Suspension acoustics: an introduction to the physics of suspensions

Samuel Temkin0521847575, 9780521847575

Originally published in 2005, this book is an introduction to the physics of suspensions of bubbles, droplets, and solid particles in both gases and fluids. Rather than treating each combination separately, a unified approach is used that permits most particle-fluid combination types to be discussed together. To do this, the book first presents a detailed discussion of the basic particle motions that small particles can sustain, paying particular attention to translations and pulsations, and to the thermal effects that occur as a result of those motions. The book then introduces the reader to the dynamics and thermodynamics of suspensions, with acoustic motions providing the main focus in the latter part of the book. The important acoustic problems of attenuation and dispersion are discussed from several fundamental perspectives. The book concludes with applications of acoustic techniques to the characterization and modification of suspensions by means of acoustic waves.

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Table of contents :
Cover……Page 1
Half-title……Page 3
Title……Page 5
Copyright……Page 6
Contents……Page 7
List of Figures and Tables……Page 13
Preface……Page 18
1.1 Introduction……Page 21
1.2 Types of Suspensions……Page 25
1.3 Particle Concentrations……Page 27
Particle-Size Distributions……Page 28
Mass Concentration……Page 29
Suspension Density……Page 30
1.4 Interparticle Separation……Page 33
Equations of Motion……Page 35
Boundary Conditions……Page 38
Kinematic Considerations……Page 41
Mass……Page 42
Linear Momentum……Page 43
Angular Momentum……Page 44
Associated Energies……Page 45
2.4 Internal Energy……Page 47
2.5 Energy Dissipation……Page 49
Damping Coefficient……Page 51
2.6 Nondimensional Parameters……Page 52
2.7 Motion at Re………Page 55
3.1 Introduction……Page 57
3.2 Harmonic Temperature Variations……Page 58
Heat Transfer Rate……Page 61
Low Frequencies……Page 62
Thermal Relaxation Time……Page 63
3.3 Particle in Oscillating Temperature Field……Page 64
Unsteady Heat Transfer Rate……Page 66
3.4 Arbitrary Time Dependence……Page 69
Sudden Temperature Change……Page 72
3.5 Nonuniform Particle Temperature……Page 75
The Function G (qi)……Page 77
Temperature Average……Page 78
3.6 Concluding Remarks……Page 80
Basic Equations……Page 81
4.2 Translational Oscillations……Page 83
Fluid Pressure……Page 89
Fluid Force on Sphere……Page 90
4.3 Stokes’ Law……Page 93
4.4 Slowly Changing Motions……Page 95
Sphere in Oscillating Fluid……Page 97
Terminal Velocity……Page 98
Very Small Particles……Page 99
Spherical Bubbles and Droplets……Page 100
Small but Finite Reynolds Numbers……Page 101
Lift Force……Page 102
Empirical Forms at Finite Re……Page 103
4.6 Curvilinear Motion at Finite Re……Page 104
4.7 The Stokeslet……Page 107
Distributions of Stokeslets……Page 111
4.8 Unsteady Effects at Re………Page 114
Sphere in Oscillatory Fluid……Page 116
4.9 The Basset-Boussinesq-Oseen Equation……Page 119
Sphere Release in Stokes Flow……Page 120
4.10 Unsteady Drag at Finite Re……Page 126
Experimental Results……Page 128
4.11 Sphere in a Sound Wave……Page 131
Inviscid Fluid……Page 134
Viscous, Compressible Fluid……Page 137
Absorption Cross-Section……Page 139
Very Small Reynolds Numbers……Page 141
Finite Reynolds Numbers……Page 143
4.13 Concluding Remarks……Page 149
5.1 Introduction……Page 150
Equilibrium Pressure in a Droplet or Bubble……Page 152
5.3 Surface Vibrations of a Droplet……Page 153
5.4 Breakup of Liquid Surfaces……Page 160
5.5 Concluding Remarks……Page 164
6.1 Introduction……Page 165
6.2 Motion Produced by Pulsating Sphere……Page 166
Incompressible Fluid……Page 167
Rayleigh’s Equation……Page 168
The Rayleigh-Plesset Equation……Page 170
Compressible Fluid……Page 171
6.3 Force on Pulsating Sphere……Page 173
6.4 Internal Fields……Page 174
Uniform Density……Page 175
Nonuniform Fields……Page 176
6.5 Surface Motion……Page 177
Driven Pulsations……Page 182
6.6 Thermal Effects……Page 184
