X30 2044 CE FFFF LOX *$FFFF40 2047 BD EOE1 JSR I1LY150 204A 39 RTS

160 *AXIS SUBROUTINE170 204B BD 202C JSR INIT180 204E CE 8004 LOX IPRX

30 2051 C690 2053 C600 2055 E710 2057 C620 2059 BO30 205C C640 205E E750 2060 C660 2062 BD70 2065 C680 2067 E790 2069 C600 206B CE10 206E BD20 2071 CE30 2074 C640 2076 E750 2078 C660 20Th CE70 2070 BtI80 2080 399000 2081 CE10 2084 8620 2086 A730 2088 7F40 208B 7F50 208E 7F60 2091 7F;70 2094 4F80 2095 LIE90 2097 E600 2099 9610 209B 08120 209C BC30 209F 2740 20A1 OF150 20A3 CE160 20A6 BD170 20A9 97180 2OAB 96190 2OAtI 8B;o 0 2OAF 19510 20B0 16520 20E 1 96530 20B3 1)7540 20B5 CE550 20B8 BLI560 2OBB 20570 2OBD CE80 2000 86

590 20C2 A7o0 20C4 3910

0034019920003C010020003401998006200080043C010080062000

80043401006500660069006A

690066

00641C6980062000666501

6565800420001)880043C01

LOA B t$00XAXIS LIJA B $PDN

STA B 1,XLIlA B D99JSR MOVLIlA B IPUPSTA B iXLDA B $$00JSR tlOV

YAXIS LIlA B WONSTA B ipXLIlA B *$99LOX WRYJRS MOVLOX *PRXLIlA B $PUPSTA B lxLIlA B *$00LOX $PRYJSR MOVRTS

* PLOT SUBROUTINELOX *PRXLBA A WONSTA A 1,XCLR OXBCLR OYBCLR HYSPCLR $006ACLR A

FLOT

LOX HYSPLIlA B XLDA A OYBI NXCPX t$0064BEQ DONESIX HYSPLOX WRYJSR MOVSTA A OYBLIlA A OXBADD A t$01I' AATABLIlA A OXBSTA B OXBLOX tFRXJSR MOVBRA PLOTLOX IFRXLIlA A tPUPSTA A 1,XRTSEN LI

175

APPENDIX 6

THICKNESS OF A WATER FILM WETTING CAPILLARY BORE

When the heptane/water dispersion is drawn through the capillary for

sampling, the water phase preferentially wets the glass. The cylindrical

slugs of heptane, therefore, travel inside a film of water, and a

correction for this must be made in the measurement of heptane slug

volumes • A simple experiment was devised to estimate the water wetting

film thickness.

Firstly the capillary was cleaned and dried thoroughly and it was positioned

between the light detection points which were 2.5cm apart. The time

for a slug of heptane to pass between the detection points was recorded

using the microprocessor. The velocity of flow in the unwetted

capillary bore was calculated. The time required for 0.5cm 3 of

heptane to pass one detection point was then recorded for the unwetted

capillary bore.

The velocity of a heptane slug to pass between the detection points

was again determined but this time water was drawn through first

followed by heptane, creating the wetting water film. Again, the

time required for 0.5cm 3 of heptane to pass one detector after water

had wetted the bore was recorded.

Because the capillary bore diameter is reduced by the wetting film of

water, the same volume of 0.5cm 3 of heptane is transformed into a

longer slug than in the case of the unwetted capillary bore test. Any

significant difference between the time required for the 0.5cm 3 of

heptane to pass one detector for the wetted and unwetted bore cases

will show the existence of the wetting film and an estimate of its

thickness can be made.

176

(1) Times of slug to pass between the detectors (unwetted bore)

The microprocessor clock counts at 100000 Hz and the following counts

were recorded for a slug to pass between the detectors 2.5cm apart:

2500 2100 2100 2400 2300 1900 2200 2300

2900 2500

2320Average time = seconds

iø

2.5 cm/sVelocity of flow =

0 .0232

= 107.7 cm/s

(ii) Times for 0.5cm3 heptane to pass one detector (unwetted bore)

16.6 16.8 16.2 16.6 16.5 seconds

Average time = 16.5 seconds

(iii) Times of slug to pass between the detectors (wetted bore)

microprocessor 2500 2200 2300 2400 2500

clock counts

2380Average time = seconds

2.5Velocity of flow = = 105.0 cm/s

0 .0238

(iv) Times for 0.5cm 3 heptane to pass one detector (wetted bore)

28.7 secs. 28.7 29.0 29.3 Average time = 28.9 seconds

The large difference in the times required by the 0.5cm 3 beptane to

pass in the wetted and unwetted capillary bore shows that there is a

177

wetting film. This wetting thickness may be estimated as follows:

0.5cm3 = ,r(Dw)tL4

where = diameter of capillary bore (vetted)

length of liquid slug

.. 0.5 = 105 x 28.9

0.14mm

The wetting water film has reduced the capillary bore diameter from

0.2mm to 0.14mm, therefore the thickness of the film is 0.03mm.

178

APPENDIX 7

CAPILLARY TECHNIQUE RESULTS lOB 11cm TANI

179

TABLE A7.1 11cm DIAMETER TANK CAPILLARY TECHNIQUE RESULTS

CAPILLARY HEIGHT 1.0cm STIRRER SPEED 800 rpm

20% VOL. HEPTANE DISPERSED IN WATER

CapillaryRadial dAM d32 Number of Variance

Distance Drops Sized(cm) (mm) (mm) (mm2)

0.5 0.202 0.245 593 0.006064

2.0 0.215 0.267 578 0.006205

2.0 0.225 0.277 501 0.006615

3.0 0.233 0.272 559 0.005502

4.0 0.240 0.280 522 0.005656

4.0 0.241 0.281 479 0.005615

5.0 0.232 0.281 470 0.007838

TABLE A72 11cm DIAMETER TANK CAPILLARY TECHNIQUE RESULTS

CAPILLARY HEIGHT 3.0cm STIRRER SPEED 800 rpm

20% VOL. HEPTANE DISPERSED IN WATER

CapillaryRadial dAM d32 Number of Variance

Distance Drops Sized(cm) (mm) (mm) (mm2)

0.5 0.208 0.249 517 0.005001

2.0 0.229 0.252 564 0.005516

2.0 0.228 0.249 513 0.005416

3.0 0.232 0.274 642 0.006005

4.0 0.237 0.271 612 0.006919

5.0 0.240 0.274 444 0.007863

5.0 0.245 0.278 501 0.005979

180

TABLE A7.3 11cm DIAMETER TANK CAPILLARY TECHNIQUE RESULTS

CAPILLARY HEIGHT 5.0cm STIRRER SPEED 800 rpm

20% VOL. HEPTANE DISPERSED IN WATER

CapillaryRadial d d32 Number of Variance

Distance Drops Sized(cm) (mm) (mm) (mm2)

0.5 0.225 0.290 451 0.008581

0.5 0.231 0.283 522 0.006953

1.0 0.224 0.280 461 0.007004

2.0 0.219 0.278 421 0.007329

2.0 0.231 0.284 395 0.007109

3.0 0.215 0.269 567 0.006495

3.0 0.223 0.273 499 0.006204

TABLE A7. 4 11cm DIAMETER TANK CAPILLARY TECHNIQUE RESULTS

CAPILLARY HEIGHT 7.0cm STIRRER SPEED 800 rpm

20% VOL. HEPTANE DISPERSED IN WATER

CapillaryRadial dAM d32 Number of Variance

Distance Drops Sized(cm) (nun) (mm) (mm2)

0.5 0.228 0.281 733 0.007210

1.0 0.236 0.292 668 0.007876

1.0 0.242 0.292 624 0.007238

2.0 0.247 0.287 606 0.005689

3.0 0.243 0.293 636 0.007333

4.0 0.251 0.289 724 0.006177

4.0 0.247 0.295 625 0.007282

0

I

z'-4

Cl)

Cl)'-I

1xz

p4rz

18]

U)

If) If) U) C) U) C)o - 0 C) CV) CV) ,C) U) CD 0 0) 0)CD If) It) t. t- U)

1 0 0 0 0 0 0I. 0 0 0 0 0 0

o o o o d d

o'.4

U) U) 0 CV) ClrI v.1 II) It) CD C')CD U) U) U) CD it)

2P.

