Note: Supplemental materials are not guaranteed with Rental or Used book purchases.
Purchase Benefits
Looking to rent a book? Rent Microhydrodynamics : Principles and Selected Applications [ISBN: 9780750691734] for the semester, quarter, and short term or search our site for other textbooks by Kim, Sangtae; Karrila, Seppo J.. Renting a textbook can save you up to 90% from the cost of buying.
Preface | p. xv |
Organization Scheme | p. xvii |
Governing Equations and Fundamental Theorems | |
Microhydrodynamic Phenomena | p. 1 |
Objective and Scope | p. 1 |
The Governing Equations | p. 6 |
The Equation of Continuity | p. 6 |
The Momentum Balance | p. 7 |
The Stokes Equations | p. 9 |
Boundary Conditions for Fluid Flows | p. 10 |
The Energy Balance | p. 11 |
Colloidal Forces on Particles | p. 12 |
General Properties and Fundamental Theorems | p. 13 |
Introduction | p. 13 |
Energy Dissipation Theorems | p. 14 |
Uniqueness | p. 14 |
Minimum Energy Dissipation | p. 15 |
Lower Bounds on Energy Dissipation | p. 15 |
Energy Dissipation in Particulate Flows | p. 16 |
Energy Dissipation in Mobility Problems | p. 18 |
Lorentz Reciprocal Theorem | p. 19 |
Integral Representations | p. 20 |
The Green's Function for Stokes Flow | p. 20 |
Integral Representation with Single and Double Layer Potentials | p. 23 |
Representation of Flows Outside a Rigid Particle | p. 25 |
The Multipole Expansion | p. 27 |
Exercises | p. 31 |
References | p. 41 |
Dynamics of a Single Particle | |
The Disturbance Field of a Single Particle in a Steady Flow | p. 47 |
Introduction | p. 47 |
The Far Field Expansion: Rigid Particles and Drops | p. 48 |
Singularity Solutions | p. 49 |
Singularity System for Spheres | p. 50 |
The Spherical Drop and Interior Flows | p. 52 |
Singularity System for Ellipsoids | p. 53 |
Singularity System for Prolate Spheroids | p. 61 |
Singularity System for Oblate Spheroids | p. 66 |
Slender Body Theory | p. 67 |
Faxen Laws | p. 73 |
Ellipsoids and Spheroids | p. 76 |
The Spherical Drop | p. 78 |
Exercises | p. 80 |
Solutions in Spherical Coordinates | p. 83 |
Introduction | p. 83 |
Lamb's General Solution | p. 83 |
The Connection with the Multipole Expansion | p. 86 |
Force, Torque, and Stresslet | p. 88 |
Matching of Boundary Conditions | p. 88 |
The Adjoint Method | p. 93 |
An Orthonormal Basis for Stokes Flow | p. 95 |
The Stokes Streamfunction | p. 97 |
Relation to the Vector Potential | p. 97 |
The Stokes Equations and the Streamfunction | p. 98 |
Boundary Conditions for the Streamfunction | p. 99 |
The Axisymmetric Stokeslet and the Drag on a Body | p. 99 |
Separation in Spherical Coordinates | p. 100 |
Exercises | p. 102 |
Resistance and Mobility Relations | p. 107 |
Introduction | p. 107 |
The Resistance Tensor | p. 108 |
Symmetry and Positive Definiteness | p. 110 |
The Hydrodynamic Center of Resistance | p. 112 |
Translation Theorems for Resistance Tensors | p. 115 |
The Mobility Tensor | p. 115 |
Translation Theorems for Mobility Tensors | p. 117 |
The Hydrodynamic Center of Mobility | p. 117 |
Relations Between the Resistance and Mobility Tensors | p. 118 |
Axisymmetric Particles | p. 121 |
General Resistance Formulation in a Linear Field | p. 121 |
A Torque-Free Axisymmetric Particle in a Linear Field: The Jeffery Orbits | p. 123 |
Rheology of a Dilute Suspension of Spheroids | p. 126 |
Electrophoresis | p. 131 |
Particles with Finite Electric Double Layers | p. 135 |
Nonuniform Surface Potentials | p. 141 |
Exercises | p. 143 |
Transient Stokes Flows | p. 147 |
Time Scales | p. 147 |
The Fundamental Solution | p. 149 |
The Oscillating Sphere | p. 150 |
Sphere Released from Rest | p. 151 |
Oscillatory Rotation of a Sphere | p. 153 |
Reciprocal Theorem and Applications | p. 154 |
Integral Representations | p. 154 |