Particle Temperature……Page 186
Particle Pressure……Page 190
The Polytropic Index……Page 191
Surface Displacement……Page 196
Bubbles and Droplets in Liquids……Page 197
Aerosol and Hydrosol Particles……Page 202
Thermal Dissipation Rate……Page 205
Absorption Cross-Sections……Page 207
Thermodynamics of a Bubble Cycle……Page 211
6.8 Concluding Remarks……Page 215
7.1 Introduction……Page 217
Mechanical Equilibrium……Page 218
Thermal Equilibrium……Page 219
Thermodynamic Equilibrium……Page 220
Isothermal Compressibility……Page 221
Isothermal Sound Speed……Page 222
Specific Heats……Page 223
Specific Heat at Constant Pressure……Page 226
Specific Heat at Constant Volume……Page 227
Specific Heat Ratio……Page 228
7.4 Isentropic Sound Speed……Page 230
7.5 Equations of State……Page 234
Isentropic Equations of State……Page 235
7.6 Concluding Remarks……Page 236
8.1 Introduction……Page 237
8.2 Conservation Equations……Page 239
Conservation of Mass……Page 241
Linear Momentum……Page 242
Internal Energy……Page 244
Equations of State……Page 246
8.3 System of Equations……Page 247
8.4 Force and Heat Transfer Rate……Page 249
8.5 Near-Equilibrium Flow……Page 251
8.6 Isothermal Sound Propagation in an Aerosol……Page 256
8.7 Isothermal Sound Propagation in a Bubbly Liquid……Page 261
8.8 Thermal Effects in Emulsions and Aerosols……Page 266
8.9 Flow of a Dusty Gas Across a Shock Wave……Page 271
The Normal Shock in a Perfect Gas……Page 273
The Normal Shock in a Dusty Gas……Page 275
Two-Phase Equations for Steady Motion……Page 276
Conditions Immediately After the Shock……Page 278
Equilibrium State Downstream of the Shock……Page 279
Remarks About the Nonequilibrium Region……Page 282
8.10 Concluding Remarks……Page 286
9.1 Introduction……Page 287
9.2 Propagation in a Fluid Without Particles……Page 288
9.3 Attenuation Coefficient……Page 291
Translational Attenuation……Page 293
Pulsational Attenuation……Page 296
Total Attenuation……Page 299
9.4 Propagation via Sound Emission……Page 302
Wave Equation with Sources of Mass, Force, and Heat……Page 303
Source Strengths……Page 305
Complex Wavenumber……Page 307
Small Attenuation……Page 309
Finite Attenuation……Page 312
Experimental Results……Page 314
9.5 Propagation via Compressibility……Page 320
Dynamic Compressibility……Page 321
Translational Contribution……Page 322
Pulsational Contribution……Page 324
Total Changes……Page 327
9.6 Propagation via Causality……Page 330
The Kramers-Kronig Relations……Page 331
The K-K Relations in Suspension Acoustics……Page 332
Propagation in an Aerosol……Page 334
9.7 Concluding Remarks……Page 337
10.2 Reflection at a Fluid-Suspension Interface……Page 338
Equilibrium Conditions……Page 339
Nonequilibrium……Page 342
10.3 Extension to Polydisperse Suspensions……Page 345
Volume Concentration……Page 351
Particle Size……Page 352
Size Distributions……Page 355
The Coagulation Equations……Page 356
Smoluchowski’s Solution……Page 361
Collision Kernel for Rectilinear Motions……Page 366
Nondimensional Equations……Page 369
Acoustic Agglomeration of Aerosols……Page 370
Large-Amplitude Waves……Page 377
10.6 Concluding Remarks……Page 378
Appendix A Material and Transport Properties of Some Substances at 1 atm and 20ºC……Page 379
General Relations……Page 380
Integral Relations……Page 381
Appendix C Explicit Expressions for Some Quantities in Spherical Polar Coordinates……Page 382
Explicit Expressions……Page 384
Expressions for Small Arguments……Page 385
Special Relations and Values……Page 386
Mechanics……Page 387
B. PARTICLES AND SUSPENSIONS……Page 388
General suspensions……Page 389
Aerosols……Page 390
Bubbly liquids……Page 391
Breakup, Collision, and Coalescence……Page 392
Cavitation and Sonoluminescence……Page 394
Miscellaneous……Page 395
Model Equations……Page 396
Sedimentation……Page 397
Translational……Page 398
Pulsational……Page 399
Size Distributions……Page 400
Aerosols (dusty gases)……Page 401
Bubbly liquids……Page 402
Transport Properties……Page 403
Author Index……Page 404
Subject Index……Page 409
Latin Letters……Page 413
Greek Letters……Page 416