Air Filtration: An Integrated Approach to the Theory and Applications of Fibrous Filters

292 Pages·1993·181.988 MB·English

by  R.C. Brown

A R
FILTRATION
An Integrated Approach to the
Theory and Applications of Fibrous Filters
R C BROWN
. .
Pergamon Press
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- A I R F I L T R A T I O N
7
An Integrated Approach to the
Theory and Applications of
Fibrous Filters Yr / /
4
R. C. BROWN
Health andSafety Executive
Research and Laboratory Services Division,
Sheffield,UK
PERGAMON PRESS X)X , <’)
I *
(\ / OXFORD NEW YORK SEOUL TOKYO 'if i
UK PergamonPress,Ltd,HeadingtonHillHall,
Oxford0X3OBW,England
USA PergamonPressInc.,660WhitePlainsRoad,
Tarrytown,NewYork10591-5153,USA
KOREA PergamonPress Korea,KPO Box315,Seoul110-603,
Korea
JAPAN PergamonPressJapan,Tsunashima BuildingAnnex,
3-20-12Yushima,Bunkyo-ku,Tokyo113,Japan
Copyright©1993R.C. Brown
AllRightsReserved.Nopartofthispublicationmaybe
reproduced,storedinaretrievalsystemortransmittedin
anyformor byanymeans:electronic,electrostatic,
magnetictape,mechanical,photocopying,recordingor
otherwise,withoutpermissioninwritingfromthe
publishers.
Firstedition1993
BritishLibraryCataloguinginPublicationData
Acataloguerecordforthisbookisavailablefromthe
BritishLibrary.
Libraryof CongressCataloginginPublicationData
Brown,R. C. (RichardColin),1944-
Airfiltration:anintegratedapproachtothetheoryand
applicationsoffibrousfilters/R.C.Brown.—1sted.
P- cm.
Includesbibliographicreferences.
1.Airfilters. 2.Fibers. 3.Air-Purification. I.Title.
TH7683.A3B76 1993
628.5'.3—dc20
ISBN0080412742
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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
Quality factor 9
Single fibre efficiency 9
References 11
2 Filter Structure 12
-i Introduction 12
Paper filters 13
Manufacture h 13
Description of structure 14
Fractal dimensidn 18
Carded filters ; " ~ 18
Manufacture i ; « 18
Description of structure 19
*
Filters with short fibres 20
Felting '!21
Porous foam
Model filters 23
(cid:127)
Standard sieves ip 25
*
Wound wire f25
Photo-etched filters 126
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 aerodynamicslip on flow pattern and pressure drop
General analysis 59
Aerodynamic slip applied tofibres 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 macroscopiclevel 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 singlefibre efficiency 73
Limitations to thesingle 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 aerodynamicslip 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
viii 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 electrostaticfilter 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
Electricforces 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 dragforce 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
Dragforce on a single particle attached to a collector 212
Dragforce 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 dendritestructure on a single 221
fibre
Experimental observations on model and real fibrousfilters 221
Behaviour related to capture mechanisms 222