E. James Davis • Gustav Schweiger The Airborne Microparticle Springer-Verlag Berlin Heidelberg GmbH E. James Davis • Gustav Schweiger The Airborne Microparticle Its Physics, Chemistry, Optics, and Transport Phenomena With 353 Figures Prof. E. James Davis University of Washington Department of Chemical Engineering Box 351750 Seattle, WA 98185-1750 USA Prof. Dr. Gustav Schweiger Ruhr-Universität-Bochum Institut für Automatisierungstechnik Lehrstuhl für Laseranwendungstechnik und Meßsysteme, Maschinenbau Universitätsstr. 150 44780 Bochum Germany e-mail: [email protected] ISBN 978-3-642-62806-1 Library of Congress Cataloging-in-Publication Data E. James Davis: The Airborne Microparticle: Its Physics, Chemistry, Optics, and Transport Phenomena / E. James Davis; G. Schweiger. - Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Tokyo: Springer 2002 (Engineering online library) ISBN 978-3-642-62806-1 ISBN 978-3-642-56152-8 (eBook) DOI 10.1007/978-3-642-56152-8 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution act under German Copyright Law, http://www.springer.de © Springer-Verlag Berlin Heidelberg 2002 Originally published by Springer-Verlag Berlin Heidelberg New York in 2002 Softcover reprint of the hardcover 1st edition 2002 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready copy from authors Cover-Design: de'blik, Berlin Printed on acid-free paper SPIN: 10796679 62/3020/kk 5 4 3 2 1 0 Foreword It has been thirty yearssince one ofthe authors (EJD) began a collaboration with ProfessorMilton Kerker atClarkson University inPotsdam, New York using light scattering methods to study aerosol processes. The development of a relatively short-lived commercial particle levitator based on a modification ofthe Millikan oil drop experiment attracted their attention and led the author to the study of single droplets and solid microparticles by levitation methods.The early work on measurements of droplet evaporation rates using light scattering techniques to determine the size slowly expanded and diversified as better instrumentation was developed, and faster computers made it possible to perform Mie theory light scattering calculations withease. Several milestones can be identified in the progress of single microparticle studies. The first is the introduction of the electrodynamic balance, which provided more robust trapping ofa particle. The electrodynamic levitator, which hasplayed an importantrole inatomic and molecularion spectroscopy, leading to the Nobel Prize in Physics in 1989 shared by Wolfgang Paul ofBonn University and Hans Dehmelt of the University of Washington, was easily adapted to trap microparticles. Simultaneously, improvements in detectors for acquiring and storing light scattering data and theoretical and experimental studies of the interesting optical propertiesofmicrospheres,especiallythework on morphology dependent resonances by Arthur Ashkin at the Bell Laboratories,Richard Chang, from Yale University, and Tony Campillo from the Naval Research Laboratories in Washington D.C. provided additional tools for precise measurements of the optical propertiesofspheresand spheroids. The work atthe Bell Laboratories also led to the optical levitator and to the 'optical tweezers' for manipulating small particles, including bacteria and other colloidal matter. A major milestone that made it possible to study the chemistry of the microparticle was the combination ofsingle particle levitation with inelastic scattering.This providedthe incentive to move from the physics ofsmall particles to theirchemistryandchemical reactions using Raman and fluorescence spectroscopies. The development of the vibrating orifice aerosol generator at the University of Minnesota provided yet another tool forprobing thesingleparticle inachain ofidentical particles. With the range of theoretical and experimental tools available it has become possible to use the many unique properties of droplets and small particles to investigate phenomena as diverse as linear and nonlinear optics, solution thermodynamics,gas/solid and gas/liquid chemical reactions, transport properties VI Foreword such asgas phase diffusion coefficients,rate processes inthecontinuumand non