It) C') Cl CD If)Cl ' - U) CD t'- C- 0)CV) Cl Cl Cl Cl Cl Cl

0 0 c 0 o d

-' C- '' C) Cl Cl CDCl i-I p-I 'Cl4

Cl Cl Cl 9 Cl Cl

0 0 c 0 d o

___ = = = =

9 9 0 0 0 00 0 r-I Cl

U

12

APPENDIX 8

CAPILLARY TECKNIQUE RESULTS FOR 22cm TANK

183

RUN 2s3r 22 LM. D1/\MF hR TANK*********t*$*********9 **********20 VOL. 1-EPTANL DISPEnSED in WATERSTIRRIR PECD 504 RPMCAPILLARY HEI(t-1T 2.0 CM.

RADiAL DiSTA NCE 2.0 CM.

3IZL MM. NU.OF DRPS TOTAL DROP UIA. [)I**2 Di**3pc ******** $4 ************* $*******W**********************$************

O-.05 '3.05 - .1 56 4.8733 7.5?30'4E-3 b.59030E-4.1 - .15 10.293 1.655132E_2 2.12991E-3.15 - .2 157 3(JQ9L45 3.247#E-2 5.85210E-3.2 - .25 75 16.4939 q.83642E-2 1.U6362E-2.25 - .3 25 6.77943 7,35371E-2 1.99416E-2.3 - •5 3b 11.7684 .10686i ..49.36E-2.35 - ol 11.582 .139585 b.21511E-2

- •45 .80243 .16U97 .u64585.45 - .5 0

sn flu nui 14 nn titin ntt nit unit n tlflH tiH fifitI tin ti ii tin nun nun nun tin nunARITHMETIC MEAN DROP ,)AMETER = .196311 MM.

SAUTEN l'EP N DROP DiAMETER , D32 = .257315 MM.

NUMBER OF DROPS SIZED 472r sin tItsn utiti is tnn nn nnunnnnnunnu#nstnns

fi$ 54 fifi p nnn tin Sifi till fi Ii s+tl itti iits ii si titi nu isSTAND,\RD OEVIA1IO = 7.99351E-2 MM.

VARiANCE 6.6ti962L-3 MM**2t$tsflfiSlPflsinfi s

SIZE MM. NUMEb PERCENTAGE CUMULAT.LVE NO. PL)CENTAGE

o - . 05 0 0 0

.05 - .1 b6 11.8644 1j.8644

.1 - .15 bO 16.9492 28.8136

.15 - .2 157 35.38j4 64.194t

.2 - .25 75 15.8898 80.084/

.25 - .3 5.29661 B5.3814

.3 - ..55 .6 7.62712 93.0085

.35 - .4 1 6.5b78 9°.576

- • 45 2 .423729 100.

184

TABLE A8.1 22cm DIAMETER TANK CAPILLARY TECHNIQUE RESULTS

CAPILLARY HEIGHT 2.0cm STIRRER SPEED 504 rpm

20% VOL. HEPTANE DISPERSED IN WATER

CapillaryRadial dAM d32 Number of Variance

Distance - Drops Sized(cm) (mm) (mm) (mm2)

2.0 0.196 0.257 472 0.006389

2.0 0.199 0.251 455 0.005255

4.0 0.214 0.262 508 0.005893

6.0 0.218 0.273 484 0.006644

8.0 0,222 0.265 486 0.005388

8.0 0.218 0.252 440 0.005249

10.0 0.220 0.265 458 0.005319

10.0 0.223 0.267 444 0.005247

TABLE A8.2 22cm DIAMETER TANK CAPILLARY TECHNIQUE RESULTS

CAPILLARY HEIGHT 6.0cm STIRRER SPEED 504 rpm

20% VOL. HEPTANE DISPERSED IN WATER

CapillaryRadial dAM d32 Number of VarianceDistance Drops Sized

(cm) (mm) (mm) (mm2)

2.0 0.219 0.247 524 0.005473

2.0 0.209 0.238 542 0.004544

4.0 O.2i3 0.268 448 0.006258

6.0 0.217 0.265 514 0.005973

6.0 0.222 0.269 425 0.006165

8.0 0.216 0.267 507 0.006222

10.0 0.225 0.274 542 0.006303

10.0 0.231 0.276 557 0.006027

185

TABLE A8.3 22cm DIAMETER TANK CAPILLARY TECHNIQUE RESULTS

CAPILLARY HEIGHT 10.0cm STIRRER SPEED 504 rpm

20% VOL. HEPTANE DISPERSED IN WATER

CapillaryRadial d d32 Number of Variance

Distance Drops Sized(cm) (mm) (mm) (2)

1.0 0.219 0.275 472 0.007274

1.0 0.225 0.273 506 0.006145

2.0 0.224 0.270 519 0.005997

4.0 0.222 0.270 485 0.006153

6.0 0.212 0.263 491 0.006050

6.0 0.215 0.265 484 0.006277

7.0 0.208 0.263 472 0.007410

TABLE A8. 4 22cm DIAMETER TANK CAPILLARY TECHNIQUE RESULTS

CAPILLARY HEIGHT 14.0cm STIRRER SPEED 504 rpm

20% VOL. HEPTANE DISPERSED IN WATER

CapillaryRadial dAM d32 Number of Variance

Distance Drops Sized() () () (2)

1.0 0.214 0.268 540 0.006607

2.0 0.224 0.276 560 0.007449

2.0 0.217 0.268 452 0.005977

4.0 0.216 0.271 523 0.005653

6.0 0.228 0.280 630 0.006556

6.0 0.235 0.285 644 0.007317

8.0 0.230 0.287 498 0.007379

0

IL,

186

0IL)

p4 F-'

z

F-'r,)

P4Cl)I-I

'-4F-'

F-'

CD 0 u-I C CD C')C) - N N 0) CD 10 N CD

c.J N ' ' ,-4 0) C. CDfl IL) N 0) N N C N

0 0 0 0 0 0 00 0 0 0 0 0 0ddo 00dd

•0

kCI) CD N 01 0) CD CD N

' ' 0) CD CD N C•O IL) IL) ' IL) IL) Il) IL)

_ 0) u-I 0 N u-I N IL)0) CD N CD 0 CD 0

C') 01 01 01 01 C') 04 C')

v #dd dddd

09 CI '' CD CD N' 01 09 u-I C') IL) C') IL)

909010904090 0 0 0 0 0 0

0 0 0 0 0 0

u-I 04 01 ' CD CD CD

0

1210

1210

187

22cm Diameter Tank

0-275

0-250

0-225 2 4 6 8

10

12

(a)

0275

0•250

-0

8

E

l 6b 0225

(b)cio 0-300a

ci 0275

TT02504-J

(c)cii0-300 r

0 -275 - __E'0

0250 2 8 10

12

(d)

:1::

0-250'2 4 6 8 10

12

(e)CapilLary RadiaL Distance (cm)

N=5O4rpm 0=0-2

CapiLLary Heights (a) 20 cm (b) 6-0cm(c) 100 cm (d) 14-0 cm(e)180 cm

a aI.J a aa U

C •Iflr-O2 0

50(0-(0

0

J Ui

Cl) U

a S

Cli C-

(0 (I,2 * -

Co 0Cli - ..jooeooa z a a

UI C 0 *W(0m0- (0 0Cli .CliUi CE WIU Ca aa 11111

. j aa a• 0UI.I _la .a.j _a' 6O4+Xci oa a I I I I ICC CIWU )

C

E

C.,

C

LUI-LU

ciiiC

D

0D

C

188

Ii,

C

ICI I I I I I I Ill I I I I 1 I I I TI I

a, C C C C C C C C C C C C C C C C C C C C C In -' Ca) O)a)L)CD C C DC DCCC C C C DDU)C'iC C

0)

0)0) 0) 0) 0) U) C C C C C C C C C U) c,i .- C C C C C

0)

0)0) 0)0) 0) a) 0 a) r- ID U) C') CI .

