Edited by
Igor Agranovski
Aerosols – Science and
Technology


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Edited by Igor Agranovski

Aerosols – Science and Technology

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The Editor
Prof. Dr. Igor Agranovski
Griffith University
Griffith School of Engineering
170, Kessels Road, Nathan Cam.
Brisbane, Queensland 4111
Australia

All books published by Wiley-VCH are
carefully produced. Nevertheless, authors,
editors, and publisher do not warrant the
information contained in these books,
including this book, to be free of errors.
Readers are advised to keep in mind that
statements, data, illustrations, procedural
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inaccurate.
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Data
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from the British Library.
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Deutsche Nationalbibliothek
The Deutsche Nationalbibliothek
lists this publication in the Deutsche
Nationalbibliografie; detailed bibliographic
data are available on the Internet at
<>.

 2010 WILEY-VCH Verlag GmbH & Co.
KGaA, Weinheim

All rights reserved (including those of
translation into other languages). No part
of this book may be reproduced in any
form – by photoprinting, microfilm, or any
other means – nor transmitted or translated
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Printed on acid-free paper
ISBN: 978-3-527-32660-0

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V

Contents
List of Contributors XIII
List of Symbols XVII

Introduction XXIX
1
1.1
1.2
1.2.1
1.2.1.1
1.2.1.2
1.2.1.3
1.2.1.4
1.2.1.5
1.2.1.6
1.2.2
1.2.2.1
1.2.2.2
1.3
1.4
1.4.1
1.4.2
1.4.3
1.4.4
1.5
1.5.1
1.5.2
1.5.2.1
1.5.2.2
1.5.2.3
1.5.2.4
1.5.3
1.5.3.1


Introduction to Aerosols 1
Alexey A. Lushnikov
Introduction 1
Aerosol Phenomenology 2
Basic Dimensionless Criteria 2
Reynolds Number 2
Stokes Number 2
Knudsen Number 3
Peclet Number 3
Mie Number 3
Coulomb Number 3
Particle Size Distributions 4
The Log-Normal Distribution 4
Generalized Gamma Distribution 5
Drag Force and Diffusivity 6
Diffusion Charging of Aerosol Particles 7
Flux Matching Exactly 8
Flux Matching Approximately 9
Charging of a Neutral Particle 9
Recombination 10
Fractal Aggregates 11
Introduction 12
Phenomenology of Fractals 13
Fractal Dimension 13
Correlation Function 14
Distribution of Voids 14
Phenomenology of Atmospheric FA 14
Possible Sources of Fractal Particles 15
Natural Sources 15


Aerosols – Science and Technology. Edited by Igor Agranovski
Copyright  2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ISBN: 978-3-527-32660-0

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VI

Contents

1.5.3.2
1.5.4
1.5.4.1
1.5.4.2
1.5.4.3
1.5.5
1.5.6
1.5.7
1.6
1.6.1
1.6.2
1.7
1.7.1
1.7.1.1
1.7.1.2
1.7.2
1.8

Anthropogenic Sources 15

Formation of Fractal Aggregates 16
Growth by Condensation 16
Growth by Coagulation 17
Aerosol–Aerogel Transition 18
Optics of Fractals 18
Are Atmospheric Fractals Long-Lived? 20
Concluding Remarks 21
Coagulation 21
Asymptotic Distributions in Coagulating Systems
Gelation in Coagulating Systems 26
Laser-Induced Aerosols 33
Formation of Plasma Cloud 33
Nucleation plus Condensational Growth 34
Coagulation 34
Laser-Induced Gelation 34
Conclusion 36
References 37
Part I

2
2.1
2.2
2.2.1
2.2.2
2.2.3
2.2.4
2.2.5
2.3
2.3.1
2.3.2

2.3.3
2.3.4
2.3.5
2.4

3
3.1
3.1.1
3.1.2
3.2

Aerosol Formation

23

43

High-Temperature Aerosol Systems 45
Arkadi Maisels
Introduction 45
Main High-Temperature Processes for Aerosol Formation 45
Flame Processes 47
Hot-Wall Processes 49
Plasma Processes 49
Laser-Induced Processes 50
Gas Dynamically Induced Particle Formation 50
Basic Dynamic Processes in High-Temperature Aerosol Systems
Nucleation 52
Coagulation/Aggregation 52
Surface Growth Due to Condensation 55

Sintering 55
Charging 57
Particle Tailoring in High-Temperature Processes 59
References 61
Aerosol Synthesis of Single-Walled Carbon Nanotubes 65
Albert G. Nasibulin and Sergey D. Shandakov
Introduction 65
Carbon Nanotubes as Unique Aerosol Particles 65
History and Perspectives of CNT Synthesis 68
Aerosol-Unsupported Chemical Vapor Deposition Methods

