Edited by

Igor Agranovski

Aerosols – Science andTechnology

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Edited by Igor Agranovski

Aerosols – Science and Technology

The Editor

Prof. Dr. Igor AgranovskiGriffith UniversityGriffith School of Engineering170, Kessels Road, Nathan Cam.Brisbane, Queensland 4111Australia

All books published by Wiley-VCH arecarefully produced. Nevertheless, authors,editors, and publisher do not warrant theinformation contained in these books,including this book, to be free of errors.Readers are advised to keep in mind thatstatements, data, illustrations, proceduraldetails or other items may inadvertently beinaccurate.

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British Library Cataloguing-in-PublicationDataA catalogue record for this book is availablefrom the British Library.

Bibliographic information published by theDeutsche NationalbibliothekThe Deutsche Nationalbibliotheklists this publication in the DeutscheNationalbibliografie; detailed bibliographicdata are available on the Internet at<http://dnb.d-nb.de>.

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

All rights reserved (including those oftranslation into other languages). No partof this book may be reproduced in anyform – by photoprinting, microfilm, or anyother means – nor transmitted or translatedinto a machine language without writtenpermission from the publishers. Registerednames, trademarks, etc. used in this book,even when not specifically marked as such,are not to be considered unprotected by law.

Composition Laserwords Private Ltd.,Chennai, IndiaPrinting and Bookbinding betz-druckGmbH, DarmstadtCover Design Formgeber, Eppelheim

Printed in the Federal Republic of GermanyPrinted on acid-free paper

ISBN: 978-3-527-32660-0

V

Contents

List of Contributors XIIIList of Symbols XVIIIntroduction XXIX

1 Introduction to Aerosols 1Alexey A. Lushnikov

1.1 Introduction 11.2 Aerosol Phenomenology 21.2.1 Basic Dimensionless Criteria 21.2.1.1 Reynolds Number 21.2.1.2 Stokes Number 21.2.1.3 Knudsen Number 31.2.1.4 Peclet Number 31.2.1.5 Mie Number 31.2.1.6 Coulomb Number 31.2.2 Particle Size Distributions 41.2.2.1 The Log-Normal Distribution 41.2.2.2 Generalized Gamma Distribution 51.3 Drag Force and Diffusivity 61.4 Diffusion Charging of Aerosol Particles 71.4.1 Flux Matching Exactly 81.4.2 Flux Matching Approximately 91.4.3 Charging of a Neutral Particle 91.4.4 Recombination 101.5 Fractal Aggregates 111.5.1 Introduction 121.5.2 Phenomenology of Fractals 131.5.2.1 Fractal Dimension 131.5.2.2 Correlation Function 141.5.2.3 Distribution of Voids 141.5.2.4 Phenomenology of Atmospheric FA 141.5.3 Possible Sources of Fractal Particles 151.5.3.1 Natural Sources 15

Aerosols – Science and Technology. Edited by Igor AgranovskiCopyright 2010 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-32660-0

VI Contents

1.5.3.2 Anthropogenic Sources 151.5.4 Formation of Fractal Aggregates 161.5.4.1 Growth by Condensation 161.5.4.2 Growth by Coagulation 171.5.4.3 Aerosol–Aerogel Transition 181.5.5 Optics of Fractals 181.5.6 Are Atmospheric Fractals Long-Lived? 201.5.7 Concluding Remarks 211.6 Coagulation 211.6.1 Asymptotic Distributions in Coagulating Systems 231.6.2 Gelation in Coagulating Systems 261.7 Laser-Induced Aerosols 331.7.1 Formation of Plasma Cloud 331.7.1.1 Nucleation plus Condensational Growth 341.7.1.2 Coagulation 341.7.2 Laser-Induced Gelation 341.8 Conclusion 36

References 37

Part I Aerosol Formation 43

2 High-Temperature Aerosol Systems 45Arkadi Maisels

2.1 Introduction 452.2 Main High-Temperature Processes for Aerosol Formation 452.2.1 Flame Processes 472.2.2 Hot-Wall Processes 492.2.3 Plasma Processes 492.2.4 Laser-Induced Processes 502.2.5 Gas Dynamically Induced Particle Formation 502.3 Basic Dynamic Processes in High-Temperature Aerosol Systems 502.3.1 Nucleation 522.3.2 Coagulation/Aggregation 522.3.3 Surface Growth Due to Condensation 552.3.4 Sintering 552.3.5 Charging 572.4 Particle Tailoring in High-Temperature Processes 59

