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9780750691734

Microhydrodynamics : Principles and Selected Applications

by ;
  • ISBN13:

    9780750691734

  • ISBN10:

    0750691735

  • Format: Hardcover
  • Copyright: 1991-01-01
  • Publisher: Butterworth-Heinemann

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Summary

Microhydrodynamics concerns the flow and related phenomena pertinent to the motion of small particles suspended in viscous fluids. This text focuses on determining the motion of a particle or particles through a viscous fluid in bounded and unbounded flow. Its central theme is the mobility relation between particle motion and forces.

Table of Contents

Prefacep. xv
Organization Schemep. xvii
Governing Equations and Fundamental Theorems
Microhydrodynamic Phenomenap. 1
Objective and Scopep. 1
The Governing Equationsp. 6
The Equation of Continuityp. 6
The Momentum Balancep. 7
The Stokes Equationsp. 9
Boundary Conditions for Fluid Flowsp. 10
The Energy Balancep. 11
Colloidal Forces on Particlesp. 12
General Properties and Fundamental Theoremsp. 13
Introductionp. 13
Energy Dissipation Theoremsp. 14
Uniquenessp. 14
Minimum Energy Dissipationp. 15
Lower Bounds on Energy Dissipationp. 15
Energy Dissipation in Particulate Flowsp. 16
Energy Dissipation in Mobility Problemsp. 18
Lorentz Reciprocal Theoremp. 19
Integral Representationsp. 20
The Green's Function for Stokes Flowp. 20
Integral Representation with Single and Double Layer Potentialsp. 23
Representation of Flows Outside a Rigid Particlep. 25
The Multipole Expansionp. 27
Exercisesp. 31
Referencesp. 41
Dynamics of a Single Particle
The Disturbance Field of a Single Particle in a Steady Flowp. 47
Introductionp. 47
The Far Field Expansion: Rigid Particles and Dropsp. 48
Singularity Solutionsp. 49
Singularity System for Spheresp. 50
The Spherical Drop and Interior Flowsp. 52
Singularity System for Ellipsoidsp. 53
Singularity System for Prolate Spheroidsp. 61
Singularity System for Oblate Spheroidsp. 66
Slender Body Theoryp. 67
Faxen Lawsp. 73
Ellipsoids and Spheroidsp. 76
The Spherical Dropp. 78
Exercisesp. 80
Solutions in Spherical Coordinatesp. 83
Introductionp. 83
Lamb's General Solutionp. 83
The Connection with the Multipole Expansionp. 86
Force, Torque, and Stressletp. 88
Matching of Boundary Conditionsp. 88
The Adjoint Methodp. 93
An Orthonormal Basis for Stokes Flowp. 95
The Stokes Streamfunctionp. 97
Relation to the Vector Potentialp. 97
The Stokes Equations and the Streamfunctionp. 98
Boundary Conditions for the Streamfunctionp. 99
The Axisymmetric Stokeslet and the Drag on a Bodyp. 99
Separation in Spherical Coordinatesp. 100
Exercisesp. 102
Resistance and Mobility Relationsp. 107
Introductionp. 107
The Resistance Tensorp. 108
Symmetry and Positive Definitenessp. 110
The Hydrodynamic Center of Resistancep. 112
Translation Theorems for Resistance Tensorsp. 115
The Mobility Tensorp. 115
Translation Theorems for Mobility Tensorsp. 117
The Hydrodynamic Center of Mobilityp. 117
Relations Between the Resistance and Mobility Tensorsp. 118
Axisymmetric Particlesp. 121
General Resistance Formulation in a Linear Fieldp. 121
A Torque-Free Axisymmetric Particle in a Linear Field: The Jeffery Orbitsp. 123
Rheology of a Dilute Suspension of Spheroidsp. 126
Electrophoresisp. 131
Particles with Finite Electric Double Layersp. 135
Nonuniform Surface Potentialsp. 141
Exercisesp. 143
Transient Stokes Flowsp. 147
Time Scalesp. 147
The Fundamental Solutionp. 149
The Oscillating Spherep. 150