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70

50


Contents

3.2.1
3.2.2
3.2.3
3.3
3.3.1
3.3.2
3.3.3
3.4
3.4.1
3.4.2

3.5
3.6

The HiPco Process 70
Ferrocene-Based Method 71
Hot-Wire Generator 73
Control and Optimization of Aerosol Synthesis 74
On-Line Monitoring of CNT Synthesis 74
Individual CNTs and Bundle Separation 76
CNT Property Control and Nanobud Production 76
Carbon Nanotube Bundling and Growth Mechanisms
Bundle Charging 78
Growth Mechanism 80
Integration of the Carbon Nanotubes 82
Summary 84
Acknowledgements 84
References 84

4

Condensation, Evaporation, Nucleation 91
Alexey A. Lushnikov
Introduction 91
Condensation 92
Continuum Transport 93
Free-Molecule Transport 93
Condensation in the Transition Regime 94
Flux-Matching Theory 95
Approximations 96
The Fuchs Approximation 96

The Fuchs–Sutugin Approximation 96
The Lushnikov–Kulmala Approximation 96
More Sophisticated Approaches 97
Evaporation 97
Uptake 99
Getting Started 100
Hierarchy of Times 101
Diffusion in the Gas Phase 101
Crossing the Interface 103
Transport and Reaction in the Liquid Phase 103
Balancing Fluxes 104
No Chemical Interaction 104
Second-Order Kinetics 106
Nucleation 108
The Szilard–Farkas Scheme 109
Condensation and Evaporation Rates 110
Thermodynamically Controlled Nucleation 111

4.1
4.2
4.2.1
4.2.2
4.3
4.3.1
4.3.2
4.3.2.1
4.3.2.2
4.3.2.3
4.3.3
4.4

4.5
4.5.1
4.5.2
4.5.3
4.5.4
4.5.5
4.6
4.6.1
4.6.2
4.7
4.7.1
4.7.2
4.7.3

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78

VII


VIII

Contents

4.7.4
4.7.5
4.8
4.8.1
4.8.2

4.8.3
4.8.4
4.9

Kinetically Controlled Nucleation 111
Fluctuation-Controlled Nucleation 113
Nucleation-Controlled Processes 114
Nucleation Bursts 114
Nucleation-Controlled Condensation 115
Nucleation-Controlled Growth by Coagulation 117
Nucleation Bursts in the Atmosphere 119
Conclusion 120
References 122

5

Combustion-Derived Carbonaceous Aerosols (Soot) in the Atmosphere:
Water Interaction and Climate Effects 127
Olga B. Popovicheva
Black Carbon Aerosols in the Atmosphere: Emissions and Climate
Effects 127
Physico-Chemical Properties of Black Carbon Aerosols 132
General Characteristics 133
Key Properties Responsible for Interaction with Water 137
Water Uptake by Black Carbons 140
Fundamentals of Water Interaction with Black Carbons 140
Concept of Quantification 143
Laboratory Approach for Water Uptake Measurements 144
Quantification of Water Uptake 146
Hydrophobic Soot 146

Hydrophilic Soot 148
Hygroscopic Soot 151
Conclusions 152
Acknowledgements 153
References 153

5.1
5.2
5.2.1
5.2.2
5.3
5.3.1
5.3.2
5.3.3
5.3.4
5.3.4.1
5.3.4.2
5.3.4.3
5.4

6

6.1
6.2
6.2.1
6.2.2
6.2.3
6.2.4
6.2.5
6.3

6.3.1
6.3.2

Radioactive Aerosols – Chernobyl Nuclear Power Plant Case
Study 159
Boris I. Ogorodnikov
Introduction 159
Environmental Aerosols 164
Dynamics of Release of Radioactive Aerosols from Chernobyl 164
Transport of Radioactive Clouds in the Northern Hemisphere 166
Observation of Radioactive Aerosols above Chernobyl 168
Observations of Radioactive Aerosols in the Territory around
Chernobyl 171
Dispersity of Aerosol Carriers of Radionuclides 183
Aerosols inside the Vicinity of the ‘‘Shelter’’ Building 185
Devices and Methods to Control Radioactive Aerosols in the
‘‘Shelter’’ 185
Control of Discharge from the ‘‘Shelter’’ 185

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Contents

6.3.3
6.3.4
6.3.5
6.3.6
6.3.7
6.3.8

6.3.9

Well-Boring in Search of Remaining Nuclear Fuel 186
Clearance of the Turbine Island of the Fourth Power
Generating Unit 188
Strengthening of the Seats of Beams on the Roof of the ‘‘Shelter’’ 189
Aerosols Generated during Fires in the ‘‘Shelter’’ 191
Dust Control System 192
Control of the Release of Radioactive Aerosols through the ‘‘Bypass’’
System 192
Radon, Thoron and their Daughter Products in the ‘‘Shelter’’ 195
References 197
Part II