References 61

3 Aerosol Synthesis of Single-Walled Carbon Nanotubes 65Albert G. Nasibulin and Sergey D. Shandakov

3.1 Introduction 653.1.1 Carbon Nanotubes as Unique Aerosol Particles 653.1.2 History and Perspectives of CNT Synthesis 683.2 Aerosol-Unsupported Chemical Vapor Deposition Methods 70

Contents VII

3.2.1 The HiPco Process 70

3.2.2 Ferrocene-Based Method 71

3.2.3 Hot-Wire Generator 73

3.3 Control and Optimization of Aerosol Synthesis 74

3.3.1 On-Line Monitoring of CNT Synthesis 74

3.3.2 Individual CNTs and Bundle Separation 76

3.3.3 CNT Property Control and Nanobud Production 76

3.4 Carbon Nanotube Bundling and Growth Mechanisms 78

3.4.1 Bundle Charging 78

3.4.2 Growth Mechanism 80

3.5 Integration of the Carbon Nanotubes 82

3.6 Summary 84

Acknowledgements 84

References 84

4 Condensation, Evaporation, Nucleation 91Alexey A. Lushnikov

4.1 Introduction 91

4.2 Condensation 92

4.2.1 Continuum Transport 93

4.2.2 Free-Molecule Transport 93

4.3 Condensation in the Transition Regime 94

4.3.1 Flux-Matching Theory 95

4.3.2 Approximations 96

4.3.2.1 The Fuchs Approximation 96

4.3.2.2 The Fuchs–Sutugin Approximation 96

4.3.2.3 The Lushnikov–Kulmala Approximation 96

4.3.3 More Sophisticated Approaches 97

4.4 Evaporation 97

4.5 Uptake 99

4.5.1 Getting Started 100

4.5.2 Hierarchy of Times 101

4.5.3 Diffusion in the Gas Phase 101

4.5.4 Crossing the Interface 103

4.5.5 Transport and Reaction in the Liquid Phase 103

4.6 Balancing Fluxes 104

4.6.1 No Chemical Interaction 104

4.6.2 Second-Order Kinetics 106

4.7 Nucleation 108

4.7.1 The Szilard–Farkas Scheme 109

4.7.2 Condensation and Evaporation Rates 110

4.7.3 Thermodynamically Controlled Nucleation 111

VIII Contents

4.7.4 Kinetically Controlled Nucleation 1114.7.5 Fluctuation-Controlled Nucleation 1134.8 Nucleation-Controlled Processes 1144.8.1 Nucleation Bursts 1144.8.2 Nucleation-Controlled Condensation 1154.8.3 Nucleation-Controlled Growth by Coagulation 1174.8.4 Nucleation Bursts in the Atmosphere 1194.9 Conclusion 120

References 122

5 Combustion-Derived Carbonaceous Aerosols (Soot) in the Atmosphere:Water Interaction and Climate Effects 127Olga B. Popovicheva

5.1 Black Carbon Aerosols in the Atmosphere: Emissions and ClimateEffects 127

5.2 Physico-Chemical Properties of Black Carbon Aerosols 1325.2.1 General Characteristics 1335.2.2 Key Properties Responsible for Interaction with Water 1375.3 Water Uptake by Black Carbons 1405.3.1 Fundamentals of Water Interaction with Black Carbons 1405.3.2 Concept of Quantification 1435.3.3 Laboratory Approach for Water Uptake Measurements 1445.3.4 Quantification of Water Uptake 1465.3.4.1 Hydrophobic Soot 1465.3.4.2 Hydrophilic Soot 1485.3.4.3 Hygroscopic Soot 1515.4 Conclusions 152

Acknowledgements 153References 153

6 Radioactive Aerosols – Chernobyl Nuclear Power Plant CaseStudy 159Boris I. Ogorodnikov

6.1 Introduction 1596.2 Environmental Aerosols 1646.2.1 Dynamics of Release of Radioactive Aerosols from Chernobyl 1646.2.2 Transport of Radioactive Clouds in the Northern Hemisphere 1666.2.3 Observation of Radioactive Aerosols above Chernobyl 1686.2.4 Observations of Radioactive Aerosols in the Territory around

Chernobyl 1716.2.5 Dispersity of Aerosol Carriers of Radionuclides 1836.3 Aerosols inside the Vicinity of the ‘‘Shelter’’ Building 1856.3.1 Devices and Methods to Control Radioactive Aerosols in the

