AIR FILTRATION An Integrated Approach to the

Theory and Applications of Fibrous Filters

R. С BROWN Health and Safety Executive

Research and Laboratory Services Division, Sheffield. UK

OXFORD

P E R G A M O N PRESS NEW YORK • SEOUL TOKYO

Contents INTRODUCTION xiii

SYMBOLIC NOTATION XV

1 Macroscopic Behaviour of Filters 1

Surface filtration and depth filtration 1 Types of filter 2 Method of filtration and assessment of efficiency 4 Layer efficiency 5

Layer efficiency for monodisperse aerosols 5 Layer efficiency for polydisperse aerosols 7 Quality factor 9

Single fibre efficiency 9 References 11

2 Filter Structure 12

Introduction 12 Paper filters 13

Manufacture 13 Description of structure 14 Fractal dimension 18

Carded filters 18 Manufacture 18 Description of structure 19 Filters with short fibres 20 Felting 21

Porous foam 21 Model filters 23

Standard sieves 25 Wound wire 25 Photo-etched filters 26 Lithographically produced filters 26

References 27

V

VI Contents

3 Flow Patterns and Pressure Drop 29

Nature of airflow through a filter 29 Steady state flow and Stokes flow 30 Simple model of airflow around a filter fibre 32 Simple description of pressure drop 33

General fluid dynamics theory 34

Microscopic airflow patterns in filters 35 Filters approximated by single layers of fibres 37 Single fibre theory 39

Cell models 40 Hydrodynamic factor 43 Flow parallel to the fibre axis, and at arbitrary 44 inclination Refinement of single fibre theory to describe arrays of 45 fibres Continuum theory 46

Flow through two-dimensional arrays of fibres 47 Many-fibre theories 48 Variational method 48 Boundary element method 51

Filters of irregular and imperfect structure 52 Empirical models of pressure drop 52 The effect of fibres of non-circular cross-section 53 Pressure drop of filters made from polydisperse fibres 54

Flow in conditions other than simple Stokes flow 56 Flow in fibre arrays at finite Reynolds number 56 Molecular nature of airflow through filters, and the effects 58 of aerodynamic slip on flow pattern and pressure drop

General analysis 59 Aerodynamic slip applied to fibres 60

Macroscopic flow patterns 62 Flow through pleats 63

Flow through filters of non-uniform structure 64 Non-ideal structure on a microscopic level 64 Non-ideal structure on a macroscopic level 66

Filters heterogeneous in directions perpendicular to the 66 flow Filters heterogeneous in directions parallel and 67 perpendicular to the flow

Flow through pin holes and leaks 68

References 70

Contents VII

4 Particle Capture by Mechanical Means 73

Introduction 73 Generalised theory of single fibre efficiency 73

Limitations to the single fibre approach 75 Particle capture by direct interception 75

Simplified approach to direct interception 75 Derivation of single fibre efficiency by direct interception 77

Relationship between single fibre efficiency by 78 interception and pressure drop Effect of aerodynamic slip on particle capture by 79 interception

Experimental observation of particle capture by 79 interception

Particle capture by inertial impaction 80 Stopping time, stopping distance and Stokes number 81 Rigorous theory of inertial effects 82 Inertial impaction at low Stokes number 83 Inertial impaction at high Stokes number 84 Calculation of inertial impaction efficiency over a range of 84 Stokes numbers Formulae for single fibre efficiency fitted to the results of 85 calculation and experiment Experimental measurements on model and real filters 86

Capture of particles by gravity 90 Simplified approach to gravitational capture 91 Experimental observation of gravitational capture 92 Theory of gravitational capture 92

Capture of particles by diffusional deposition 93 Diffusive motion of particles 94

Simplified calculation of single fibre efficiency 96 Rigorous theory of diffusional capture 98 Experimental observation of diffusional capture 99 Effect of aerodynamic slip on diffusional capture 100

Capture of non-spherical particles by fibrous filters 101 Dynamics of fibrous aerosols 101

Interception and fibre aspect ratio 102 Inertial impaction and aerodynamic diameter 103 Diffusive motion in translation and rotation 104

Alignment of fibres in shear flow 104 Measurements of filtration efficiency against fibrous 105 aerosols

Combined effects of two or more capture mechanisms 106 Diffusion and interception 107

Most penetrating particle 108

V I I I Contents

Gravity and interception 109 Interception, diffusion and gravity 111 Inertial impaction and gravity 111

Size-selection by interception, gravity and inertial 111 impaction

Specification of mechanism-dependent regimes 112 Variation of deposition site with capture process 113 Effect of leakage on filter performance 114 Potential problems with model filters 115 References 116

5 Electrically Charged Filter Material 120

Introduction 120 Basic mechanisms of action 120 Classification of material 121

Triboelectrically charged material 122 Resin wool material 122 Mixed-fibre material 125

Corona charged material 126 Split-fibre material 127 Material charged as a whole 127

Material charged by induction 127 Air currents in electric charging 129 Non-fibrous electrostatic filter 129

The importance of electric charge configuration 130 Measurement of filter charge 131

Measurement by ionising radiation 131 Fibre-scanning 133 Dipolar charge measurement 133