Sphere Released from Restp. 151
Oscillatory Rotation of a Spherep. 153
Reciprocal Theorem and Applicationsp. 154
Integral Representationsp. 154
The Faxen Law: Particles of Arbitrary Shapep. 155
The Faxen Law: Force on a Rigid Spherep. 156
The Faxen Law: Viscous Dropp. 157
The Oscillating Spherical Dropp. 158
The Faxen Law: Force on a Spherical Dropp. 160
The Low-Frequency Limitp. 161
Exercisesp. 162
Referencesp. 165
Hydrodynamic Interactions
General Formulation of Resistance and Mobility Relationsp. 175
Introductionp. 175
Resistance and Mobility Relationsp. 178
The Resistance Matrixp. 178
The Mobility Matrixp. 179
Relations Between the Resistance and Mobility Tensorsp. 180
Axisymmetric Geometriesp. 180
Exercisesp. 183
Particles Widely Separated: The Method of Reflectionsp. 187
The Far Fieldp. 187
Resistance Problemsp. 189
Mobility Problemsp. 196
Renormalization Theoryp. 202
Multipole Expansions for Two Spheresp. 206
Translations Along the Axisp. 209
Electrophoresis of Particles with Thin Double Layersp. 213
Hydrodynamic Interaction Between Spheresp. 213
Multiple Ellipsoidsp. 215
Exercisesp. 215
Particles Near Contactp. 219
Overviewp. 219
Shearing Motions of Rigid Surfacesp. 220
Squeezing Motions of Rigid Surfacesp. 226
Squeezing Flow Between Viscous Dropsp. 231
Nearly Rigid Dropsp. 233
Fully Mobile Interfacesp. 233
Solution in Bispherical Coordinatesp. 233
Nearly Touching Bubblesp. 235
Shearing Flow Between Viscous Dropsp. 237
Exercisesp. 238
Interactions Between Large and Small Particlesp. 239
Multiple Length Scalesp. 239
Image System for the Stokeslet Near a Rigid Spherep. 240
The Axisymmetric Stokesletp. 242
The Transverse Stokesletp. 244
Singularity Solutions for the Image of a Stokesletp. 246
Image for the Stokeslet Near a Viscous Dropp. 249
Image Systems for Stokes Dipolesp. 254
The Axisymmetric Stressletp. 255
The Stresslet in Hyperbolic Flow (m = 1)p. 255
The Stresslet in Hyperbolic Flow (m = 2)p. 258
Image System for the Degenerate Stokes Quadrupolep. 259
The Axisymmetric Problemp. 260
The Transverse Problemp. 261
Hydrodynamic Interactions Between Large and Small Spheresp. 261
Mobility Functions x[subscript 12] and x[superscript a subscript 22]p. 262
Mobility Functions x[subscript 11] and x[superscript a subscript 21]p. 265
Hydrodynamic Interactions Between Large and Small Dropsp. 266
Exercisesp. 268
The Complete Set of Resistance and Mobility Functions for Two Rigid Spheresp. 271
Regimes of Interactionp. 271
Examples of the Usage of Resistance and Mobility Functionsp. 272
Two Spheres Moving in Tandem Along their Line of Centersp. 272
Two Spheres Approaching Each Otherp. 273
Heavy Sphere Falling Past a Neutrally Buoyant Spherep. 273
Two Almost-Touching Spheres in Rigid-Body Rotationp. 275
Two Force-Free and Torque-Free Spheres in a Linear Fieldp. 276
Tables of the Resistance and Mobility Functionsp. 277
Particle-Wall Interactionsp. 311
The Lorentz Imagep. 311
Stokeslet Near a Rigid Wallp. 312
A Drop Near a Fluid-Fluid Interfacep. 317
Exercisesp. 319
Boundary-Multipole Collocationp. 321
Introductionp. 321
Two-Sphere Problemsp. 323
Equal Spheresp. 326
Resistance Functionsp. 327
Collocation Schemesp. 328
Error Analysis for Spheresp. 329
Axisymmetric Stokesletp. 330
The Transverse Stokesletp. 334
Error Analysis for Spheroidsp. 339
Stokeslet on the Axisp. 341
Stokeslet on the Equatorial Planep. 343
Exercisesp. 345
Referencesp. 347
Foundations of Parallel Computational Microhydrodynamics
The Boundary Integral Equations for Stokes Flowp. 355
The Setting for Computational Microhydrodynamicsp. 355