‘‘Shelter’’ 1856.3.2 Control of Discharge from the ‘‘Shelter’’ 185

Contents IX

6.3.3 Well-Boring in Search of Remaining Nuclear Fuel 1866.3.4 Clearance of the Turbine Island of the Fourth Power

Generating Unit 1886.3.5 Strengthening of the Seats of Beams on the Roof of the ‘‘Shelter’’ 1896.3.6 Aerosols Generated during Fires in the ‘‘Shelter’’ 1916.3.7 Dust Control System 1926.3.8 Control of the Release of Radioactive Aerosols through the ‘‘Bypass’’

System 1926.3.9 Radon, Thoron and their Daughter Products in the ‘‘Shelter’’ 195

References 197

Part II Aerosol Measurement and Characterization 203

7 Applications of Optical Methods for Micrometer and SubmicrometerParticle Measurements 205Aladar Czitrovszky

7.1 Introduction 2057.2 Optical Methods in Particle Measurements 2067.3 Short Overview of Light Scattering Theories 2087.4 Classification of Optical Instruments for Particle Measurements 2137.4.1 Multi-Particle Instruments 2137.4.2 Single-Particle Instruments 2147.5 Development of Airborne and Liquid-borne Particle Counters and

Sizers 2157.5.1 Development of Airborne Particle Counters 2167.5.2 Development of Liquid-borne Particle Counters 2227.6 New Methods Used to Characterize the Electrical Charge and Density

of the Particles 2257.7 Aerosol Analyzers for Measurement of the Complex Refractive Index

of Aerosol Particles 2277.8 Comparison of Commercially Available Instruments and Analysis of

the Trends of Further Developments 2297.8.1 Portable Particle Counters 2307.8.2 Remote Particle Counters 2307.8.3 Multi-Particle Counters 2337.8.4 Handheld Particle Counters 2337.9 Conclusions 233

References 234

8 The Inverse Problem and Aerosol Measurements 241Valery A. Zagaynov

8.1 Introduction 2418.2 Forms of Representation of Particle Size Distribution 2438.3 Differential and Integral Measurements 245

X Contents

8.4 Differential Mobility Analysis 2468.5 Diffusion Aerosol Spectrometry 2528.5.1 Raw Measurement Results and their Development – Parameterization

of Particle Size Distribution 2548.5.2 Fitting of Penetration Curves 2568.5.3 Transformation of the Integral Equation into Nonlinear Algebraic

Form 2578.5.4 Effect of Experimental Errors on Reconstruction of Particle Size

Distribution 2598.5.5 Reconstruction of Bimodal Distributions 2618.5.6 Mathematical Approach to Reconstruct Bimodal Distribution from

Particle Penetration Data 2648.5.7 Solution of the Inverse Problem by Regularization Method 2668.6 Conclusions 268

References 269

Part III Aerosol Removal 273

9 History of Development and Present State of Polymeric Fine-FiberUnwoven Petryanov Filter Materials for Aerosol Entrapment 275Bogdan F. SadovskyReferences 282

10 Deposition of Aerosol Nanoparticles in Model Fibrous Filters 283Vasily A. Kirsch and Alexander A. Kirsch

10.1 Introduction 28310.2 Results of Numerical Modeling of Nanoparticle Deposition in

Two-Dimensional Model Filters 28710.2.1 Fiber Collection Efficiency at High Peclet Number: Cell Model

Approach 28710.2.2 Fiber Collection Efficiency at Low Peclet Number: Row of Fibers

Approach 28910.2.3 Deposition of Nanoparticles upon Ultra-Fine Fibers 29210.2.4 Deposition of Nanoparticles on Fibers with Non-Circular

Cross-Section 29410.2.5 Deposition of Nanoparticles on Porous and Composite Fibers 29810.3 Penetration of Nanoparticles through Wire Screen Diffusion

Batteries 30210.3.1 Deposition of Nanoparticles in Three-Dimensional Model Filters 30210.3.2 Theory of Particle Deposition on Screens with Square Mesh 30410.3.3 Comparison with Experiment 30510.4 Conclusion 310

Acknowledgements 311References 311

Contents XI

11 Filtration of Liquid and Solid Aerosols on Liquid-Coated Filters 315Igor E. Agranovski

11.1 Introduction 31511.2 Wettable Filtration Materials 31611.2.1 Theoretical Aspects 31811.2.2 Practical Aspects 32011.2.3 Inactivation of Bioaerosols on Fibers Coated by a Disinfectant 32611.3 Non-Wettable Filtration Materials 32711.3.1 Theoretical Aspects 32711.3.2 Practical Aspects of Non-Wettable Filter Design 33011.4 Filtration on a Porous Medium Submerged into a Liquid 33011.4.1 Theoretical Approach 33011.4.2 Application of the Technique for Viable Bioaerosol Monitoring 337