7

7.1
7.2
7.3
7.4
7.4.1
7.4.2
7.5
7.5.1
7.5.2
7.6
7.7
7.8
7.8.1
7.8.2

7.8.3
7.8.4
7.9

8
8.1
8.2
8.3

Aerosol Measurement and Characterization

203

Applications of Optical Methods for Micrometer and Submicrometer
Particle Measurements 205
Alad´ar Czitrovszky
Introduction 205
Optical Methods in Particle Measurements 206
Short Overview of Light Scattering Theories 208
Classification of Optical Instruments for Particle Measurements 213
Multi-Particle Instruments 213
Single-Particle Instruments 214
Development of Airborne and Liquid-borne Particle Counters and
Sizers 215
Development of Airborne Particle Counters 216
Development of Liquid-borne Particle Counters 222
New Methods Used to Characterize the Electrical Charge and Density
of the Particles 225
Aerosol Analyzers for Measurement of the Complex Refractive Index
of Aerosol Particles 227

Comparison of Commercially Available Instruments and Analysis of
the Trends of Further Developments 229
Portable Particle Counters 230
Remote Particle Counters 230
Multi-Particle Counters 233
Handheld Particle Counters 233
Conclusions 233
References 234
The Inverse Problem and Aerosol Measurements 241
Valery A. Zagaynov
Introduction 241
Forms of Representation of Particle Size Distribution 243
Differential and Integral Measurements 245

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IX


X

Contents

8.4
8.5
8.5.1
8.5.2
8.5.3
8.5.4
8.5.5

8.5.6
8.5.7
8.6

Differential Mobility Analysis 246
Diffusion Aerosol Spectrometry 252
Raw Measurement Results and their Development – Parameterization
of Particle Size Distribution 254
Fitting of Penetration Curves 256
Transformation of the Integral Equation into Nonlinear Algebraic
Form 257
Effect of Experimental Errors on Reconstruction of Particle Size
Distribution 259
Reconstruction of Bimodal Distributions 261
Mathematical Approach to Reconstruct Bimodal Distribution from
Particle Penetration Data 264
Solution of the Inverse Problem by Regularization Method 266
Conclusions 268
References 269
Part III

Aerosol Removal 273

9

History of Development and Present State of Polymeric Fine-Fiber
Unwoven Petryanov Filter Materials for Aerosol Entrapment 275
Bogdan F. Sadovsky
References 282


10

Deposition of Aerosol Nanoparticles in Model Fibrous Filters 283
Vasily A. Kirsch and Alexander A. Kirsch
Introduction 283
Results of Numerical Modeling of Nanoparticle Deposition in
Two-Dimensional Model Filters 287
Fiber Collection Efficiency at High Peclet Number: Cell Model
Approach 287
Fiber Collection Efficiency at Low Peclet Number: Row of Fibers
Approach 289
Deposition of Nanoparticles upon Ultra-Fine Fibers 292
Deposition of Nanoparticles on Fibers with Non-Circular
Cross-Section 294
Deposition of Nanoparticles on Porous and Composite Fibers 298
Penetration of Nanoparticles through Wire Screen Diffusion
Batteries 302
Deposition of Nanoparticles in Three-Dimensional Model Filters 302
Theory of Particle Deposition on Screens with Square Mesh 304
Comparison with Experiment 305
Conclusion 310
Acknowledgements 311
References 311

10.1
10.2
10.2.1
10.2.2
10.2.3
10.2.4

10.2.5
10.3
10.3.1
10.3.2
10.3.3
10.4

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Contents

11
11.1
11.2
11.2.1
11.2.2
11.2.3
11.3
11.3.1
11.3.2
11.4
11.4.1
11.4.2

Filtration of Liquid and Solid Aerosols on Liquid-Coated Filters 315
Igor E. Agranovski
Introduction 315
Wettable Filtration Materials 316
Theoretical Aspects 318

Practical Aspects 320
Inactivation of Bioaerosols on Fibers Coated by a Disinfectant 326
Non-Wettable Filtration Materials 327
Theoretical Aspects 327
Practical Aspects of Non-Wettable Filter Design 330
Filtration on a Porous Medium Submerged into a Liquid 330
Theoretical Approach 330
Application of the Technique for Viable Bioaerosol Monitoring 337
References 340
Part IV

12
12.1
12.2
12.2.1
12.2.2
12.2.3
12.2.4
12.2.4.1
12.2.4.2
12.2.4.3
12.2.5
12.3
12.3.1
12.3.1.1
12.3.1.2
12.4