Integral Operators and Integral Equationsp. 358
Motivationp. 358
First- and Second-Kind Equationsp. 358
Weakly Singular Kernelsp. 359
Ill- and Well-Posednessp. 359
Compact Operatorsp. 360
Numerical Solution Methodsp. 363
Applications to Boundary Integral Equationsp. 365
Notation and Definitionsp. 367
The Boundary Integral Equation in the Primary Variablesp. 368
Physically Occurring Boundary Conditionsp. 371
Difficulties with the BIE in the Primary Variablesp. 372
On Solving Problems with Velocity BCsp. 372
Exercisesp. 374
Odqvist's Approach for a Single Particle Surfacep. 375
Smoothness of the Boundary Surfacesp. 375
Single and Double Layer Potentials, and Some of Their Propertiesp. 376
Results for a Single Closed Surfacep. 380
The Completion Method of Power and Miranda for a Single Particlep. 384
Exercisesp. 385
Multiparticle Problems in Bounded and Unbounded Domainsp. 389
The Double Layer on Multiple Surfacesp. 389
The Lyapunov-Smooth Containerp. 393
The Canonical Equationsp. 396
The Bordering Method in Generalp. 396
On Removing the Null Functionsp. 397
Additions to the Range Spacep. 398
Summary of the Canonical Equations for Resistance and Mobility Problemsp. 398
RBM-Tractions from the Riesz Representation Theoremp. 403
The Riesz Representation Theoremp. 403
Force and Torque from the Lorentz Reciprocal Theoremp. 404
Tractions for Rigid-Body Motionp. 405
The Stressletp. 407
Exercisesp. 407
Iterative Solutions for Mobility Problemsp. 409
Conditions for Successful Direct Iterationp. 409
The Spectrum of the Double Layer Operatorp. 410
The Spectrum for the Spherep. 412
Double Layer Eigenfunctions for Ellipsoids in Rate-of-Strain Fieldsp. 418
The Spectrum for Two Spheres: HI-Induced Spectral Splittingp. 425
Wielandt's Deflationp. 428
Deflation for a Single Particlep. 431
Deflation for a Containerp. 434
Multiparticle Problems in Bounded and Unbounded Domainsp. 435
Iterative Solution of the Tractions for a Mobility Problemp. 440
Exercisesp. 444
Fourier Analysis for Axisymmetric Boundariesp. 449
How the Components Separate in Wave-numberp. 449
Another Symmetry Argument for the Fourier Decompositionp. 450
Analytical Fourier Decomposition of the Kernel with Toroidalsp. 451
Numerical Computation of the Toroidal Functionsp. 452
The Numerical Solution Procedurep. 453
The Choice of the Numerical Methodp. 453
Theory of Singularity Subtractionp. 454
Axial Torque as an Examplep. 455
The Azimuthal Integrationsp. 455
Discretizing with Quadrature and Singularity Subtractionp. 456
Transverse Force and Torquep. 458
Fourier Decomposition of the Double Layer Kernelp. 459
Other Details of Implementationp. 461
Limitations of the Fourier Analysis Approachp. 461
Results from the Axisymmetric Codesp. 462
Prolate Spheroids; Comparison of Surface Tractions with Known Analytical Resultsp. 462
Mesh Effects: Grooved Particlesp. 462
The Effect of Sharp Edges: Finite Circular Cylinderp. 465
A Container Problemp. 468
Possibilities for Improvement and Generalizationp. 469
Exercisesp. 470
Three-Dimensional Numerical Resultsp. 471
Discretization with Constant Elementsp. 472
Resistance and Mobility of Spheresp. 476
Sedimentation of Platonic Solidsp. 477
Benchmarksp. 481
CDL-BIEM and Parallel Processingp. 482
Reducing Communication Between Processorsp. 485
Asynchronous Iterationsp. 485
Compactification of Distant Informationp. 488
Exercisesp. 488
Referencesp. 489
Notationp. 495
Table of Contents provided by Ingram. All Rights Reserved.

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