References 340

Part IV Atmospheric and Biological Aerosols 343

12 Atmospheric Aerosols 345Lev S. Ivlev

12.1 General Concepts 34512.2 Atmospheric Aerosols of Different Nature 34812.2.1 Soil Aerosols 34812.2.2 Marine Aerosols 35112.2.3 Volcanic Aerosols 35412.2.4 Aerosols In situ – Secondary Aerosols 35812.2.4.1 Photochemical Oxidation – Heterogeneous Reactions 35912.2.4.2 Catalytic Oxidation in the Presence of Heavy Metals 36012.2.4.3 Reaction of Ammonia with Sulfur Dioxide in the Presence of Water

Droplets (Reaction of Cloud Droplets) 36012.2.5 Biogenic Small Gas Compounds and Aerosols 36012.3 Temporal and Dimensional Structure of Atmospheric Aerosols 36312.3.1 Aerosols in the Troposphere 36312.3.1.1 Terrigenous Elements 36312.3.1.2 The Group of Ions 36312.4 Aerosols in the Stratosphere 371

References 377

13 Biological Aerosols 379Sergey A. Grinshpun

13.1 Introduction 37913.2 History of Bioaerosol Research 37913.3 Main Definitions and Types of Bioaerosol Particles 38113.4 Sources of Biological Particles and their Aerosolization 38313.5 Sampling and Collection 38413.5.1 Impaction 386

XII Contents

13.5.2 Collection into Liquid 38813.5.3 Filter Collection 38913.5.4 Gravitational Settling 39013.5.5 Electrostatic Precipitation 39013.6 Analysis 39113.7 Real-Time Measurement of Bioaerosols 39313.8 Purification of Indoor Air Contaminated with Bioaerosol Particles and

Respiratory Protection 39313.8.1 Air Purification 39313.8.2 Respiratory Protection 396

References 398

14 Atmospheric Bioaerosols 407Aleksandr S. Safatov, Galina A. Buryak, Irina S. Andreeva, Sergei E.Olkin, Irina K. Reznikova, Aleksandr N. Sergeev, Boris D. Belan andMikhail V. Panchenko

14.1 Introduction 40714.2 Methods of Atmospheric Bioaerosol Research 40814.2.1 Methods and Equipment for Atmospheric Bioaerosol Sampling 40914.2.2 Methods to Analyze the Chemical Composition of Atmospheric

Bioaerosols and their Morphology 41114.2.3 Methods Used to Detect and Characterize Microorganisms in

Atmospheric Bioaerosols 41614.3 Atmospheric Bioaerosol Studies 42114.3.1 Time Variation of Concentrations and Composition of Atmospheric

Bioaerosol Components 42114.3.2 Spatial Variation of the Concentrations and Composition of

Atmospheric Bioaerosol Components 43214.3.3 Possible Sources of Atmospheric Bioaerosols and their Transfer in the

Atmosphere 43614.3.4 The Use of Snow Cover Samples to Analyze Atmospheric

Bioaerosols 43814.3.5 Potential Danger of Atmospheric Bioaerosols for Humans and

Animals 44214.4 Conclusion 446

References 448

Index 455

XIII

List of Contributors

Igor E. AgranovskiGriffith UniversitySchool of Engineering170 Kessels RoadNathan CampusBrisbaneQueensland 4111Australia

Irina S. AndreevaFederal Service for Surveillance inConsumer Rights Protection andHuman Well-BeingState Research Center of Virologyand Biotechnology ‘‘Vector’’Koltsovo, 630559NovosibirskRussia

Boris D. BelanSiberian Branch of the RussianAcademy of SciencesV.E. Zuev Institute forAtmospheric OpticsAkademicheskii Avenue 1634055 TomskRussia

Galina A. BuryakFederal Service for Surveillance inConsumer Rights Protection andHuman Well-BeingState Research Center of Virologyand Biotechnology ‘‘Vector’’Koltsovo, 630559NovosibirskRussia

Aladar CzitrovszkyResearch Institute for SolidState Physics and OpticsDepartment of Laser ApplicationP.O. Box 491525 BudapestHungary

Sergey A. GrinshpunUniversity of CincinnatiDepartment ofEnvironmental Health3223 Eden Avenue107 Kettering BuildingCincinnati, OhioOH 45267USA