13
13.1

13.2
13.3
13.4
13.5
13.5.1

Atmospheric and Biological Aerosols

343

Atmospheric Aerosols 345
Lev S. Ivlev
General Concepts 345
Atmospheric Aerosols of Different Nature 348
Soil Aerosols 348
Marine Aerosols 351
Volcanic Aerosols 354
Aerosols In situ – Secondary Aerosols 358
Photochemical Oxidation – Heterogeneous Reactions 359
Catalytic Oxidation in the Presence of Heavy Metals 360
Reaction of Ammonia with Sulfur Dioxide in the Presence of Water
Droplets (Reaction of Cloud Droplets) 360
Biogenic Small Gas Compounds and Aerosols 360
Temporal and Dimensional Structure of Atmospheric Aerosols 363
Aerosols in the Troposphere 363
Terrigenous Elements 363
The Group of Ions 363
Aerosols in the Stratosphere 371
References 377
Biological Aerosols 379

Sergey A. Grinshpun
Introduction 379
History of Bioaerosol Research 379
Main Definitions and Types of Bioaerosol Particles 381
Sources of Biological Particles and their Aerosolization 383
Sampling and Collection 384
Impaction 386

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XI


XII

Contents

13.5.2
13.5.3
13.5.4
13.5.5
13.6
13.7
13.8
13.8.1
13.8.2

14

14.1

14.2
14.2.1
14.2.2
14.2.3
14.3
14.3.1
14.3.2
14.3.3
14.3.4
14.3.5
14.4

Collection into Liquid 388
Filter Collection 389
Gravitational Settling 390
Electrostatic Precipitation 390
Analysis 391
Real-Time Measurement of Bioaerosols 393
Purification of Indoor Air Contaminated with Bioaerosol Particles and
Respiratory Protection 393
Air Purification 393
Respiratory Protection 396
References 398
Atmospheric Bioaerosols 407
Aleksandr S. Safatov, Galina A. Buryak, Irina S. Andreeva, Sergei E.
Olkin, Irina K. Reznikova, Aleksandr N. Sergeev, Boris D. Belan and
Mikhail V. Panchenko
Introduction 407
Methods of Atmospheric Bioaerosol Research 408
Methods and Equipment for Atmospheric Bioaerosol Sampling 409

Methods to Analyze the Chemical Composition of Atmospheric
Bioaerosols and their Morphology 411
Methods Used to Detect and Characterize Microorganisms in
Atmospheric Bioaerosols 416
Atmospheric Bioaerosol Studies 421
Time Variation of Concentrations and Composition of Atmospheric
Bioaerosol Components 421
Spatial Variation of the Concentrations and Composition of
Atmospheric Bioaerosol Components 432
Possible Sources of Atmospheric Bioaerosols and their Transfer in the
Atmosphere 436
The Use of Snow Cover Samples to Analyze Atmospheric
Bioaerosols 438
Potential Danger of Atmospheric Bioaerosols for Humans and
Animals 442
Conclusion 446
References 448
Index 455

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XIII

List of Contributors
Igor E. Agranovski
Griffith University
School of Engineering
170 Kessels Road
Nathan Campus

Brisbane
Queensland 4111
Australia

Galina A. Buryak
Federal Service for Surveillance in
Consumer Rights Protection and
Human Well-Being
State Research Center of Virology
and Biotechnology ‘‘Vector’’
Koltsovo, 630559
Novosibirsk
Russia

Irina S. Andreeva
Federal Service for Surveillance in
Consumer Rights Protection and
Human Well-Being
State Research Center of Virology
and Biotechnology ‘‘Vector’’
Koltsovo, 630559
Novosibirsk
Russia
Boris D. Belan
Siberian Branch of the Russian
Academy of Sciences
V.E. Zuev Institute for
Atmospheric Optics
Akademicheskii Avenue 1
634055 Tomsk

Russia

Alad´ar Czitrovszky
Research Institute for Solid
State Physics and Optics
Department of Laser Application
P.O. Box 49
1525 Budapest
Hungary
Sergey A. Grinshpun
University of Cincinnati
Department of
Environmental Health
3223 Eden Avenue
107 Kettering Building
Cincinnati, Ohio
OH 45267
USA

Aerosols – Science and Technology. Edited by Igor Agranovski
Copyright  2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ISBN: 978-3-527-32660-0

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XIV

List of Contributors


Lev S. Ivlev
Saint Petersburg
State University
7–9 Universitetskaya
Naberezhnaya
Saint Petersburg 1999034
Russia

Arkadi Maisels
Evonik Degussa GmbH
Industriepark Wolfgang
Rodenbacher Chaussee 4
63457 Hanau
Germany
Albert G. Nasibulin
NanoMaterials Group
Department of Applied Physics
and Center for New Materials
Aalto University
Puumiehenkuja 2
00076 Espoo
Finland