Jl1NJJJJd èJ]9flN JAI1d1flIJfl

U)

C

a aUI Cl. C- a ua5 0 2 (nO) (C) * ** .zoci acicicici-(00

(Ci (Ci

(I, U

a z

II C-

2 (1) Cl)

S - -

a o oICC -. .J00000a a a aCu C 0 -CC*(D0

- 0 0 -UI 1.CICJ Ca aa aa II

IC'-iaa C• 01C11 .Ja >a..i _iU

ci a-a a I I I I Ici CIWU IC)

0)a)

0)0)

C

C.,

C

LUI-

LU

ii

a-0

C

ICII I I I I I I I I I I I I I I I I I Ill ICD C C C C C C C C C C C C C C C C C CDII) - C0) a) ID C C C C C C C C C C C C C C C It) Ci -. C C

0)0) 0) 0) 0) Ii) C C C C C C C C C U) Ci . C C C C C0)0)0)0)0) 0)0) a)rWDCfl CS -

1I4JJJJd L9L.JflN AI1U1flI4fl3

a.Wft.E- a. 1.3a.5 0 Z

• .ZD• a.— hI —C

haJ sQ

hI LI

a. zw —hi)

z —

a. 0 0

sQ - _J00000

a. z a.sQ a. 0- -0 — 0SQ .IQ%U a.E .JWZ a.a. za 11111

U

..Ja.a. a.• euJ_I _ir S'a...J .Jo

;:N 0-a. a. IDi L'JIOCJ LI

a

CS,

O

LiJI-LiJ

c. ctc;'—•

D

a—CD

0

U,0

0'

C.,0

LUI-Lu

c0

CD

0CD

0

189

U)

0

0) 00 000 0 0 0 0 000 0 0 0 0 000 DOLt)

0) 0) LDO 0 0 0 0 0 000 0 0 0 0 00 LI) C'J.-.0

0) 0)0) 0)0) 0) U) 0 0 0 DOD 0 0 0 U) C.J 0 ODD

0) 0)0)0)CJ)0) 0)0) 0)LI0U)(')CI -

OU1NJJèJd J9JflN AI1I1flJfl3

- a. LIa.

0 5 Ii) hi) 5)1)1)V • 0

50 0 a. Di Di C,h N N— Li) —0

SQ 531(I) U

a. Sa.

a. -

S UI SD

z -. -

a. 0 0

SQ h 0 0 0 00

a. S a.SQ a. C -- 50 CSQ a.su1a a.S LSJIQX a.a. EO4+X.-ia.a. a.• OIQJ _J

S a._J _J

N Da. a. I I IN N1DLI LI

0) 00 0 00 0 0 0 0 000 0 0 0 0 0 0 0 CD LI)0) 0)0) U) 0 0 0 0 0 0 000 0 0 0 0 00 Il) 04-.0

0) 0)0) 0) 0) 0) U) 0 0 0000 0 0 0 to -. 0 000

0) 0)0)0)0)0) 0)0) 0) CS,C.J ..

IN3d JJ9I4flN AI1U1flI4flJ

99.9099 .80

99 .5099.00

cc 98.00

95.00

90.00

a 80.00

70.00

Ui 60.00n 50.00

40.0030.00

uJ 20.00>

10.00

a: 6.00-J

2.001 .00

ci 0 .50

0.200.100.05

0.01

190

22 CII. DIAMETER TANK

20X VOL. HEPTANE DISPERSED IN WATERSTIRRER SPEED 504 RPMCAPILLARY HEIGHT 18.0 CII.

CAPILLARY RADIAL DISTANCE RUN

-O-- 1.0 2.66-ø--O-- 2.0 2.66-&-A-- 4.0 2.68-+-+-- 6.0 2.69-X---X- 8.0 2.71

99.99

0.0 0.1 0.2 0.3 0.4 0.5

DROP DIRMETER (tIM.)

191

APPENDIX 9

CAPILLARY TECHNIQUE RESULTS FOR 44cm TANK

KUN 2.72 't+ .l. UIAMEILI T/N\*********** ************4 ********2u VOL. LPIM,g t. UlSe'EI<SLO JIJ WMTEKSIIP'J'U:..R SPtLU 31F I<PM

CIILLt p Y hLIbnT 8.0 CM.CJ'1LLARY RAL)IML D1ST,NCE 2.0 CM.

SILt- MM. Nu.UF ORjI-'S TOAL DROP VIM. OI**2

- .1

5.2lUUê 5.114b1-3

.1 - .15 09

11.L1279

- .2 72 t9.O34 6.21.9ebE_2

.2 - .5

54.0965 +.9U2UbE-2

.2 - .3

2.i6O2 7.16261E-2

.3-..5 2 .600616 .O9318

.35 - . u

4 .qb'46o-'4

2.11705E-3

•

1 .U535E-2• 1695E-2

2.70833E-2

UU0RUUUUU#R#UP0H SI UUUUUU UUflUtS

ARIIHr'ETIC MEMN DROP DIAMETER = .18927 MM.

SAUILK MEJN 1)KUP D I AME ILR , D32 = .212t14 L4 MM.

NuMbEK OF CRO-'S SIEO = 656UUUHUUUPUHUU#UUURR#UUU#

U U 000 U U U U a U 0 U U flU U o n U H U 5$ SI U fits 5$ 5$ U U nfl U $4 U U

S1ANL)iRD 1JLVluIIO(. = 5.23772E-2 MM.

V4P'UANCE 2.I+37L-3 MM**25$ U UP fi#n P U U U H U U #0 5$ U tin H U HUH PSi SI SI U U U U U U $4 U 5$ U

SILt. MM. PERLLNTAC,[ CUMULATIVE 'JU • I'ERCEISflMbE********* 4 44********U - .05 0 u.0 - . 64024Ls.1 - .15 13.5671 L9.'695

- .2 b1.q.29.2 - .25 2.4756 bLl.9U85

- .3 1&,./866 '9.b51- .3c .U487i3 .LLj(j.

193

TABLE A9.1 44cm DIAMETER TANK CAPILLARY TECHNIQUE RESULTS

CAPILLARY HEIGHT 4.0cm STIRRER SPEED 317 rpm

20% VOLUME REPTANE DISPERSED IN WATER

CapillaryRadial dAM d32 Number of Variance

Distance Drops Sized(cm) (mm) () (mm2)

2.0 0.189 0.213 656 0.002743

2.0 0.207 0.229 677 0.003335

4.0 0.194 0.213 554 0.004520

8.0 0.204 0.227 650 0.003637

12.0 0.208 0.231 612 0.003811

12.0 0.200 0.217 540 0.004849

16.0 0.203 0.223 673 0.003061

TABLE A9.2 44cm DIAMETER TANK CAPILLARY TECHNIQUE RESULTS

CAPILLARY HEIGHT 1LOcmSTIRRER SPEED 317 rpm

20% VOLUME HEPTANE DISPERSED IN WATER

CapillaryRadial dAM d32 Number of VarianceDistance Drops Sized

(cm) (mm) (mm) (mm2)

2.0 0.187 0.211 450 0.003101

4.0 0.206 0.221 910 0.002853

8.0 0.208 0.229 677 0.002810

8.0 0.219 0.235 831 0.003025

12.0 0.201 0.227 532 0.003495

12.0 0.214 0.227 489 0.004928

16.0 0.218 0.228 491 0.003581

194

TABLE A9.3 44cm DIAMETER TANK CAPILLARY TECHNIQUE RESULTS

CAPILLARY HEIGHT 20.0cm STIRRER SPEED 317 rpm

20% VOL. HEPTANE DISPERSED IN WATER

CapillaryRadial dAM d32 Number of Variance

Distance Drops Sized(cm) (mm) (mm) (mm2)

2.0 0.195 0.226 615 0.003927

4.0 0.188 0.214 529 0.003673

8.0 0.189 0.202 531 0.003216

8.0 0.183 0.208 538 0.002888

12.0 0.179 0.199 602 0.002574

TABLE A9.4 44cm DIAMETER TA1K CAPILLARY TECHNIQUE RESULTS

CAPILLARY HEIGHT 28.0cm STIRRER SPEED 317 rpm

20% VOL. HEPTANE DISPERSED IN WATER

CapillaryRadial dAM d32 Number of Variance

Distance Drops Sized(cm) (mm) (mm) (mm2)

2.0 0.193 0.226 419 0.003688

2.0 0.195 0.215 501 0.003516

40 0.223 0.234 646 0.002149

4.0 0.206 0.225 644 0.003408

8.0 0.228 0.236 639 0.004241

12.0 0.221 0.255 550 0.004543

16.0 0.204 0.231 543 0.003823

16.0 0.225 0.251 367 0.004643

I.-'

p1

195

cl

U)a)

C) ' C) 0 C) NU C) co t- c cv) co

-' It) C') CC 0 CC

C') C') C') '- 0 0 0 0 0 00 0 0 0 0 0. . . .