continuum regimes, trace gas uptake by aerosol droplets related to atmospheric chemistry and ozone depletion, phoretic phenomena, Raman spectroscopy, single molecule identification (by fluorescence methods), the physics and chemistry of bioaerosols, particle charge,evaporationandcondensation processes and others. The happy collision of the authors came about because of their mutual interest in elastic and inelastic light scattering from small particles when Professor Schweiger was at the Gerhard-Mercator-Universitat in Duisburg, Germany, and Professor Davis had moved to the University of Washington in Seattle. Their interaction grew when Professor Schweiger accepted his position at the Ruhr Universitat in Bochum where itbecame possible todevelop awide range of laser based instrumentation for microparticle research. The authors are grateful that their interaction was supported bythe Deutscher AkademischerAustausdienst and the international cooperation program of the National Science Foundation (Grants CTS-9528897 and INT-9725216). One must give credit where it is due, and it isthe wonderful group of graduate students and post-doctoral researchers that have made this book areality.It is not reasonable to provide a list covering thirty years, but we must recognize the contributionsof many ofour younger colleagues.First and foremost isour mutual friend and colleague, Professor Asit K. Ray of the University of Kentucky. It was he who brought to our attention the papers of Paul on the quadrupole and who built the first such instrument for Professor Davis. His doctoral work earned him the first Kenneth Whitby Award of the American Association for Aerosol Research. That work was followed by Dr. Ravidran Perisasamy at Clarkson and the University of New Mexico, Dr. Randolph Chang, Dr. Christopher Guzy, Professor Timothy Ward of the University of New Mexico, Dr. Shu-Hua Zhang, John Fulton, Dr. Daniel Taflin, Dr.Theresa M. Allen, Dr. Mark Buehler,Dr. Scot Rassat, Dr. Willard Foss, Dr. Wanguang Li, Dr. Christopher Aardahl, Dr. John Widmann, Research Professor Brian Swanson, Dr. Mary Laucks, Dr. Richard Zheng andothers. Ontheother sideof theocean Dr.Reinhard Vehring, Dr.Cemal Esen, Dr. Thomas Kaiser, Dr. GUnterRoll, Dr. Chao Liu, Dr. Bin Xu, Dr. Helge Moritz, Dr. Jorg Schulte, Thomas Weigel and many students have contributed to extend the knowledge of microparticles and their interaction with light and the surroundinggas. The comprehensiveness and rigor of the theoretical treatment were generally sacrificed in favor of the presentation of the basic concepts. More space was devoted totheory whenthe authors felt that noorfew comprehensivedescriptions of the phenomena were available. Throughout this book the main concern of the authors was to provide the reader with a visualization of the significance and application of theory.To emphasize this point experimental results are presented asfaraspossible. Bochum, Seattle Gustav Schweiger Spring 2002 James Davis Contents 1Background 1 1.1Introduction 1 1.2Light Scattering .4 1.2.1Tyndall'sObservations .4 1.2.2RayleighScattering 6 1.2.3Lorenz-Mie-DebyeTheory 8 1.2.4 Inelastic Scattering 12 1.2.5Quasi-ElasticScattering 16 1.3MicroparticleTransportPhenomena 16 1.3.1Kinetic Theory 17 1.3.2ContinuumTheory 19 1.4TransportintheTransition Regime 22 1.4.1Transition Regime MassTransfer. 24 1.4.2 TransitionRegime HeatTransfer. 26 1.4.3The CunninghamCorrection 26 1.5Particle Charge 27 1.5.1The CavendishLaboratoryExperiments 28 1.5.2Millikan'sExperiments 30 1.6Applicationsand AdaptationsofMODE 32 1.6.1Brownian Motion inGases 33 1.6.2MicrodropletEvaporation 34 1.6.3 Knudsen Aerosol Evaporation .37 1.6.4A Kinetic Theory Approximation 39 1.6.5Light ScatteringMeasurements .40 1.7Particle LevitationInstrumentation .42 1.7.1 Magnetic Suspension .42 1.7.2Electrostatic Suspension .43 1.7.3Electrodynamic Suspension .44 1.7.4Optical Levitation .47 1.7.5Acoustic Levitation ..49 1.8The Vibrating Orifice Generator ..49 1.9ApplicationsofSingle ParticleDevices 50 1.9.1ConcentratedElectrolyteSolutions 51 1.9.2 Microparticle Spectroscopies 51 1.9.3GasIParticle ChemicalReactions .53 VIII Contents 1.9.4Evaporation/CondensationProcesses 54 1.9.5Physical