Alexander A. Kirsch
Russian Research Center
‘‘Kurchatov Institute’’
Kurchatov Square, 1
123182 Moscow
Russia
Vasily A. Kirsch

Russian Academy of Sciences
Frumkin Institute of Physical
Chemistry and Electrochemistry
Leninski Prospect, 31
119991 Moscow
Russia
Alexey A. Lushnikov
Karpov Institute of
Physical Chemistry
10, ul Vorontsovo Pole
103062 Moscow
Russia

Boris I. Ogorodnikov
Karpov Institute of
Physical Chemistry
10, ul Vorontsovo pole
105064 Moscow
Russia
Sergei E. Olkin
Federal Service for Surveillance in
Consumer Rights Protection and
Human Well-Being
State Research Center of Virology
and Biotechnology ‘‘Vector’’
Koltsovo, 630559
Novosibirsk
Russia

and

University of Helsinki
Faculty of Mathematics and
Natural Sciences
Physics, Atmospheric Sciences
and Geophysics Department
Gustav Hăallstrăomin katu 2
00014 Helsingen Yliopisto
Finland

Mikhail V. Panchenko
Siberian Branch of the Russian
Academy of Sciences
V.E. Zuev Institute for
Atmospheric Optics
Akademicheskii Avenue 1
634055 Tomsk
Russia

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List of Contributors

Alexander N. Sergeev
Federal Service for Surveillance in
Consumer Rights Protection and
Human Well-Being
State Research Center of Virology
and Biotechnology ‘‘Vector’’
Koltsovo, 630559

Novosibirsk
Russia

Olga B. Popovicheva
Skobeltsyn Institute of
Nuclear Physics
Division of Microelectronics
Moscow State University
1(2) Leninskie gory
119991 Moscow
Russia
Irina K. Reznikova
Federal Service for Surveillance in
Consumer Rights Protection and
Human Well-Being
State Research Center of Virology
and Biotechnology ‘‘Vector’’
Koltsovo, 630559
Novosibirsk
Russia

Sergey D. Shandakov
Laboratory of Carbon
NanoMaterials
Department of Physics
Kemerovo State University
Krasnaya 6
Kemerovo, 650043
Russia


Bogdan F. Sadovsky
Karpov Institute of
Physical Chemistry
10, ul Vorontsovo Pole
103062 Moscow
Russia

Valery A. Zagaynov
Karpov Institute of
Physical Chemistry
10, ul Vorontsovo pole
105064 Moscow
Russia

Aleksandr S. Safatov
Federal Service for Surveillance in
Consumer Rights Protection and
Human Well-Being
State Research Center of Virology
and Biotechnology ‘‘Vector’’
Koltsovo, 630559
Novosibirsk
Russia

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XV


XVII


List of Symbols

a
a
a
a0
ag
am
am
as
av
A
A
A(t), B(t)

amount of vapor adsorbed (Chapter 5)
fiber radius (Chapter 10)
particle radius (Chapter 1)
radius of molecule of condensable substance
radius of g-mer
molecular radius
monolayer coverage
characteristic particle radius, for normalization of particle size
equilibrium concentration of vapor
acceleration (Chapter 7)
Hamaker constant (Chapter 11)
algebraic functions of time

B

B

ion mobility (Chapter 1)
particle mobility (Chapter 6)

c
c∗
c0 (Zp )
c/cc
ce
cg (t)
cM
cout (Zp , r, t)
cp
c(r, t)
C
C
C
C
C0 (t)

filter packing density
critical vapor concentration level
concentration of particles at inlet
supersaturation
equivalent filter packing density
g-mer concentration
concentration of M-mer
concentration of particles at outlet
filter packing density

particle concentration at point r at time t
condition number (Chapter 8)
Cunningham correction coefficient (Chapter 11)
monomer number concentration (Chapter 4)
vapor concentration (Chapter 4)
concentration at time t

Aerosols – Science and Technology. Edited by Igor Agranovski
Copyright  2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ISBN: 978-3-527-32660-0

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XVIII

List of Symbols

Ca
C(a)
Cc
Cc (Kn)
CD
C(r)
CS
Cu

aerosol concentration at filter inlet
correction factor
Millikan correction factor

slip correction factor
drag coefficient
density–density correlation function
slip correction factor
Coulomb number

d
d
d
d1
d1
d50
dA
db
df
dk
dm
dmax
dmc
dmk
dN
dopt
dp
dS
dV
dσe /d
D
D
D
D

D
D
D
Dd
Df
DgA
Di
Dion
DS
Dst
DX (X = A,B)