The Faxen Law: Particles of Arbitrary Shape | p. 155 |
The Faxen Law: Force on a Rigid Sphere | p. 156 |
The Faxen Law: Viscous Drop | p. 157 |
The Oscillating Spherical Drop | p. 158 |
The Faxen Law: Force on a Spherical Drop | p. 160 |
The Low-Frequency Limit | p. 161 |
Exercises | p. 162 |
References | p. 165 |
Hydrodynamic Interactions | |
General Formulation of Resistance and Mobility Relations | p. 175 |
Introduction | p. 175 |
Resistance and Mobility Relations | p. 178 |
The Resistance Matrix | p. 178 |
The Mobility Matrix | p. 179 |
Relations Between the Resistance and Mobility Tensors | p. 180 |
Axisymmetric Geometries | p. 180 |
Exercises | p. 183 |
Particles Widely Separated: The Method of Reflections | p. 187 |
The Far Field | p. 187 |
Resistance Problems | p. 189 |
Mobility Problems | p. 196 |
Renormalization Theory | p. 202 |
Multipole Expansions for Two Spheres | p. 206 |
Translations Along the Axis | p. 209 |
Electrophoresis of Particles with Thin Double Layers | p. 213 |
Hydrodynamic Interaction Between Spheres | p. 213 |
Multiple Ellipsoids | p. 215 |
Exercises | p. 215 |
Particles Near Contact | p. 219 |
Overview | p. 219 |
Shearing Motions of Rigid Surfaces | p. 220 |
Squeezing Motions of Rigid Surfaces | p. 226 |
Squeezing Flow Between Viscous Drops | p. 231 |
Nearly Rigid Drops | p. 233 |
Fully Mobile Interfaces | p. 233 |
Solution in Bispherical Coordinates | p. 233 |
Nearly Touching Bubbles | p. 235 |
Shearing Flow Between Viscous Drops | p. 237 |
Exercises | p. 238 |
Interactions Between Large and Small Particles | p. 239 |
Multiple Length Scales | p. 239 |
Image System for the Stokeslet Near a Rigid Sphere | p. 240 |
The Axisymmetric Stokeslet | p. 242 |
The Transverse Stokeslet | p. 244 |
Singularity Solutions for the Image of a Stokeslet | p. 246 |
Image for the Stokeslet Near a Viscous Drop | p. 249 |
Image Systems for Stokes Dipoles | p. 254 |
The Axisymmetric Stresslet | p. 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 Quadrupole | p. 259 |
The Axisymmetric Problem | p. 260 |
The Transverse Problem | p. 261 |
Hydrodynamic Interactions Between Large and Small Spheres | p. 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 Drops | p. 266 |
Exercises | p. 268 |
The Complete Set of Resistance and Mobility Functions for Two Rigid Spheres | p. 271 |
Regimes of Interaction | p. 271 |
Examples of the Usage of Resistance and Mobility Functions | p. 272 |
Two Spheres Moving in Tandem Along their Line of Centers | p. 272 |
Two Spheres Approaching Each Other | p. 273 |
Heavy Sphere Falling Past a Neutrally Buoyant Sphere | p. 273 |
Two Almost-Touching Spheres in Rigid-Body Rotation | p. 275 |
Two Force-Free and Torque-Free Spheres in a Linear Field | p. 276 |
Tables of the Resistance and Mobility Functions | p. 277 |
Particle-Wall Interactions | p. 311 |
The Lorentz Image | p. 311 |
Stokeslet Near a Rigid Wall | p. 312 |
A Drop Near a Fluid-Fluid Interface | p. 317 |
Exercises | p. 319 |
Boundary-Multipole Collocation | p. 321 |
Introduction | p. 321 |
Two-Sphere Problems | p. 323 |
Equal Spheres | p. 326 |
Resistance Functions | p. 327 |
Collocation Schemes | p. 328 |
Error Analysis for Spheres | p. 329 |
Axisymmetric Stokeslet | p. 330 |
The Transverse Stokeslet | p. 334 |
Error Analysis for Spheroids | p. 339 |
Stokeslet on the Axis | p. 341 |
Stokeslet on the Equatorial Plane | p. 343 |
Exercises | p. 345 |
References | p. 347 |
Foundations of Parallel Computational Microhydrodynamics | |
The Boundary Integral Equations for Stokes Flow | p. 355 |
The Setting for Computational Microhydrodynamics | p. 355 |
Integral Operators and Integral Equations | p. 358 |
Motivation | p. 358 |
First- and Second-Kind Equations | p. 358 |
Weakly Singular Kernels | p. 359 |