Aerosols – Science and Technology. Edited by Igor AgranovskiCopyright 2010 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-32660-0

XIV List of Contributors

Lev S. IvlevSaint PetersburgState University7–9 UniversitetskayaNaberezhnayaSaint Petersburg 1999034Russia

Alexander A. KirschRussian Research Center‘‘Kurchatov Institute’’Kurchatov Square, 1123182 MoscowRussia

Vasily A. KirschRussian Academy of SciencesFrumkin Institute of PhysicalChemistry and ElectrochemistryLeninski Prospect, 31119991 MoscowRussia

Alexey A. LushnikovKarpov Institute ofPhysical Chemistry10, ul Vorontsovo Pole103062 MoscowRussia

and

University of HelsinkiFaculty of Mathematics andNatural SciencesPhysics, Atmospheric Sciencesand Geophysics DepartmentGustav Hallstromin katu 200014 Helsingen YliopistoFinland

Arkadi MaiselsEvonik Degussa GmbHIndustriepark WolfgangRodenbacher Chaussee 463457 HanauGermany

Albert G. NasibulinNanoMaterials GroupDepartment of Applied Physicsand Center for New MaterialsAalto UniversityPuumiehenkuja 200076 EspooFinland

Boris I. OgorodnikovKarpov Institute ofPhysical Chemistry10, ul Vorontsovo pole105064 MoscowRussia

Sergei E. OlkinFederal Service for Surveillance inConsumer Rights Protection andHuman Well-BeingState Research Center of Virologyand Biotechnology ‘‘Vector’’Koltsovo, 630559NovosibirskRussia

Mikhail V. PanchenkoSiberian Branch of the RussianAcademy of SciencesV.E. Zuev Institute forAtmospheric OpticsAkademicheskii Avenue 1634055 TomskRussia

List of Contributors XV

Olga B. PopovichevaSkobeltsyn Institute ofNuclear PhysicsDivision of MicroelectronicsMoscow State University1(2) Leninskie gory119991 MoscowRussia

Irina K. ReznikovaFederal Service for Surveillance inConsumer Rights Protection andHuman Well-BeingState Research Center of Virologyand Biotechnology ‘‘Vector’’Koltsovo, 630559NovosibirskRussia

Bogdan F. SadovskyKarpov Institute ofPhysical Chemistry10, ul Vorontsovo Pole103062 MoscowRussia

Aleksandr S. SafatovFederal Service for Surveillance inConsumer Rights Protection andHuman Well-BeingState Research Center of Virologyand Biotechnology ‘‘Vector’’Koltsovo, 630559NovosibirskRussia

Alexander N. SergeevFederal Service for Surveillance inConsumer Rights Protection andHuman Well-BeingState Research Center of Virologyand Biotechnology ‘‘Vector’’Koltsovo, 630559NovosibirskRussia

Sergey D. ShandakovLaboratory of CarbonNanoMaterialsDepartment of PhysicsKemerovo State UniversityKrasnaya 6Kemerovo, 650043Russia

Valery A. ZagaynovKarpov Institute ofPhysical Chemistry10, ul Vorontsovo pole105064 MoscowRussia

XVII

List of Symbols

a amount of vapor adsorbed (Chapter 5)a fiber radius (Chapter 10)a particle radius (Chapter 1)a0 radius of molecule of condensable substanceag radius of g-meram molecular radiusam monolayer coverageas characteristic particle radius, for normalization of particle sizeav equilibrium concentration of vaporA acceleration (Chapter 7)A Hamaker constant (Chapter 11)A(t), B(t) algebraic functions of time

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

c filter packing densityc∗ critical vapor concentration levelc0(Zp) concentration of particles at inletc/cc supersaturationce equivalent filter packing densitycg (t) g-mer concentrationcM concentration of M-mercout(Zp, r, t) concentration of particles at outletcp filter packing densityc(r, t) particle concentration at point r at time tC condition number (Chapter 8)C Cunningham correction coefficient (Chapter 11)C monomer number concentration (Chapter 4)C vapor concentration (Chapter 4)C0(t) concentration at time t

Aerosols – Science and Technology. Edited by Igor AgranovskiCopyright 2010 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-32660-0

XVIII List of Symbols

Ca aerosol concentration at filter inletC(a) correction factorCc Millikan correction factorCc(Kn) slip correction factorCD drag coefficientC(r) density–density correlation functionCS slip correction factorCu Coulomb number

d diameter of adsorbate molecule (Chapter 5)d dipole momentd particle diameter (Chapter 2)d1 spherule diameterd′

