Suspension acoustics: an introduction to the physics of suspensions

418 Pages·2005·18.38 MB·English

by  Samuel Temkin

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SUSPENSION ACOUSTICS
This book examines, from a fundamental point of view, the response of
singleparticlesinfluidsandusestheresultsofsuchadetailedexamination
toconsidersuspensionmotionsasawhole–payingparticularattentionto
acousticmotions(i.e.,tothepropagationofsoundwaves).Suchpropagation
isexaminedfromdifferentperspectivesinaunifiedmannerthatappliesto
severalparticle-fluidcombinations.Amongthepossibleapplicationsofthe
theorypresented,thisbookdiscussesthecharacterizationofsuspensionsby
acousticmeansandtheagglomerationofparticleswithsoundwaves.
Samuel Temkin is Professor Emeritus, Department of Mechanical and
AerospaceEngineering,RutgersUniversity.
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Suspension Acoustics
An Introduction to the Physics of Suspensions
SAMUEL TEMKIN
RutgersUniversity
iii
cambridge university press
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
TheEdinburghBuilding,Cambridgecb22ru,UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Informationo nthi stitle :www.cambri dge.org/9780521847575
© Cambridge University Press 2005
Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionof
relevantcollectivelicensingagreements,noreproductionofanypartmaytakeplace
withoutthewrittenpermissionofCambridgeUniversityPress.
Firstpublishedinprintformat 2005
isbn-13 978-0-511-12749-6 eBook(EBL)
isbn-10 0-511-12749-9 eBook(EBL)
isbn-13 978-0-521-84757-5 hardback
isbn-10 0-521-84757-5 hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofurls
forexternalorthird-partyinternetwebsitesreferredtointhispublication,anddoesnot
guaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.
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Contents
ListofFiguresandTables pagexi
Preface xvi
1 Preliminaries 1
1.1 Introduction 1
1.2 Typesofsuspensions 5
1.3 Particleconcentrations 7
Particle-sizedistributions 8
Volumeconcentration 9
Massconcentration 9
Massandvolumeloadings 10
Suspensiondensity 10
1.4 Interparticleseparation 13
2 ConservationEquations 15
2.1 Introduction 15
Equationsofmotion 15
Boundaryconditions 18
2.2 Smallparticles 21
Volumeaverages 21
Kinematicconsiderations 21
2.3 Conservationequationsforasmallparticle 22
Mass 22
Linearmomentum 23
Angularmomentum 24
Uniformexpansion/compression 25
Associatedenergies 25
2.4 Internalenergy 27
2.5 Energydissipation 29
Dampingcoefficient 31
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vi Contents
2.6 Nondimensionalparameters 32
2.7 Motion at Re → 035
3 Rigid-ParticleHeatTransferatRe(cid:4)1 37
3.1 Introduction 37
3.2 Harmonictemperaturevariations 38
Heattransferrate 41
Lowfrequencies 42
Thermalrelaxationtime 43
3.3 Particleinoscillatingtemperaturefield 44
Unsteadyheattransferrate 46
3.4 Arbitrarytimedependence 49
Sudden temperature change 52
3.5 Nonuniform particle temperature 55
ThefunctionG(q )57
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Temperatureaverage 58
3.6 Concludingremarks 60
4 TranslationalMotionatRe(cid:4)1 61
4.1 Introduction 61
Basicequations 61
4.2 Translationaloscillations 63
Fluidpressure 69
Fluidforceonsphere 70
Decayofoscillations 73
4.3 Stokes’law 73
4.4 Slowlychangingmotions 75
Sphereinoscillatingfluid 77
Terminalvelocity 78
4.5 ExtensionstoStokes’law 79
Verysmallparticles 79
Sphericalbubblesanddroplets 80
Nonuniformflows 81
Nonsphericalparticles 81
SmallbutfiniteReynoldsnumbers 81
Liftforce 82
EmpiricalformsatfiniteRe 83
4.6 CurvilinearmotionatfiniteRe 84
4.7 Thestokeslet 87
Distributionsofstokeslets 91
4.8 Unsteady effects at Re (cid:4) 194
Sphereinoscillatoryfluid 96
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Contents vii
4.9 TheBasset–Boussinesq–Oseenequation 99
SpherereleaseinStokesflow 100
4.10 UnsteadydragatfiniteRe 106
Experimentalresults 108
4.11 Sphereinasoundwave 111
Inviscidfluid 114
Viscous,compressiblefluid 117
Absorptioncross-section 119
4.12 Forcereductionduetoparticleinteractions 121
VerysmallReynoldsnumbers 121
FiniteReynoldsnumbers 123
4.13 Concludingremarks 129
5 ShapeDeformations 130
5.1 Introduction 130
5.2 Energyconsiderations 132
Equilibriumpressureinadropletorbubble 132
5.3 Surfacevibrationsofadroplet 133
5.4 Breakupofliquidsurfaces 140
5.5 Concludingremarks 144
6 VolumePulsations 145
6.1 Introduction 145
6.2 Motionproducedbypulsatingsphere 146
Incompressiblefluid 147
Rayleigh’sequation 148
TheRayleigh–Plessetequation 150
Compressiblefluid 151
6.3 Forceonpulsatingsphere 153
6.4 Internalfields 154
Uniformdensity 155
Nonuniformfields 156
6.5 Surfacemotion 157
Dampingcoefficients 162
Drivenpulsations 162
6.6 Thermaleffects 164
Particletemperature 166
Particlepressure 170
Thepolytropicindex 171
Surfacedisplacement 176
Bubblesanddropletsinliquids 177
Aerosolandhydrosolparticles 182
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viii Contents
6.7 Energyconsiderations 185
Thermaldissipationrate 185
Absorptioncross-sections 187
Thermodynamicsofabubblecycle 191
6.8 Concludingremarks 195
7 ThermodynamicsofSuspensions 197
7.1 Introduction 197
7.2 Equilibrium 198
Mechanicalequilibrium 198
Thermalequilibrium 199
Thermodynamicequilibrium 200
7.3 Thermodynamicproperties 201
Isothermalcompressibility 201
Isothermalsoundspeed 202
Coefficientofthermalexpansion 203
Specificheats 203
Specificheatatconstantpressure 206
Specificheatatconstantvolume 207
Specificheatratio 208
7.4 Isentropicsoundspeed 210
7.5 Equationsofstate 214
Isentropicequationsofstate 215
7.6 Concludingremarks 216
8 TheTwo-PhaseModel 217
8.1 Introduction 217
8.2 Conservationequations 219
Conservationofmass 221
Linearmomentum 222
Internalenergy 224
Equationsofstate 226
Particulatepressure 227
8.3 Systemofequations 227
8.4 Forceandheattransferrate 229
8.5 Near-equilibriumflow 231
8.6 Isothermalsoundpropagationinanaerosol 236
8.7 Isothermalsoundpropagationinabubblyliquid 241
8.8 Thermaleffectsinemulsionsandaerosols 246
8.9 Flowofadustygasacrossashockwave 251
Thenormalshockinaperfectgas 253
Thenormalshockinadustygas 255
Two-phaseequationsforsteadymotion 256