0 0 0 0 0 0

.1Wop

'' 0 U) C) N

N C') t- CC t- '

CD co C) U) '

N L- It) N 0c'1 It) It) It)C" N N N N N N

0 0 0 0 0 0

C') CD N CD t- It)0 0 N N N CV)N N N N N N

011,_I C.)0 0 0 0 0 0'-I E • •

N CC CC N CO

C.)

024

0-22

020

0•2'.

0-22

G' 0.20-4-,

E• 0-23a

cioLD 0-21

CCC)

019C)

4-aJC

u-I

025

0-225

0-20

0275

0

o 0

2 4

OZ0I I

2 4

0

2 4

2 6

19644cm Diameter Tank

0

0

I I

- 6 8 10 12 16 16

(ci)

0

0

6 8 10 12 16. 16

(b)

1s

(c)

6 8 10 12 14 16

(d)

.:::r TrT:(e)

Capit(ciry Rada( Distance (mm)

N=3l7rpm 0=0-2

Capfttary Heights (a) 4-0cm (b) 12-0 cm (C) 20-0 (d) 280 cm Ce) 36.0cm

a rLi- aa

0

z - Cd- Cfl -

0LiU)aLia-U)

z -a 0

Li -a ZLi- 0Li a-LiLJE LiLi

- CD,-o - a_, a aaC_I a-

C-: - a-

- C-:WU

O - C ID I-a c C C C C

C Cd Cd CM Cd Cd

LiI-,a

U,aJ 00 0 00a .....- C4 C Cd ID

a - -CC

EJO• +xC-J-i

£104 +Xa III I II-I

C

C,,

C

LU

LU

C

C

C,,

C

LUI-LU

Cd---I

C D

a-

C

197

LI,

C

0)0)

0)0)

CI I I I I I I 1 T I I U C I III

CC C C C C C C CCC C C C C C CCC CCLI, - C

0)0 U) C C C C C C DCC C C C C C C U) (.J.0 C

0)0) 0)0)0 U) C C CCCC C C C tO Cd -. C CCC C

0)0)0)0)0) 0) 0) 0WU,0Cd -.

OU1NJJd 9WflN AI!U1flI.1fl3

LI)

C

a

Li a. a- C

C CMIOIDC0 ZNFFt

C-.- - -C NCdCdOJ

- In

0

Li LiU,

a a

Li C

a_ -

Ci) CD

a -. -

CD 0

- Li - 0000

C C C • • -Li a 0 NCCM- -0- C) -Li 3.LIU cr

CC- (0C--

CC C• CIi.C.J _Ja ,-aj _IC-'

- o.-a a I I- CMCDCJ C.)

0)0)

0)0)

-

ICI I I I II I I I I III I

CC C C C C C C C C C C C C C C C C C C C U) CO)0%DCC C C C C DCCC C C C CC)CJ.0 C

0)0) 0)0) 0 Ii) C C C C C C C C C LI) Cd — C C C C C0)0) 0) 0) 0) 0) 0) 0 r- (OW C') Ci

JU1NJJd 1J9WflN ]AI1J1flWflJ

C.J a.- I_I

0I-

z -- I., C.

a"ain

-sa.

t Inz

aLi -z z

Li 0- '-0.-.LiE 1UkJ

ra.- s0)..o

_J• 0-s__i

C_i -.- a.

,. 0_-NWU

o -a a a aZ 0)0) - - -I.J N N d N

'SiLIaIn

C

J 00 0 a a- N N IDa .- -I'll'

-j-j

o4+xI'll'

U

C,)

O

LU

LU

c. a:D

0

0

C,,O

LUI-LU

Da-

0

198

U,

0

0) D0OQ 0 0 0000000) 0)a)00 0 0 000000

0) 0)0) 0 0) a) U) 0 0 0 D) 0 00 O)0 a) 0) 0) 0) 0) a) C CD CD 0)

Cd1NJd 9I4flN

IDI I I IT I0 0 0 000 00W -c C 0 DDU)C.J-0 cO 0 U) C4 -. 0 000 0c.J —

Ah1J1flL4flJ

to0

= rLa a.- LI

C 00Naa-c CNNeiC.4

I•) N0

Li Li

U) CI

a a

Li C

a. -

CO UIa - -

CO 0Iii - j e 000

a a C •"a C 0- -o aLi a.lSiISi C

aC G. I II

.'° BO4+C

0-s__i j>a.i ._i

N0C C INUILI (.1

0) 00 0 0 0 0 0 0 0 000 0 0 0 0 000 DOW - 00) 0) a) U) 0 0 0 0 0 0 000 0 0 0 0 00 U) C.i -0 00) 0)0) 0)0)0) ID 0 0 0 000 0 0 0 CD C.J -. 0 000 00) 0)0)0)0)0) ala) a)ICDW0) C'J

Th1N]3dd I9WflN tI1U1flWfl3

199

44 CII. DIAMETER TANPI

20X VOL. HEPTANE DISPERSED IN WATERSTIRRER 6PEED 317 RPMCAPILLARY HEIQHT 36.0 CM.

CAPILLARY RADIAL OISTANCE RUN

-W-- 2.0 2.104-0-0- 4.0 2.105-A-A- 8.0 2.107-+-+- 12.0 2.108-X-X- 16.0 2.109

99.99

99.9099.80

99.5099.00

a: 96.00

95.00

90.00

80.00

70.00

LU 60.00D 50.00

40.0030.00

20.00>*-4 10.00I-a: 5.00-j

2 00t.00

(_.) 0.50

0.200.100.05

0.01 I I I I

0.0 0.1 0.2 0.3 0.4 0.6

DROP DIRMETER (MM.)

averagedifference

10%

averagedifference

21.4%

200

From the photographic work the values of d 32 in the three tanks for

different heights of photography are given below:

11cm tank

2cm 3cm 5cm 7cm 9cm

d32 (mm) 0.246 0.277 0.280 0.281 0.285 photography))

0.249 0.283 0.289 0.277 capillary )

average d32 = 0.274

average interfacial area 43.82 cm2/cm3

22cm tank

2cm 6cm 10cm 14cm 18cm

d32 (mm) 0.188 0.218 0.204 0.201 0.213 photography))

0.251 0.247 0.273 0.268 0.268 capillary )

average d32 = 0.205 mm

average interfacial area = 58.6 cm2/cm3

averagedifference

22.4%

44cm tank

4cm 12cm 20cm 28cm 36cm

d32 (mm) 0.179 0.173 0.164 0.174 0.174 photography))

0.213 0.211 0.226 0.214 0.242 capillary )

average d32 = 0.173 mm

average interfacial area = 69.4 cln2/cm3

From the capillary technique the average d 32 in the three tanks are

given below

number of geometrically 23 25 24

similar points

d3 20.275 0.272 0.229

corrected d3 20.248 0.212 0.183

a(cm2/cm3 ) 48.4 56.6 65.6

(a)

(b)

(c)

201

APPENDIX 10

PHYSICAL PROPERTIES OP REPTANE AND WATER

Correlations of impeller power input and Reynolds number for liquid-

liquid dispersions involve the use of mean values of density and

viscosity. Laity and Treybal (68) used the expressions

= p + (1.0 - t'cdcc

and= u, 1.0 + 6.O4JoPol

,w I

p 0 _______

=

11.0 - l.5+wpwl

+ 1.IoJ

Equation (b) is used for dispersions with more than 40% water by

volume and equation (c) is used for dispersions with less than 40%

water by volume.