andInterfacial Properties of Microparticles 55 1.10References 57 2Particle Levitation 67 2.1 IntroductiontoLevitation Phenomena 67 2.2ElectrostaticBalances 69 2.3 ElectrodynamicBalances 71 2.4 PrinciplesofElectrodynamicTrapping 78 2.4.1The Equationof Particle Motion 78 2.4.2 Trapping inaPotential Well 79 2.5EDB Electric Fields 82 2.5.1Spherical HarmonicsSolution 84 2.5.2 Ring Charge Simulation 94 2.5.3ElectrodeAsymmetries 101 2.5.4 OptimumBalanceShapes 103 2.6Particle StabilityinanEDB 104 2.6.1The IonTrap 106 2.6.2The MicroparticleTrap 109 2.6.3 MUller's Solution 110 2.6.4ContinuedFractions 110 2.6.5 Numerical Solutions 113 2.7 Nonhyperboloidal Balances 114 2.7.1The Single Ring 115 2.7.2 Straubel'sThree Disk Balance 115 2.8 Optical Levitation 117 2.8.1The Optical Levitator. 117 2.8.2The Single-Beam GradientForce Trap 120 2.9AcousticLevitation 123 2.9.1Acoustic Pressure 123 2.9.2The BarotropicFluid 125 2.9.3Energy Density ofan Acoustic Wave 126 2.9.4 Acoustic Pressureon aSphere 127 2.9.5Particle Velocity andPhase Shift.. 130 2.9.6Acoustic Levitators 132 2.9.7Acoustic Measurements 133 2.10References 137 3Elastic Light Scattering 143 3.1Introduction 143 3.2MaxwellEquations 145 3.2.1ConstitutiveRelations 146 3.2.2Time-HarmonicFields 147 3.2.3 Power andEnergy Density 148 3.2.4 Polarization 150 Contents IX 3.3Dipole Radiation 151 3.4Cross SectionsandRadiation Pressure 153 3.4.1 CrossSectionsandEfficiencies 154 3.4.2 Radiation Pressure 155 3.4.3 Radiation Pressure Measurement... 156 3.5Rayleigh Scattering 157 3.5.1 IrradianceofScatteredLight 158 3.5.2PolarizationoftheScatteredLight... 159 3.6ElectromagneticTheory 160 3.6.1MultipoleExpansion 161 3.6.2 Lorenz-MieTheory 162 3.6.3CrossSectionsand Efficiencies 166 3.6.4 Angular Scattering 167 3.6.5Morphology-DependentResonances 169 3.6.6Polarization Ratio 179 3.6.7Electromagnetic Energy Absorption 180 3.6.8Coated Spheres 183 3.7CoupledDipole Theory 185 3.8GeneralizedLorenz-MieTheory 187 3.9The T-matrix Method 190 3.10 Geometrical Optics 192 3.10.1BasicLawsofGeometrical Optics 193 3.10.2 Interfaces 195 3.10.3 Transmitted andScatteredFields 196 3.10.4 Opticsof the Rainbow 201 3.11 Resonances 203 3.11.1 The Localization Principle 204 3.11.2 Resonance Conditions 205 3.11.3 ResonanceCondition forSpherical Geometry 208 3.11.4 Quality factor QandLine Width 210 3.12References 213 4 BasicSingle Particle Measurements 221 4.1 Force Measurement 221 4.2 AerodynamicDrag 223 4.3 LevitationCharacteristics 23I 4.3.1Direct MeasurementofC 231 o 4.3.2 Stability Measurements 233 4.3.3SHEL Data 233 4.3.4 Double-RingMeasurements 234 4.3.5Multiple Particle Trapping 237 4.4 Radiometric andPhoretic Forces 238 4.4.1 Radiation Pressure Force 238 4.4.2 Optical Trap Measurement 239 4.4.3 PhoreticForces 243 X Contents 4.4.4 PhotophoresisMeasurements 243 4.4.5ThennophoresisMeasurements 245 4.5 MassMeasurement. 247 4.6Aerodynamic SizeMeasurement.. 249 4.6.1TheLaminarJet EDB 249 4.6.2Sedimentation 250 4.6.3 Particle StabilityMeasurements 252 4.6.4 PhaseLagMeasurements 254 4.7Optical Size 262 4.7.1 PhaseFunctions 262 4.7.3Polarization Ratio Measurement... 265 4.7.4 Resonance Spectra 266 4.7.5 Diffraction 270 4.7.6 PhaseDopplerAnemometry 276 4.8 Charge Measurement. 287 4.8.1EvaporatingDroplets 287 4.8.2The Rayleigh Limit ofCharge 289 4.8.3Droplet Chain ChargeMeasurement.. 290 4.9 PhotoelectricWork Function 290 4.10References 295 5ContinuumTransport Processes .301 5.1Transport Regimes 301 5.2ThermalEnergyEquation 303 5.3ConvectiveDiffusion Equation .305 5.4 EquationsofMotion 306 5.4.1 StokesFlow 307 5.4.2HigherOrder Solutions .308 5.4.3 Fluid Spheres .309 5.4.4Ellipsoidal Particles 310 5.4.5 Other Non-spherical Particles 314 5.5HeatTransfer .317 5.5.1 StagnantFluid 317 5.5.2Electromagnetic Heating .320 5.5.3Internal Temperatureswith Pulsed Heating 321 5.5.4 External TemperaturesinPulsed Heating 330 5.5.5Particle Cooling byThermal Emission 332 5.6MassTransfer 333 5.6.1 HeatandMassFlux Relations 334 5.6.2 Single Component Droplet Evaporation 336 5.6.3 Quasi-SteadyState 345 5.6.4 MulticomponentEvaporation Measurements .357 5.6.5Condensational Particle Growth 361 5.7ConvectiveTransportProcesses 363 5.7.1 HeatandMassTransfer withStokesFlow 363