1 diameter of monomerd50 particle diameter at which 50% of particles are collecteddA radius of the equivalent projected spheredb diameter of bubbledf fiber diameterdk diameter of particle in size class kdm transition mobility diameterdmax maximal size of a fractal aggregatedmc mobility diameter of fractal aggregate in continuum regimedmk mobility diameter of fractal aggregate in kinetic regimedN number of particles within size range from x to x + dxdopt optical diameterdp particle diameterdS element of particle surfacedV volume equivalent diameterdσe/d� differential elastic cross-sectionD active factor dose (Chapter 14)D average coefficient of diffusion (Chapter 10)D diffusivity (Chapter 1)D ion diffusivity (Chapter 1)D molecular diffusivity (Chapter 1)D tube diameter (Chapter 3)〈D〉 average diffusion coefficientDd diameter of dropDf fractal dimensionDgA diffusivity of reactant molecule A in gas phaseDi particle diffusion coefficient for spherical particle of diameter di

Dion diffusion coefficient for ionsDS diffusion coefficientDst geomagnetic disturbance storm time indexDX (X = A,B) diffusivity of reactant molecules inside particle

List of Symbols XIX

e coefficient of restitution (plastic and elastic deformation)(Chapter 11)

e elementary charge (Chapter 4)e/m ion’s charge-to-mass ratioepl coefficient of restitution (plastic deformation only)epl microscopic yield pressureE filter efficiency (Chapter 10)E kinetic energy for single vapor molecule (Chapter 4)E electric field strengthEa activation energyEA activation energyEf filter efficiencyEg bandgapE(r, t) distribution of electric fieldEr(r, z) electrical intensity along radial coordinateEz(r, z) electrical intensity along longitudinal coordinate

f + velocity distribution function of molecules flying toward particlesurface

f − velocity distribution function of molecules flying outward fromparticle

f (a) particle size distributionfA distribution function of A molecules over coordinates and velocitiesfG(a) generalized gamma distributionfL total fiber length in filter samplefL(a) log-normal distributionf (x) particle size distributionF drag coefficientF electric forceF∗ drag force acting on unit length of fiberFdrag drag force acting on particle

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

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

XX List of Symbols

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

I(t) particle productivity (number of particles produced per unit volumeper unit time)

j density of total flux of particlesjA total flux of A molecules trapped by particleJm Bessel functionsjr normal component of density of overall flux of particlesj(r) steady-state density of ion fluxj(x) dimensionless nucleation rateJ flux of evaporated atoms (Chapter 1)J total flux of condensable vapor (Chapter 4)J0 nucleation rateJ(a) steady-state ion fluxJ(a) steady-state molecular fluxJ(t) nucleation rateJ = ACG∗ nucleation rate for fluctuation-controlled nucleationJ steady-state rate of new particle productionJ2(c1) rate of dimerization

k Boltzmann constant (Chapter 1)k hydrodynamic factor (Chapter 10)k∗ number of condensable monomers in critical size nucleuskB Boltzmann constantkD fractal prefactorK particle breakthroughK0(z) modified Bessel functionKd dissolution coefficientK(g, l) coagulation kernelKn Knudsen numberKnion Knudsen number for ionsKX enrichment coefficient of element XK(x, y) coagulation kernel

l distance deflected from original trajectory (Chapter 7)l mean free path of carrier gas molecules (Chapter 1)l mean free path of condensing molecule in carrier gas

(Chapter 4)lC Coulomb lengthlm height of mid-sectionL characteristic length of the flow (Chapter 1)L fiber length per unit surface area of filter (Chapter 4)L fiber length per unit volume of filter (Chapter 10)Lc total length of fibers in cell

List of Symbols XXI

m mass of foreign molecule (Chapter 1)m mass of particle (Chapter 2)〈m〉 mean particle massm0 mass of monomerm1 mass of monomermel mass of electronmg mass of g-merm(r) density at point rM total mass of fractal aggregatesM particle mass (Chapter 1)Mie Mie number

n dimensionless particle concentration (Chapter 4)n refractive index of particle (Chapter 7)n0 inlet particle concentrationn(1,2) first and second moments of fractal aggregate size distribution

functionn∞ ion density far away from particlena number concentration of vapor molecules at particle surfacen∗