diameter of adsorbate molecule (Chapter 5)
dipole moment
particle diameter (Chapter 2)
spherule diameter
diameter of monomer
particle diameter at which 50% of particles are collected
radius of the equivalent projected sphere
diameter of bubble
fiber diameter
diameter of particle in size class k
transition mobility diameter
maximal size of a fractal aggregate
mobility diameter of fractal aggregate in continuum regime
mobility diameter of fractal aggregate in kinetic regime
number of particles within size range from x to x + dx
optical diameter
particle diameter
element of particle surface

volume equivalent diameter
differential elastic cross-section
active factor dose (Chapter 14)
average coefficient of diffusion (Chapter 10)
diffusivity (Chapter 1)
ion diffusivity (Chapter 1)
molecular diffusivity (Chapter 1)
tube diameter (Chapter 3)
average diffusion coefficient
diameter of drop
fractal dimension
diffusivity of reactant molecule A in gas phase
particle diffusion coefficient for spherical particle of diameter di
diffusion coefficient for ions
diffusion coefficient
geomagnetic disturbance storm time index
diffusivity of reactant molecules inside particle

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List of Symbols

e
e
e/m
epl
epl
E
E

E
Ea
EA
Ef
Eg
E(r, t)
Er (r, z)
Ez (r, z)
f+

coefficient of restitution (plastic and elastic deformation)
(Chapter 11)
elementary charge (Chapter 4)
ion’s charge-to-mass ratio
coefficient of restitution (plastic deformation only)
microscopic yield pressure
filter efficiency (Chapter 10)
kinetic energy for single vapor molecule (Chapter 4)
electric field strength
activation energy
activation energy
filter efficiency
bandgap
distribution of electric field
electrical intensity along radial coordinate
electrical intensity along longitudinal coordinate

f (a)
fA
fG (a)

fL
fL (a)
f (x)
F
F
F∗
Fdrag

velocity distribution function of molecules flying toward particle
surface
velocity distribution function of molecules flying outward from
particle
particle size distribution
distribution function of A molecules over coordinates and velocities
generalized gamma distribution
total fiber length in filter sample
log-normal distribution
particle size distribution
drag coefficient
electric force
drag force acting on unit length of fiber
drag force acting on particle

g
g
g
G
Gg
Gy


gravity (Chapter 11)
number of spherules comprising fractal aggregate (Chapter 1)
particle mass (Chapter 1)
cutoff particle mass
gas flow rate
total liquid supply at filter cross-section at height y

h
h
H
H
H

half distance between neighboring fibers (Chapter 10)
Planck constant (Chapter 2)
classical Hamiltonian (Chapter 4)
dimensionless Henry’s constant (Chapter 4)
filter thickness (Chapter 10)

f−

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XIX


XX

List of Symbols


HC
HS

Henry’s constant for reaction product C
Henry’s constant as defined by Seinfeld and Pandis

I(t)

particle productivity (number of particles produced per unit volume
per unit time)

j
jA
Jm
jr
j(r)
j(x)
J
J
J0
J(a)
J(a)
J(t)
J = ACG∗
J
J2 (c1 )

density of total flux of particles
total flux of A molecules trapped by particle
Bessel functions

normal component of density of overall flux of particles
steady-state density of ion flux
dimensionless nucleation rate
flux of evaporated atoms (Chapter 1)
total flux of condensable vapor (Chapter 4)
nucleation rate
steady-state ion flux
steady-state molecular flux
nucleation rate
nucleation rate for fluctuation-controlled nucleation
steady-state rate of new particle production
rate of dimerization

k
k
k∗
kB
kD
K
K0 (z)
Kd
K(g, l)
Kn
Knion
KX
K(x, y)

Boltzmann constant (Chapter 1)
hydrodynamic factor (Chapter 10)
number of condensable monomers in critical size nucleus

Boltzmann constant
fractal prefactor
particle breakthrough
modified Bessel function
dissolution coefficient
coagulation kernel
Knudsen number
Knudsen number for ions
enrichment coefficient of element X
coagulation kernel

l
l
l

distance deflected from original trajectory (Chapter 7)
mean free path of carrier gas molecules (Chapter 1)
mean free path of condensing molecule in carrier gas
(Chapter 4)
Coulomb length
height of mid-section
characteristic length of the flow (Chapter 1)
fiber length per unit surface area of filter (Chapter 4)
fiber length per unit volume of filter (Chapter 10)
total length of fibers in cell

lC
lm
L
L

L
Lc

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List of Symbols

m
m
m
m0
m1
mel
mg
m(r)
M
M
Mie

mass of foreign molecule (Chapter 1)
mass of particle (Chapter 2)
mean particle mass
mass of monomer
mass of monomer
mass of electron
mass of g-mer
density at point r
total mass of fractal aggregates
particle mass (Chapter 1)