In the above equation p = density

p = viscosity

• = dispersed phase fraction

subscripts m = mean

C = continuous phase

d = dispersed phase

o = organic phase

03 = water phase

International Critical Tables (69) were used to obtain the density

and viscosity for water and heptane at the temperatures for the

experiments.

202

(a) Density of Water

t(°C) 18 19 20 21 22 23 24 25

water 0.99862 0.99843 0.99823 0.99802 0.99779 0.99757 0.99733 0.00707(g/cm )

(b) Density of Beptane

p = p 9 + 10 a (t) + 10- 6(t)2 + 1O y (t)3

where p9 = 0.70048

a = -0.8476

= +0.1880

y = -5.23

t = 0 -+ 100°C

(c) Viscosity of Water

t(°C) 18 19 20 21 22 23 24 25

lwater(cP) 1.0603 1.0340 1.0087 0.9843 0.9608 0.9380 0.9161 0.8949

(d) Viscostly of Beptane

A 10.-it = (°C)xheptane (B + t)" ins

where A 445.97

B = 180.14

n = 2.1879

203

At 25°C

water = 997.1 Kg/rn3

heptane 679.3 Kg/in3

u = 0.8949 x 10 Kg/mswater

heptane 0.3897 x i0 Kg/ms

At 19°C

p = 998.4 Kg/rn3water

heptane 684.4 Kg/rn3

1water = 1.0340 x i0 Kg/ms

11heptane 0.4159 x icr 3 Kg/ms

204

APPENDIX 11

CALCULATED POWER REQUIREMENT POR 11cm TANK

205

DIM X(50)DIM Y(50)DIM Z(50)DIM U(50)DIM 0(50)DIM V(50)0=11T=2501=0.997102=0. 6793V10.8949V2=0, 3897C=0,000672o L=62.4o P1=0.9000o P2=0.10005 1=1B PRINT9 PRINT0 PRINT1 PRINT2 PRINT3 FRINT4 PRINT TANK DIAMETER 11.0 CM.'5 PRINT'B PRINT0 D(I)=(P1*D1)+(1-P1)*D20 V(I)=(V1/P1)*(1+(6*P2*V2)/(V1+V2))5 PRINT'************************************************************0 PRINT* VOLUME PERCENTAGE HEPTANE =';p2*100,'0 PRINT* VOLUME PERCENTAGE WATER ='Pl*lOO,' *1

0 PRINT'* DISPERSION DENSITY =';D(I)'GM/Cr130 PRINT'* DISPERSION VISCOSITY =;V(I)CP5 PRINT* TEMPERATURE =T' C0 PRINT'*2 PRINT'* STIRRER * REYNOLDS * STIRRER * STIRRER *'4 PRINT'* SPEED * NUMBER * POWER * POWER5 PRINT'* (RPM) * * (GM CM/SEC) * (WATTS) *6 PRINT'************************************************************'0 N=6005 S=16 A=3,670 R=D(I)*(N/60)*A**2/(V(I)/100)11 X(S)=6.1*D(I)*L*((N/60)**3)*((A*0.0328)**5)/177102 P=6.1*D(I)*(N/60)**3*A**53 G=P/9814 PRINT'* ';N,'* . ;R,'* . ;G,'* ';P/lo**7;' *'15 S=S+1;o N=N+1000 IF N>1100 GOTO 3600 GOTO 2300 PRINT'************************************************************'2 PRINT'************************************************************'5 P1=P1-0.1'0 P2=P2+0.130 1=1+10 PRINT)0 PRINTLO PRINTao IF P2>0.5 GOTO 100030 GOTO 140)00 END

0•000000000000000* *0

* *0

* **W U)*r'I 004 N-* *

Ui I- * l) 0 ) N ) N * *3 I- * 1) .4 N 0. N * *

,-. 0 0 V) 0 r) -a '0 .-i * *p-0.30r)V)0) . • .0*

U) ' 9* • •.4 -I N * *

* 0*

* 0*

* *00*0*0*0*00* *

* 0*

* *0

-. 0 *00* 0*WU)*0NN • • •0*•3 Z*.40.NN0* *-0 LI *0-I ) .4 'C .4* *1-0. *'0NVN'CN**U) Z*r,,w,,4.4r4o*

0* 0*

-'0 0*

* 0*0* *0* *0*0*0 *

* 0** 00* *0

U) * *00) *0) 1I 0 * *..iW ON NO.40)0*00) 0.0*ZE *0O.40N4**- *q'O'o.4r.r)**LIZ *n)r)O0)b)l',00

* 0*

* *0

* 0** * *0* * * * * * * *

* 0*

* *0

* *0

* *0

* *0

* *0

* 0*00*0Lii ZOO 0000 e * *IiJ0.*O0OOO-a**.-.0. *'0 N0)0. .4.4* **0

0) * *0

* *0*0*0*0*0*0*0*00*

MC.,ZU0) N0)00 N UO N'0*0) .v,•NNUI.

I-).-4J I-U))-40- z(n

UiJ 03 Uizz.1 0 0' _. _. -

U) (flJ= wUiwJ cnU)z) - 4 Lii0 0 I-

*0*0********************000-10'*Oh**tij

*1-Ui*0.1-*13*0 Ui Lii0009* I- 1-*zZ*0 C.)oc*t.JI&I*0.0.**Uiw

0-i_I*000*0******0*

***0********0***0********

206

*0* *00*0*00*0 0*0** 0 * 0 0** * *0* * 0** -oqv)0) 0.v*** Uicn*...oO0oo**** 3)-*QQ'C1'f%0.**** I-0.3*P)V)0) • •0** U) * •* l) * *0* Z * *0* 00. * *0* ".0 000000000000* E * *0* 00) * *0* '0 ".0 *0* N0)U 0* *0* 0).4* • • I)O UiU)*0I)P) • • •0**000) . 1') UJ"'.* • •*W) • 1)N 3Z*OOV).i'C0)*** a4000N.4NN01)***11111 1-0. *1n)C9.4'O.4000 (0 Z*I0).4.4N**OW 0* 0**1 -* *0* *0*1-Ui *0*0*0*0*0*0*0.1- 0 0**LiI )- * *0*13 I- * 0** )-4 U) * *0*WWI-U) o *4'r)c.l-. 0.0*0001-10 ..iLiI *I')N.4)D'N**0U)U 00) * ......0**I-l--ZU) ZE *NNl)P0l)4'0**ZZLaJS• . > *OW')ONOV***WLii0) LIZ *1)Wt0.V)000000 LI0 0**WWQO * 0*

* 0** U)(fl. 000000000000

* 0**EZLaJWLU * * 000.0.Q. * *0*...J.J0)CflE * 0*

* *0

* *0* * *00 W0).* 00*0* LiiZ*O0000O*** Ui0.*O0000.l**** I-U)'-* 0** U) 0 0** * *00* 00000****00000000

*0*00*0*0*0* *0** *0

* * 0*

* 0*-"*.NNO N0*IJJCfl*00W-I N.0*. LI I- * 0 V) N I) WI ') * *3 I- * ri C'I 0'. N .4 .1 * *

• • .0*II 01 * • •z * *0U * *0

* *0EU0 * *0N * 0*N ?' -0 *0r) I,, LI 0* *0lflN'0-4 • •0 •W • •• . r.i 3E*'0'0N0)ON**U..