A concentration of reactant in liquid phase immediately beneathsurface

n+A concentration of particles flying outward (Chapter 4)

n+A concentration of reactant immediately above particle surface

(Chapter 4)nA∞ concentration of A far away from particlenAe equilibrium concentration of A moleculesnexact(r) exact ion/vapor concentration profile (Chapter 1)nfm(r) ion/vapor concentration profile in free-molecule zone (Chapter 4)ng concentration of clusters of mass gng (t) average occupation numbern−

ion concentration of negative ionsn(J)(r) steady-state ion concentration profile corresponding to total ion

flux Jn(J)(r) steady-state vapor concentration profile corresponding to flux J(a)np,i number of primary particles of fractal aggregate inR ion/vapor concentration at distance R from particle centerns equilibrium concentration of vapor molecules over planar surface of

liquidnX(r) concentration profilen(y,τ ) particle mass spectrumn, m number of screens in diffusion battery(n, m) chiral indicesN molecular number concentration (Chapter 4)N number of spores (Chapter 13)N total particle concentration (Chapter 8)

XXII List of Symbols

N0 particle number concentration/total number of particlesN1 fraction of condensed-matter particles of smallest sizeN′

1(t) number concentration of condensing monomersNA, NB total number of molecules of reactantsNC number of molecules of reaction productNEi (Yi) distribution function of aerosol particles with respect to Yi

Ni density of ionsNq

i aerosol fraction with particle diameter di and charge qNk(t) fraction of particles containing k monomers at time tNp number of primary particlesN(t) total number concentration of coagulating particlesN(x) number of particles with size less than x

p pressure (Chapter 5)p probability of causing reaction in organism (Chapter 14)ps saturation vapor pressurePe Peclet numberPf perimeter of fibersPi penetration through battery with ni screensPint internal pressure at embryo surfacePl

m associated Legendre polynomialP(n) penetration functionP(n, D) penetration of particles with diffusion coefficient D through diffusion

battery with n screensP(x) reading of instrument measuring property x

q electrical chargeQ volumetric flow rateQa flow rate of aerosol gas carrierQsh flow rate of buffer gas or filtered air

r position of particler radial coordinate of particler0 radius of spheruler2 correlation coefficientr2 radius of outer cylinder surfacerE equivalent film radiusrf fiber radiusri position of the ith spherule〈ri〉 average particle size of fraction irp nanoparticle radius(r,θ ) dimensionless polar coordinatesR channel radius (Chapter 8)R distance (Chapter 1)R gas constant (Chapter 5)

List of Symbols XXIII

R gyration radius of fractal aggregate (Chapter 1)R radius of limiting/constraining sphereRe Reynolds numberR(x, a) linear response function of instrument

s particle surface areas1 monomer surface areasSC surface area of the completely sintered particle

(volume-equivalent sphere)S ratio of the jet-to-plate distance (Chapter 13)S measured specific surface area (Chapter 5)S total particle area (Chapter 2)S1(Θ) normalized amplitude of flux polarized normal to the scattering

plane scattered through angle �S2(Θ) normalized amplitude of flux polarized parallel to the scattering

plane scattered through angle �Sc critical supersaturationSe equivalent surface area of filterSH2O surface area covered by waterStk Stokes number

t number of years/timet∗ time at which spontaneous nucleation process startst∗∗ time at which spontaneous nucleation process stopstc critical timeT absolute temperatureT fluid temperature (Chapter 2)T thickness of filter (Chapter 11)T0 bulk melting temperature (1535 ◦C)T0 spot temperature (Chapter 1)T1/2 half-lifeTf front temperatureTm melting temperature for given particle

u constant uniform velocity of incoming flowu flow velocity vectoru0 average flow velocityu(r) flow field at time tur(r, z) particle velocity along cylinder radiusut tangential component of velocityuz(r, z) particle velocity along cylinder axisuξ normal component of velocityU potential difference between platesU(r) ion–particle interaction potential

XXIV List of Symbols

Uz(r) velocity distribution of flow across cylinder radiusUτ velocity of circulating gas at surface of bubble

v macroscopic flow velocity speed of carrier gasv1 molecular volumeva volume per added molecule of Ava,b,c molecular volume of reactants A, B, and Cvi,j relative thermal velocity between particles i and jvk molecular velocitiesvT thermal velocity of condensable gas moleculesV filter face velocity of aerosol carrier (Chapter 11)V mole volume (Chapter 5)V volume of metal molecule (Chapter 3)V0 initial particle volume (Chapter 4)V0 potential difference (Chapter 8)V(a) average volume of a void of size aVb velocity of rise of bubbleVc critical velocityVfiber fiber volumeVR volume of constraining sphereVT average speed of ion’s thermal movement