Charge stability and the effect of storage on filter 134 performance

Theory of charge loss 134 Observed behaviour of filters at elevated temperature 135

References 137

6 Particle Capture by Electric Forces 139

Introduction 139 Capture by permanently charged fibres 139

Electric charge on aerosol particles 140 Breakdown charge distribution 141 Equilibrium charge distribution 141

Contents IX

Miscellaneous charge distributions 142 Capture of charged particles 142 Capture of neutral particles 143 Effect of particle size and filtration velocity 145 Mathematical theory of capture 145

Capture of particles by solenoidal forces 145 Capture by central forces 148 Iterative numerical calculations 148

Calculation of single fibre efficiency for polarisation forces 149 Particle capture by fibres with non-uniform charge 150 Electric field caused by fibres with complicated charge 150 configurations

Particle capture by multipole charge configurations 152 Combined effect of electrostatic forces with interception 156 and other mechanisms

Capture by image forces 158 Combined effects of image forces and interception 160

Experimental observation of electrostatic capture 161 Capture efficiency compared with dimensionless capture 166 parameters Functional form of single-fibre efficiency by electrostatic 167 effects and diffusion

Augmentation of filtration efficiency by external electric 168 fields

Capture of charged particles 168 Capture of neutral particles 169 Direct observation of particle trajectories 170 Experimental measurements on model filters 171 Effect of single fibre position and composition 172 Measurements on real filters in an external electric field 173

Augmentation of filtration efficiency by charging of particles 174 References 174

7 Particle Adhesion and Particle Bounce 178

Introduction 178 Elementary description of capture mechanism and bounce 178 probability Relative importance of bounce and re-entrainment 180 Re-suspension of particles by the airstream or by 180 particle-particle impact

Adhesion forces between particles and fibres 181 Van der Waals forces 181 Surface tension (capillary) forces 183

X Contents

Electric forces 184 Relative magnitude of adhesion forces 185 Range of values of adhesion forces 186

Effect of particle and fibre properties 188 Influence of filtration conditions 189

Dynamics of impact 190 Face velocity and impact velocity 192 Factors influencing bounce probability 193

Effect of oil on the fibre surface 193 Effect of particle size and shape 194 Effect of collector surface 194

Critical impact velocity and direct observation of impact 195 Adhesion and bounce of very small particles 196 Transfer of electric charge on contact 197 Capture of liquid droplets 198 Fibre shedding 198

References 199

8 Effects of Loading 201

Introduction 201 Qualitative description of filter clogging 201

Dendrite formation 202 Dendrite formation by interception 203 Dendrite formation by inertial impaction 203 Dendrite formation by diffusional deposition 204 Dendrite formation by electric forces 204

Illustrations of deposit pattern 205 The influence of aerosol properties on clogging rate 205 Macroscopic theory of filter clogging 206 Airflow pattern and drag force acting on particle complexes 208

Theory of airflow around an isolated sphere 208 Aerodynamic slip 210

Drag force acting on agglomerates 210 Aerodynamic slip 211

Drag force on a single particle attached to a collector 212 Drag force on a dendrite attached to a collector 213

Theoretical description of clogging 214 Calculation of dendrite formation 216 Numerical simulation of dendrite growth 218

Experimental observation of dendrite structure on a single 221 fibre

Experimental observations on model and real fibrous filters 221 Behaviour related to capture mechanisms 222

Contents XI

Effect of filter properties on the pattern of clogging 223 Particle bounce from clogged filters 225

Fractal structure of particle deposits 226 Effect of loading with liquid aerosols 229 Time-dependent effects in filter clogging 231 The effect of dust loading on the performance of electrically 231 charged filters

Empirical theory of charge loss 233 Loading with solid aerosols 234

Effect of aerosol charge 235 Loading with liquid aerosols 235

References 236

9 Filter Testing 240

Introduction 240 Pressure drop measurement 240 Area weight measurement 241 General problems of aerosol penetration measurement 241

Sample uniformity and consistency 241 Filter scanning 242 Line losses 243 Uniformity of air velocity through the filter 243

Re-circulating filters 243 Aerosol detectors 244 Testing with monodisperse aerosols 245

Methods of production of monodisperse aerosols 245 Aerosol produced from liquid droplets 245 Aerosols produced from condensation nuclei 246 Polystyrene latex aerosols 247 Aerosols produced by classification 247 Fibrous aerosols 248

Quantification and minimisation of random errors 249 Application to layer efficiency or quality factor 250

Automated methods of obtaining penetration curves with 250 monodisperse aerosols

Size-selective testing with polydisperse aerosols 251 Technical problems with instrumentation 251 Methods of production of polydisperse test aerosols 252 Size distribution of polydisperse aerosols 253 Filter testing by sample collection and analysis 253

Non size selective testing with polydisperse aerosols 254 Aerosol number distributions and mass distributions 255

Effect of detection method on ascribed penetration 258

xii Contents

Testing of high efficiency filters 259 Tests with electrically charged aerosols 260

Neutralisation of aerosols 260 Worst possible case testing 261 Realistic prediction of filter performance 263 Standard filters 263 References 264

CONCLUSION 268

INDEX 269