Ill- and Well-Posedness | p. 359 |
Compact Operators | p. 360 |
Numerical Solution Methods | p. 363 |
Applications to Boundary Integral Equations | p. 365 |
Notation and Definitions | p. 367 |
The Boundary Integral Equation in the Primary Variables | p. 368 |
Physically Occurring Boundary Conditions | p. 371 |
Difficulties with the BIE in the Primary Variables | p. 372 |
On Solving Problems with Velocity BCs | p. 372 |
Exercises | p. 374 |
Odqvist's Approach for a Single Particle Surface | p. 375 |
Smoothness of the Boundary Surfaces | p. 375 |
Single and Double Layer Potentials, and Some of Their Properties | p. 376 |
Results for a Single Closed Surface | p. 380 |
The Completion Method of Power and Miranda for a Single Particle | p. 384 |
Exercises | p. 385 |
Multiparticle Problems in Bounded and Unbounded Domains | p. 389 |
The Double Layer on Multiple Surfaces | p. 389 |
The Lyapunov-Smooth Container | p. 393 |
The Canonical Equations | p. 396 |
The Bordering Method in General | p. 396 |
On Removing the Null Functions | p. 397 |
Additions to the Range Space | p. 398 |
Summary of the Canonical Equations for Resistance and Mobility Problems | p. 398 |
RBM-Tractions from the Riesz Representation Theorem | p. 403 |
The Riesz Representation Theorem | p. 403 |
Force and Torque from the Lorentz Reciprocal Theorem | p. 404 |
Tractions for Rigid-Body Motion | p. 405 |
The Stresslet | p. 407 |
Exercises | p. 407 |
Iterative Solutions for Mobility Problems | p. 409 |
Conditions for Successful Direct Iteration | p. 409 |
The Spectrum of the Double Layer Operator | p. 410 |
The Spectrum for the Sphere | p. 412 |
Double Layer Eigenfunctions for Ellipsoids in Rate-of-Strain Fields | p. 418 |
The Spectrum for Two Spheres: HI-Induced Spectral Splitting | p. 425 |
Wielandt's Deflation | p. 428 |
Deflation for a Single Particle | p. 431 |
Deflation for a Container | p. 434 |
Multiparticle Problems in Bounded and Unbounded Domains | p. 435 |
Iterative Solution of the Tractions for a Mobility Problem | p. 440 |
Exercises | p. 444 |
Fourier Analysis for Axisymmetric Boundaries | p. 449 |
How the Components Separate in Wave-number | p. 449 |
Another Symmetry Argument for the Fourier Decomposition | p. 450 |
Analytical Fourier Decomposition of the Kernel with Toroidals | p. 451 |
Numerical Computation of the Toroidal Functions | p. 452 |
The Numerical Solution Procedure | p. 453 |
The Choice of the Numerical Method | p. 453 |
Theory of Singularity Subtraction | p. 454 |
Axial Torque as an Example | p. 455 |
The Azimuthal Integrations | p. 455 |
Discretizing with Quadrature and Singularity Subtraction | p. 456 |
Transverse Force and Torque | p. 458 |
Fourier Decomposition of the Double Layer Kernel | p. 459 |
Other Details of Implementation | p. 461 |
Limitations of the Fourier Analysis Approach | p. 461 |
Results from the Axisymmetric Codes | p. 462 |
Prolate Spheroids; Comparison of Surface Tractions with Known Analytical Results | p. 462 |
Mesh Effects: Grooved Particles | p. 462 |
The Effect of Sharp Edges: Finite Circular Cylinder | p. 465 |
A Container Problem | p. 468 |
Possibilities for Improvement and Generalization | p. 469 |
Exercises | p. 470 |
Three-Dimensional Numerical Results | p. 471 |
Discretization with Constant Elements | p. 472 |
Resistance and Mobility of Spheres | p. 476 |
Sedimentation of Platonic Solids | p. 477 |
Benchmarks | p. 481 |
CDL-BIEM and Parallel Processing | p. 482 |
Reducing Communication Between Processors | p. 485 |
Asynchronous Iterations | p. 485 |
Compactification of Distant Information | p. 488 |
Exercises | p. 488 |
References | p. 489 |
Notation | p. 495 |
Table of Contents provided by Ingram. All Rights Reserved. |
The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.