1-0. *O'.P)01)W0**(0 EOr)'00'...-1C400

0* *41

-0 0** 0**0 *00*0* 0 0* *

* 00>. * 0*I- * 0*-4 (0 * 0*I- U) 0 *0.40)WII) *0

a-la _lW * ......0*LOU 00) *rI'CO'.r)p-'..-.**zC1) ZE *'CO1'0'.l)0)**Wa-. >- 000'NWION0*LIZ o-ar44-'00)000

LI 0.4.4.4.4.4(9*0zZ * *000 * *0

-4 '-II- * *0(flUId 0*0* *00*00* *

0 0*WUJLIJ * *00,0,0. 0 *0U)U)Z * 0*

* 0*00)1- * *0

* 0*00*0WE*000OOO**CU 0.000000.4* *-. 0. * '0 N 0) 0. .4.4* 00*(0 0 0** 0*

0*00*0*00*0* 00 ** *0 -***0** 10.300 r 0) '.'0* Z 0* U *4* '.'.O. 0* EU 0*0** 0 ** 0 ** 00)0 fltfl0 0** rON UJ*0 IIWI WUI*0000.• WI W'..*0(90) . .4N 3E*0 1-100**11111 1-0. 4*4* 0) Z*OW 0*'-0**1-Ui 0*0**0.1- 4**Uid >- 0*13 1- 4*4* ).l.4 (0 **WWI-U) 0) **00l40 .JUJ **CdOIU O **1-1-ZU) ZZ **ZZWI4 >- 0*WW0 LIZ **00 Lii 0*czzc 0*wW00 **0.0.1-Ill)- *4* U1U)d 0*0***ZZUJWW ***..J..J(flU)E **00W 00* 0** WZ****4* (0 ** *

*0*00*0*0*0**00.40.0) *10* *r) *10) *1 NN 0*.1 O'C 0. WI'0 * 0N 00. N N 10 * 4*

•* *0*0**00* 0* * *0 4**0*0*0N '0*10.0*r'...G•..o*• •

ON 0*' 0..4 * 4*'C P1 '000)0) * *0) -4-' 10 N 1') * 4*P1 '00. .4.4 N 0 4*

*00*0 *

* *0 * * * 4* 4**0* *0** 0N *100) N 'C * *

•0P00)'O 1000*('I '00(410*14*4*0)0.-4.4-4-i * *0** ** 4**0*0*0*0

* **0*00** 0* ** *

000*000000 4* 4*00000-10*'0N(00.I-I *0

* ** 4*0*

0*0*0*0*

0 4* 0* * 4*4*04*4*4*004*4*0 1*4* Z* (34* .0.0 ZU0 0)* N4*0 N'CO0 .-IN0 • .00-*000. W1011 N -I N*Olin..0*UJ0 d* I- U* 0. I.-*LiJd I-*13 I-0 4-1-.0 Iii WI- U)4* 0000 (0 U4* I-I- Z (00 Z Z Ui .4* lii Ui 0)*UCJ LI* z z c* Iii WOO4* 0. , .- )-* 0)(fl'* Ui U Ct* Z Li Li Li* 0.0.0.0 J ,J LI) 01 Z4* 00 a-I Li* - - 01-4*4*4**4*4*4**0 * *0 * 4*

*00*0*0* 0*0

* * *0

* 0*

* *0..4*0)'C)fl('4 .40*UJCt0)*t'lV0'.OWIN**CtW1-*r'IVlO'CIfl'C**

I-IOd 0 '0 0) '0 N '0 ('1* 01-0.3*10*10) • -0*0) '-0 •

* *0

* 0*

4* 0** 4* * * * * * 0* * * *

* *0

* 0*

-* *0

0* 0*W*-I 0)'C4C'I**WCtCfl*NC1O • • .0*• • .0.1000*Ct3Z *100)00.0)O**-.00 * II N 0 *1 N 0* *1-0. *N0-0)rlNrl**UI Z*rlV)W-a-4No*

0* *0

'-0 *0

* 0** 0* *0*0*0 0*0

* *0

* *0

* *00) * *0OCt * N4-IN0)**_lLi * .4l1*1*.**00) * • • •ZE oWI0.r)I.o'C**)- 00'CO.-IC'IN**LIZ *-4.4.4N0..**Ct

* 0*

* 0*

* *0* * * * * * * * * * * *

* 0*

4* 0*

* **

* *0

* *0

4* *0

Ct * 0*000*

Ct LiZ *0000000*Ct Ui 0.4*00000.4*0.40. Ct * 'ON 0) 0..4.l * *0*

(0 * 0*

4* 0**0*0*0*0*00*

2•C

10

207

2• 5

;15

0'

10 20 30 60 50

% vot. Heptane 0 Spersed

Ccilcu(ated Stirrer Power for

11cm Tank

208

APPENDIX 12

POWER MEASUREMENT RESULTS FOR 22cm AND 44cm TANKS

209

15 Th63Q

10'I)

4-d

LU

Q

10 20 30 40 50

%voL. Heptane Dispersed

Measured Stirrer Power for

22cm Tank

60

In4-4-

40

0

20

10 20 30 40 50

% voL. Heptane Dispersel

Measured Stirrer Power for44cm Tank

210

TABLE Al21 IMPELLER TORQUE MEASUREMENTS ON 22cm TANK

DispersedPhase

Stirrer Speed (rpm)

(% Vol.)630 600 550 500 450 400

10 0.225 0.200 0.170 0.140 0.115 0.095

20 0.210 0.195 0.165 0.140 0.110 0.090

30 0.205 0.190 0.155 0.135 0.105 0.085

40 0.200 0.180 0.155 0.130 0.100 0.085

50 0.190 0.175 0.145 0.125 0.100 0.080

(Torque Measured in Nm)

TABLE Al2.2 IMPELLER POWER REQUIREMENTS FOR 22cm TANK

StirrerSpeed 630 600 550 500 450 400(rpm)

DispersedPhase Impeller Power Consumption (watts)(% Vol.)

10 14.84 12.57 9.79 7.33 5.42 3.98

20 13.85 12.25 9.50 7.33 5.18 3.77

30 13.52 11.94 8.93 7.07 4.95 3.56

40 13.19 11.31 8.93 6.81 4.71 3.56

50 12.53 11.00 8.35 6.54 4.71 3.35

211

TABLE Al2. 3 22cm TANK REYNOLDS NUMBERS

StirrerSpeed 630 600 550 500 450 400(rpm)

DispersedPhase REYNOLDS NUMBER(% Vol)

10 40512 38582 35367 32152 28937 25722

20 30380 28933 26522 24111 21700 19289

30 22775 21690 19882 18075 16267 14460

40 16922 16117 14773 13430 12087 10744

50 12337 11750 10770 9791 8812 7833

TABLE Al2.4 22cm TANK NEWTON NUMBERS

StirrerSpeed 630 600 550 500 450 400(rpm)

DispersedPhase NEWTON NUMBER(% Vol)

10 6.27 6.14 6.21 6.19 6.28 6.55

20 6.05 6.20 6.23 6.39 6.21 6.42

30 6.11 6.24 6.06 6.39 6.13 6.28

40 6.17 6.12 6.28 6.37 6.06 6.51

50 6.08 6.18 6.09 6.35 6.28 6.36

212

TABLE A].2.5 IMPELLER TORQUE MEASUREMENTS ON 44cm TANK

Dispersed Stirrer Speed (rpm)Phase_______ ________ _______ ________ ________ ________(% Vol) 317 300 280 260 [ 240 220

10 1.80 1.64 1.46 1.28 1.06 0.92

20 1.75 1.58 1.42 1.22 1.00 0.88

30 1.70 1.55 1.40 1.16 0.98 0.84

40 1.62 1.50 1.34 1.12 0.98 0.82

50 1.62 1.44 1.30 1.11 0.94 0.82

(Torque measured in Nfl)

TABLE Al2.6 IMPELLER POWER REQUIREMENTS FOR 44cm TANK

StirrerSpeed 317 300 280 260 240 220(rpm)

DispersedPhase Impeller Power Consumption (watts)(% Vo1)