Mie number

n
n
n0
n(1,2)

dimensionless particle concentration (Chapter 4)
refractive index of particle (Chapter 7)
inlet particle concentration
first and second moments of fractal aggregate size distribution
function
ion density far away from particle
number concentration of vapor molecules at particle surface
concentration of reactant in liquid phase immediately beneath
surface
concentration of particles flying outward (Chapter 4)
concentration of reactant immediately above particle surface
(Chapter 4)
concentration of A far away from particle
equilibrium concentration of A molecules
exact ion/vapor concentration profile (Chapter 1)
ion/vapor concentration profile in free-molecule zone (Chapter 4)
concentration of clusters of mass g
average occupation number
concentration of negative ions
steady-state ion concentration profile corresponding to total ion
flux J
steady-state vapor concentration profile corresponding to flux J(a)
number of primary particles of fractal aggregate i

ion/vapor concentration at distance R from particle center
equilibrium concentration of vapor molecules over planar surface of
liquid
concentration profile
particle mass spectrum
number of screens in diffusion battery
chiral indices
molecular number concentration (Chapter 4)
number of spores (Chapter 13)
total particle concentration (Chapter 8)

n∞
na
n∗A
n+
A
n+
A
nA∞
nAe
nexact (r)
nfm (r)
ng
ng (t)
n−
ion
n(J) (r)
n(J) (r)
np,i
nR

ns
nX (r)
n(y,τ )
n, m
(n, m)
N
N
N

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XXI


XXII

List of Symbols

N0
N1
N1 (t)
NA , NB
NC
NEi (Yi )
Ni
q
Ni
Nk (t)
Np
N(t)

N(x)

particle number concentration/total number of particles
fraction of condensed-matter particles of smallest size
number concentration of condensing monomers
total number of molecules of reactants
number of molecules of reaction product
distribution function of aerosol particles with respect to Yi
density of ions
aerosol fraction with particle diameter di and charge q
fraction of particles containing k monomers at time t
number of primary particles
total number concentration of coagulating particles
number of particles with size less than x

p
p
ps
Pe
Pf
Pi
Pint
l
Pm
P(n)
P(n, D)
P(x)

pressure (Chapter 5)
probability of causing reaction in organism (Chapter 14)

saturation vapor pressure
Peclet number
perimeter of fibers
penetration through battery with ni screens
internal pressure at embryo surface
associated Legendre polynomial
penetration function
penetration of particles with diffusion coefficient D through diffusion
battery with n screens
reading of instrument measuring property x

q
Q
Qa
Qsh

electrical charge
volumetric flow rate
flow rate of aerosol gas carrier
flow rate of buffer gas or filtered air

r
r
r0
r2
r2
rE
rf
ri
ri

rp
(r,θ )
R
R
R

position of particle
radial coordinate of particle
radius of spherule
correlation coefficient
radius of outer cylinder surface
equivalent film radius
fiber radius
position of the ith spherule
average particle size of fraction i
nanoparticle radius
dimensionless polar coordinates
channel radius (Chapter 8)
distance (Chapter 1)
gas constant (Chapter 5)

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List of Symbols

R
R
Re
R(x, a)


gyration radius of fractal aggregate (Chapter 1)
radius of limiting/constraining sphere
Reynolds number
linear response function of instrument

s
s1
sSC

Sc
Se
SH2 O
Stk

particle surface area
monomer surface area
surface area of the completely sintered particle
(volume-equivalent sphere)
ratio of the jet-to-plate distance (Chapter 13)
measured specific surface area (Chapter 5)
total particle area (Chapter 2)
normalized amplitude of flux polarized normal to the scattering
plane scattered through angle
normalized amplitude of flux polarized parallel to the scattering
plane scattered through angle
critical supersaturation
equivalent surface area of filter
surface area covered by water
Stokes number


t
t∗
t∗∗
tc
T
T
T
T0
T0
T1/2
Tf
Tm

number of years/time
time at which spontaneous nucleation process starts
time at which spontaneous nucleation process stops
critical time
absolute temperature
fluid temperature (Chapter 2)
thickness of filter (Chapter 11)
bulk melting temperature (1535 ◦ C)
spot temperature (Chapter 1)
half-life
front temperature
melting temperature for given particle

u
u
u0

u(r)
ur (r, z)
ut
uz (r, z)
uξ
U
U(r)

constant uniform velocity of incoming flow
flow velocity vector
average flow velocity
flow field at time t
particle velocity along cylinder radius
tangential component of velocity
particle velocity along cylinder axis
normal component of velocity
potential difference between plates
ion–particle interaction potential

S
S
S
S1 (Θ)
S2 (Θ)