W binding energy of surface film (Chapter 5)W impactor’s nozzle size (Chapter 13)W width of filter (Chapter 11)WDF dry filter weightWp,q

i,j stability functionWL weight of liquid remaining on filter after drainageW(ng ,t) probability for realization of given set at time tW(N, t) probability to find exactly N particles at time t

x distance of separation between center of mass of particle and surface(Chapter 11)

x particle geometry (Chapter 8)x, y masses of colliding particles (Chapter 1)

Yi scattered light intensity

z longitudinal coordinate of particleZ partition function for single vapor molecule (Chapter 4)Z total particle charge in units of e (Chapter 1)Zg partition function of g molecules inside sphereZi charge on ion in units of eZp charge on particle in units of e

List of Symbols XXV

α particle polarizability (Chapter 1)α filter packing density (Chapter 10)α1 rate of dimer formationα(a) charging efficiency as function of a (Chapter 1)α(a) condensation efficiency (Chapter 4)α(a, R) charging efficiency as function of a at distance Rαcoll collision parameterαfm(a) condensation efficiency in free-molecule regimeαfm(a, R) free-molecule form of α(a, R)αg condensation coefficientα(g) condensation efficiency

β coagulation kernel (coefficient) of two colliding particlesβ sticking probabilityβ ′ collision frequency of particles and monomersβC sticking probability of molecules Cβi,j projected surface area between particles i and jβ

qi ion attachment coefficientβM scattering coefficient from Mie scattering theoryβp particle scattering coefficientβq→q−1 ion attachment coefficientβR scattering coefficient from Rayleigh scattering theory

γ shape factor� velocity gradient�(x) Euler gamma function (Chapter 1)�(γ ) Euler’s gamma function (Chapter 8)

δ Kronecker delta (Chapter 2)δD thickness of diffusion boundary layerδE equilibrium film thicknessδmax maximum thickness of the filmδ(x) Dirac delta functionδ(y) film thickness on fibers at filter vertical elevation y three-dimensional Laplace operator (Chapter 10) Hfus latent heat of fusion t time between pulses v change in velocity x width of thin slot[ p] standard resistance of material

ε dielectric permeability (Chapter 1)ε fraction of water-soluble compoundsε rate of dissipation of kinetic energy of the turbulent flow

XXVI List of Symbols

η dynamic gas viscosity (Chapter 2)η fiber collection efficiency (Chapter 10)η trapping efficiency (Chapter 8)ηD efficiency of diffusion depositionηi efficiency of inertial depositionθ adsorption coverage (in monolayers) (Chapter 5)θ latitude angle measured from zero at direction of rise (Chapter 11)θ/Θ scattering angle (Chapter 1)θ (ε) Heaviside step functionϑ

qi combination coefficient

�(x) Heaviside step function

κ binary reaction rate constant

λ homogeneity exponent (Chapter 1)λ mean free path of carrier gas moleculesλg mean free path of gas moleculesλu average length of ion’s mean free pathΛ thermal conductivity of carrier gas

µ dynamic viscosityµ liquid viscosity (Chapter 11)µ smallness parameter (Chapter 4)µ± ion mobilityµg dynamic viscosity of gas

ν kinematic viscosity of carrier gasvion mean ion thermal velocity

ξm, ψm Riccati–Bessel functions

ρ densityρ0 density of spheruleρf front densityρFM filter material densityρg carrier gas densityρp density of particle/particulate materialρL liquid density

σ average distribution width (Chapter 8)σ scattering coefficient (Chapter 12)σ surface tensionσabs absorption cross-sectionσi average distribution width of fraction iσsca elastic scattering cross-sectionσsl surface tension between liquid and solidΣ dimensionless surface tension parameter

List of Symbols XXVII

τ lifetimeτA characteristic time for chemical reaction of A molecules in

liquid phaseτchanges characteristic time of substantial chemical changes inside particleτchem characteristic reaction time for diffusion-controlled reactionτg characteristic time of non-stationarity in gas phaseτl characteristic time in liquid phaseτS characteristic sintering time

ϕ potential functionϕ2 second momentϕ(D) diffusion coefficient distributionϕ(l, q) interaction potential between ion and q-charged particle�q→q+1 work function

ψ stream functionψ(x) universality functionΨ (z, t) generating function for probability

�(Zp) transfer function for the differential mobility analyser

∇ gradient operator (Chapter 11)∑β activity concentration of mixture of beta-emitting nuclides