10 59.75 51.52 42.81 34.85 26.64 21.20

20 58.10 49.64 41.64 33.22 25.13 20.27

30 56.43 48.69 41.05 31.58 24.63 19.35

40 53.78 47.12 39.29 30.49 24.63 18.89

50 53.78 45.24 38.12 30.22 23.62 18.89

213

TABLE Al2.7 44cm TANK REYNOLDS NUMBERS

StirrerSpeed 317 300 280 260 240 220(rpm)

DispersedPhase REYNOLDS NUMBER

(% Vol)

10 81613 77235 72086 66937 61788 56639

20 61201 57919 54058 50197 46335 42474

30 45880 43419 40525 37630 34735 31841

40 34091 32262 30111 27961 25810 23659

50 24853 23520 21952 20384 18816 17248

TABLE Al2 .8 44cm TANK NEW0N NUMBERS

StirrerSpeed 317 300 280 260 240 220(rpm)

DispersedPhase NEWTON NUMBER

(% Vol)

10 6.18 6.28 6.42 6.53 6.35 6.55

20 6.21 6.26 6.46 6.43 6.19 6.48

30 6.24 6.35 6.59 6.33 6.28 6.40

40 6.16 6.37 6.53 6.33 6.50 6.47

50 6.39 6.34 6.57 6.51 6.47 6.71

214

APPENDIX 13

CALCULATION OP NUMBER AND CLEARANCE OF DROPS IN DISPERSION

The number of drops in the dispersion based on the average drop

diameter can be calculated from the phase fraction dispersed and the

total volume of the dispersion.

(A) Drop arranged on Cubic Lattice

Let d32 = Sauter mean drop diameter

DT = Tank diameter

a = Interfacial area /unit volume

c = Clearance between drops

• = Volume fraction of dispersed phase

V = Total dispersion volume

3Average drop volume = 32 (a)

6

irD3total volume of dispersion = T (b)

4

ffD3volume of dispersed phase = T • Cc)

4

using (a) and (c)

Number of drops = 7rD+ / Trd24/6

= .. 1"r}2 d3

using Cd) and (b)

3volume associated with each drop = 1E /

4 / 2 d32

3= - d32

(d)

215

assuming drops are arranged on a cubic lattice

(1/3

cube side =

d32

I , )1/3

Clearance, c - d32

-d32 -1

For 4, = 0.2 c/d32 = 0.378

(B) Drops arranged on Closely Packed Hexagonal Lattice

c) 34, V = n(d32+-jmax

3V/n = 7rd32/6+

3• ____max 6

and fmax] 1/3

¶1= - Id +-•6 1 2

Cd32 = d32 +-

2

2- d32 [ (+max } 1/3 -

d32 - 2 [[maxh/3 -

4, =0.76max

For 4, = 0.2 c/d32 = 1.120

5

4

-*—*- 22.0

-Q---D- 44.0

216

4

3

2

2

1

200 400 600 800 1000

POWER/ VOLUME (wa1fs/ii3)

5

1

20 40 60 80 100

INTERFACIAL AREA (cn/cm')

217

APPENDIX 14

INTERFACIAL AREA CALCULATIONS USING DIFFERENT SCALE-UP CRITERIA

Comparison of the interfacial area of the dispersions can be made on

the basis of different scale-up criteria e.g. kinematic and dynamic

similarities and also the concept of constant impeller power input

per unit volume. The following calculations are based on

(i) constant impeller tip speed T.S a ND a u

(ii) constant Reynolds number

Re a ND a uD

(iii) constant Weber number

We a N2D u2D1

(iv) constant Power/unit volume

P/V a N3D2 !!

We I viscous forces

)Note a u I

Re surface tension forces

(i) qual Tip Speed, u

11cm tank

600

700

800

900

1000

1100

T.S (cm/sec)

115.3

134.5

153.7

172.9

192.2

211.4

a (cm2/cm3)

27.4

36.1

42.9

54.7

61.9

63.2

218

A = 0.053 N1"5

A = 0.054 N125

44cm tank

rpm

238

265

280

300

317

22cm tank

378

441

504

567

630

T • S (cm/sec)

145.1

169.3

193.5

217.7

241.9

a (cm2/cm3)

51.4

59.3

58.9

77.5

82.9

T.S (cm/sec)

182.8

203.5

215.0

230.4

243.4

a(cm2/cm3)

47.8

56.7

61.6

62.3

73.1

(Ii) Constant uDj

11cm 22cm 44cmuDi

rpm a(cm2/cm3 ) rpm a(cm2/cm3 ) rpm a(cm2/cm3)

563.6 800 42.9 200 23.5 50 7.2

633.9 900 54.7 225 26.9 56 8.3

704.9 1000 61.9 250 30.3 63 9.6

775.1 1100 63.2 276 33.9 69 10.7

219

(lii) Constant u2Dj

11cm 22cm 44cmu2D

rpm a(cm2/cm 3 ) rpm a(cm2/cm 3 ) rpm a(cm2/cm3)

8.7x10' 800 42.9 284 35.1 100 17.1

10.9x1& 900 54.7 318 40.0 112 19.7

13.6x10 1' 1000 61.9 355 45.4 125 22.6

16.4x10' 1100 63.2 390 50.6 138 25.5

220

NOMENCLATURE

a, A

A(ho)

C

Ca

C

C 1 to C9

C*

d

d

d32,D32

dmax

dmm

D

0

D1

De

Da

DT

Dw

E

- Interfacial area per unit volume of dispersion

- Energy required to separate two drops of unit radius from

an initial distance h0 to infinity

- Clearance between drops in the dispersion

- Concentration of absorbent

- Capacitance

- Constants

- Solubility of solute

- Drop diameter

- Arithmetic mean drop diameter

- Sauter mean drop diameter

- Maximum drop diameter

- Drop diameter for which energy due to turbulence is equal

to the energy of adhesion

- Diffusivity of solute in solution

- Droplet size as volume fraction dispersed tends to zero.

- Impeller diameter

- Impeller diameter in equipment

- Impeller diameter in model

- Tank Diameter

- Wetted capillary bore diameter

- Power dissipation per unit mass of continuous phase

221

E - Energy of adhesion of two drops

F(h0) - Force of adhesion between two drops a distance h 0 apart

g - Acceleration due to gravity

- Impeller height from tank bottom

- Liquid height in tank

I - Light intensity

10 - Incident light intensity

k, K - Constants

Ka - Absorption coefficient

KL - Liquid side mass transfer coefficient

to K10 - Constants

K - pseudo-first order rate constant

1 - Distance between capillary detection points

L - Kolmogoroff eddy length

- Impeller blade length

L - Length of liquid slug in capillaryB

- Number of drops in the dispersion

N - Stirrer speed

Ne - Stirrer speed in equipment

Nm - Stirrer speed in model

p - Impeller power input

Pe - Impeller power in equipment

pm - Impeller power in model

222

r - Characteristic length dimension

rj - Impeller shaft diameter

Sj - Length of impeller blade mounted on central disc

S - Scale of energy containing eddies

t - Light transmission

T - Total number of impeller revolutions

Tq - Torque

U - Velocity

U - Root mean square fluctuating velocity over the maximum

drop diameter

- Mean square fluctuating velocity over the maximum drop

diameter

V - Volume of the system

wi - Impeller blade width

w - Rate of absortpion/unit volume dispersion

Wb - Baffle width

x - Constant

xv - Volume fraction dispersed phase

y - Constant

z - Number of moles of absorbent reacting with one mole of

solute

GREEK SYMBOLS

8 - Constant

c - Dielectric Constant

223

- Kinematic viscosity

vc - Kinematic viscosity of continuous phase

- Kinematic viscosity of dispersed phase

P - Viscosity

PC - Viscosity of continuous phase

lid - Viscosity of dispersed phase

Pm - Mean dispersion viscosity

- Density

PC - Density of continuous phase

- Density of dispersed phase

Pm - Mean dispersion density

a - Interfacial Tension

- Volume fraction

"C - Volume fraction continuous phase

- Volume fraction dispersed phase

- Angular velocity

DIMENSIONLESS GROUPS

Fr - Froude number

Ne - Newton number

Re - Reynolds number

We - Weber number

1. Holland, P.A. and

Chapman, P.S.