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XXIII



XXIV

List of Symbols

Uz (r)
Uτ

velocity distribution of flow across cylinder radius
velocity of circulating gas at surface of bubble

v
v1
va
va,b,c
vi,j
vk
vT
V
V
V
V0
V0
V(a)
Vb
Vc
Vfiber
VR
VT

macroscopic flow velocity speed of carrier gas

molecular volume
volume per added molecule of A
molecular volume of reactants A, B, and C
relative thermal velocity between particles i and j
molecular velocities
thermal velocity of condensable gas molecules
filter face velocity of aerosol carrier (Chapter 11)
mole volume (Chapter 5)
volume of metal molecule (Chapter 3)
initial particle volume (Chapter 4)
potential difference (Chapter 8)
average volume of a void of size a
velocity of rise of bubble
critical velocity
fiber volume
volume of constraining sphere
average speed of ion’s thermal movement

W
W
W
WDF
p,q
Wi,j
WL
W(ng ,t)
W(N, t)

binding energy of surface film (Chapter 5)
impactor’s nozzle size (Chapter 13)

width of filter (Chapter 11)
dry filter weight
stability function
weight of liquid remaining on filter after drainage
probability for realization of given set at time t
probability to find exactly N particles at time t

x
x
x, y

distance of separation between center of mass of particle and surface
(Chapter 11)
particle geometry (Chapter 8)
masses of colliding particles (Chapter 1)

Yi

scattered light intensity

z
Z
Z
Zg
Zi
Zp

longitudinal coordinate of particle
partition function for single vapor molecule (Chapter 4)
total particle charge in units of e (Chapter 1)

partition function of g molecules inside sphere
charge on ion in units of e
charge on particle in units of e

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List of Symbols

α
α
α1
α(a)
α(a)
α(a, R)
αcoll
αfm (a)
αfm (a, R)
αg
α(g)

particle polarizability (Chapter 1)
filter packing density (Chapter 10)
rate of dimer formation
charging efficiency as function of a (Chapter 1)
condensation efficiency (Chapter 4)
charging efficiency as function of a at distance R
collision parameter
condensation efficiency in free-molecule regime
free-molecule form of α(a, R)

condensation coefficient
condensation efficiency

β
β
β
βC
βi,j
q
βi
βM
βp
β q→q−1
βR

coagulation kernel (coefficient) of two colliding particles
sticking probability
collision frequency of particles and monomers
sticking probability of molecules C
projected surface area between particles i and j
ion attachment coefficient
scattering coefficient from Mie scattering theory
particle scattering coefficient
ion attachment coefficient
scattering coefficient from Rayleigh scattering theory

γ

shape factor
velocity gradient

Euler gamma function (Chapter 1)
Euler’s gamma function (Chapter 8)

(x)
(γ )
δ
δD
δE
δmax
δ(x)
δ(y)
Hfus
t
v
x
[ p]

ε

Kronecker delta (Chapter 2)
thickness of diffusion boundary layer
equilibrium film thickness
maximum thickness of the film
Dirac delta function
film thickness on fibers at filter vertical elevation y
three-dimensional Laplace operator (Chapter 10)
latent heat of fusion
time between pulses
change in velocity
width of thin slot

standard resistance of material
dielectric permeability (Chapter 1)
fraction of water-soluble compounds
rate of dissipation of kinetic energy of the turbulent flow

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XXV


XXVI

List of Symbols

η
η
η
ηD
ηi
θ
θ
θ/Θ
θ( )
q
ϑi
(x)

dynamic gas viscosity (Chapter 2)
fiber collection efficiency (Chapter 10)
trapping efficiency (Chapter 8)

efficiency of diffusion deposition
efficiency of inertial deposition
adsorption coverage (in monolayers) (Chapter 5)
latitude angle measured from zero at direction of rise (Chapter 11)
scattering angle (Chapter 1)
Heaviside step function
combination coefficient
Heaviside step function

κ

binary reaction rate constant

λ
λ
λg
λu
Λ

homogeneity exponent (Chapter 1)
mean free path of carrier gas molecules
mean free path of gas molecules
average length of ion’s mean free path
thermal conductivity of carrier gas

µ
µ
µ
µ±
µg


dynamic viscosity
liquid viscosity (Chapter 11)
smallness parameter (Chapter 4)
ion mobility
dynamic viscosity of gas

ν
v ion

kinematic viscosity of carrier gas
mean ion thermal velocity

ξm , ψm

Riccati–Bessel functions

ρ
ρ0
ρf
ρFM
ρg
ρp
ρL

density
density of spherule
front density
filter material density
carrier gas density

density of particle/particulate material
liquid density

σ
σ
σ
σabs
σi
σsca
σsl
Σ

average distribution width (Chapter 8)
scattering coefficient (Chapter 12)
surface tension
absorption cross-section
average distribution width of fraction i
elastic scattering cross-section
surface tension between liquid and solid
dimensionless surface tension parameter

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