2. Bilche, W.

3. Brotbman, A. and

Kaplan, H.

4. Miller, S.A. and

Mann, C.A.

5. Hixaon, A,W. and

Baum, S.J.

6. Chilton, T.H., Drew, T.B.

and Jebens, R.H.

7. Rushton, J.H.

9. De Coursey, W.J.

10. Verineulen, T, Williams, G.M

and Langlois, G.E.

11. Kolmogoroff, A.N.

224

REFERENCES

8. Kramers, H.

12. Kolmogoroff, A.N.

13. Batchelor, G.K.

"Liquid Mixing and Processing in

Stirred Tanks" (1966) New York

Zelt. VDI, 81, 1065 (1937)

Chem. Met. Eng.

46, 633, 639 (1939)

Trans. A.I.Ch.E.

40, 709 (1944)

md. Engng. Chem.

33, 478 (1941)

md. Eugng. Chem.

36, 510 (1944)

Chem. Engng. Progr.

47, 485 (1951)

Chem. Engng. Sci.

2, 35 (1953)

PhD Thesis, Univ. London (1955)

Chem. Eng. Prog.

85 (1955)

Comp. Rend. Acad. Sd. (URSS)

30, 301 (1939); 32, 16 (1941)

Doki. Akad. Nauk (SSSR)

66, 825 (1949)

"The Theory of Homogeneous Turbulence"

Cambridge Univ. Press, London (1953)

14. Hinze, J.O. A.I. Ch.E. Ji.

1, 289 (1955)

15. Shinnar, R. Jr. Fluid Mech.

10, 259 (1961)

16. Chen, H.T. and

Middleman, S.

17. Sprow, F.B.

19. Rushton, J.H,, Costich, E.W.

and Everett, H.J.

20. Taylor, G.I.

23. Rodger, W.A., Trice, V.0.

and Rushton, J.H.

24. Kintner, R.C.

225

18. Brown, D.E. and Pitt, K.

21. Bradley, R.S.

22. Hanson, C.

25. Ward, P.J. and Knudsen, J.G.

26. Trice, V.0., and Rodger, W.A.

27. Mylnek, Y and Resnick, W.

28. Karabelas, A.J.

A.I.Ch.E. Ji.

13, 989 (1967)

Chem. Eng. Sci.

22, 435 (1967)

"Cheaca '70", Inst. Chem. Engra.

Symposium Series 33, 83 (1970)

Chem. Eng. Prog.

46, 395 (1950); 46, 467 (1950)

Proc. Roy. Acad. Sc (Amsterdam)

43, 852 (1940)

Phil. Mag.

13, 853 (1932)

"Recent Advances in Liquid-Liquid

Extraction", Permagon, Oxford (1970)

Chem. Eng. Prog.

515 (1956)

Can. Ji. Chem. Eng.

39, 235 (1961)

A.I.Ch.E. J]..

13, 356 (1967)

A.ICh.E. Ji.

2, 205 (1956)

AI.Ch.E. Ji.

18, 122 (1972)

A.I.Ch.E. Ji.

24, 170 (1978)

29. Coulaloglou, C.A. and A.I.Ch.E. Jl.

Tavlarides, L.L. 22, 289 (1976)

30. Adler, C.R., Mark, A.M., Chem. Eng. Prog.

Marshall Jr., W.R. and Parent, R.J. 50, 14 (1954)

31. Bouyatiotis, B.A. and

Thornton, J.D.

32. Lee, J.C. and Lewis, G.

34. Brown, R.A.S. and

Govier, G.W.

35. Yoshida, F. and Yamada, T.

36. Collins, S.B. and

Knudsen, J.G.

37. Giles, J.W., Hanson, C.

and Marsiand, J.G.

38. Van de Huist, H.C.

40. Rodriguez, F., Grotz, L.C.

and Engle, P.L.

41. Sullivan, D.M. and

Lindsay, E.E.

42. Sloan, A.

226

33. Sleicher Jr., C,A.

39. Calderbank, P.H.

Inst. Chea. Engrs. Symposium Series

26, 43 (1967)

Inst. Chein. Engrs. Symposium Series

26, 13 (1967)

A.I.,Ch.E. 31.

8, 471 (1962)

Can. 31. Chem. Eng.

39, 159 (1961)

"Chemca '70" Inst. Chem Engrs.

Symposium Series

33, 88 (1970)

A.I.Ch.E. 31.

16, 1072 (1970)

Proc. mt. Solvent Extraction Comp.

1, 94 (1971)

"Optics of Spherical Particles"

Duwaer and Son, Amsterdam (1946)

Trans. Inst. Chem. Engrs.

36, 443 (1958)

A.I.Ch.E. 31.

! 663 (1961)

Ind. Engng. Chem. (fundamentals)

1, 87 (1962)

"Angular-Dependence Light Scattering"

Communications to R.S. Stein,

Chemistry Dept. Univ. of Mass., USA

43. Princen, L.H. and

Rev. Sci. Inst.

Kwolek, S.L. 36, 646 (1965)

44. Wachtel, R.E. and

Jr. Colloid Sd.

La Mer, V.K. 17, 531 (1962)

227

45. Westerterp, K.R., De Kraa, J,A.

and Van Dierendonck, L.L.

46. Nanda, A.K. and Sharma, M.M.

47. Nanda, AK. and Sharma, M.M.

48. Pernandes, J.B. and

Sharma, M.M.

49. Fernandes, J.B.

50. Shah, A.K. and Sharina, M.M.

51. Javeri, A.S. and Sharma, M.M.

52. Danckwerts, P.V.

Chem. Eng. Sd.

18, 157 (1963)

Chem. Eng. Sci.

21, 707 (1966)

Trans. Inst. Chem. Engrs.

44, 744 (1968)

Chen. Eng. Sd.

22, 1267 (1967)

23, 9 (1968)

A.I.Ch.E. Symp. Series No. 120

68, 124 (1972)

Can. Ji. Chem. Eng.

49, 596 (1971)

Chem. Eng. Sd.

23, 669 (1968)

md. Eng. Chem. (1951), 1460

53. Sridhar, T. and Potter, 0.E.

54. Hofer, H. and Mersmann, A.

55. Mitsis, G.J.

56. Church, J.M. and

Shinnar, R.

57. Brooks, B.W.

58. Weiland, P., Brentrup, L.

and Onken, U.

59. Wijffels, J.B. and

Rietema, K.

Chem. Engng. Sd.

33, 1347 (1978)

German Chem. Engng.

3, 347 (1980)

A.I.Ch.E. J1.

6, 505 (1960)

md. Eng. Chem.

53, 479 (1961)

Trans. Inst. Chem. Engrs.

57, 210 (1979)

German Chem. Eng.

3, 296 (1980)

Proceedings ISEC '71

711 (1971)

60. Verhoff, F.H., Ross, S.L.

and Curl, R.L.

61. Hartland, S. and

Steiner, L.

62. Luhning, R.W.

63. Clarke, 8.1.

64. Holland, F.A.

228

65. Godfrey, J.C. and

Grilc, V.

md. Eng. Chem. (fundamentals) No. 3

16, 371 (1977)

Proceedings of NATO ASI meeting

Cesme (1981)

PhD Thesis, Univ. London (1970)

PhD Thesis, Univ. London (1974)

Chem. Engng.

17, 179 (1962)

2nd European Conf. on Mixing

March 1977

BHRA Fluid Engineering

66. Kafarov, V.V. and

Babanov, B.M.

67. Paviushenko, I.S. and

Yanishevskii, A.V.

68. Laity, D.S. and Treybal, R.E.

69. West, C.J.

Zhur, Prikl. Khimo

32, 189 (1959)

Thur. Priki. Khimo

31, 1348 (1958)

A.I.ch.E. J1.

3, 176 (1956)

"International Critical Tables of

Numerical Data, Physics, Chemistry

and Technology", McGraw Hill,

New York, 1933

70. Nagata, S. and

Mem. Fac. Eng. Kyoto,

Yamaguchi, I. University XXII,

2, 249 (1960)