Microhydrodynamics

PrefaceOrganization SchemeI Governing Equations and Fundamental Theorems 1 Microhydrodynamic Phenomena 1.1 Objective and Scope 1.2 The Governing Equations 1.3 Colloidal Forces on Particles 2 General Properties and Fundamental Theorems 2.1 Introduction 2.2 Energy Dissipation Theorems 2.3 Lorentz Reciprocal Theorem 2.4 Integral Representations 2.5 The Multipole Expansion Exercises ReferencesII Dynamics of a Single Particle 3 The Disturbance Field of a Single Particle in a Steady Flow 3.1 Introduction 3.2 The Far Field Expansion: Rigid Particles and Drops 3.3 Singularity Solutions 3.4 Slender Body Theory 3.5 Faxen Laws Exercises 4 Solutions in Spherical Coordinates 4.1 Introduction 4.2 Lamb's General Solution 4.3 The Adjoint Method 4.4 An Orthonormal Basis for Stokes Flow 4.5 The Stokes Streamfunction Exercises 5 Resistance and Mobility Relations 5.1 Introduction 5.2 The Resistance Tensor 5.3 The Mobility Tensor 5.4 Relations between the Resistance and Mobility Tensors 5.5 Axisymmetric Particles 5.6 Rheology of a Dilute Suspension of Spheroids 5.7 Electrophoresis Exercises 6 Transient Stokes Flows 6.1 Time Scales 6.2 The Fundamental Solution 6.3 Reciprocal Theorem and Applications 6.4 The Low-Frequency Limit Exercises ReferencesIII Hydrodynamic Interactions 7 General Formulation of Resistance and Mobility Relations 7.1 Introduction 7.2 Resistance and Mobility Relations Exercises 8 Particles Widely Separated: The Method of Reflections 8.1 The Far Field 8.2 Resistance Problems 8.3 Mobility Problems 8.4 Renormalization Theory 8.5 Multipole Expansions for Two Spheres 8.6 Electrophoresis of Particles with Thin Double Layers Exercises 9 Particles Near Contact 9.1 Overview 9.2 Shearing Motions of Rigid Surfaces 9.3 Squeezing Motions of Rigid Surfaces 9.4 Squeezing Flow between Viscous Drops 9.5 Shearing Flow between Viscous Drops Exercises 10 Interactions between Large and Small Particles 10.1 Multiple Length Scales 10.2 Image System for the Stokeslet Near a Rigid Sphere 10.3 Image Systems for Stokes Dipoles 10.4 Image System for the Degenerate Stokes Quadrupole 10.5 Hydrodynamic Interactions between Large and Small Spheres 10.5.1 Mobility Functions x12 and x22a 10.5.2 Mobility Functions x11 and x21a 10.6 Hydrodynamic Interactions between Large and Small Drops Exercises 11 The Complete Set of Resistance and Mobility Functions for Two Rigid Spheres 11.1 Regimes of Interaction 11.2 Examples of the Usage of Resistance and Mobility Functions 11.3 Tables of the Resistance and Mobility Functions 12 Particle-Wall Interactions 12.1 The Lorentz Image 12.2 Stokeslet Near a Rigid Wall 12.3 A Drop Near a Fluid-Fluid Interface Exercises 13 Boundary-Multipole Collocation 13.1 Introduction 13.2 Two-Sphere Problems 13.3 Error Analysis for Spheres 13.4 Error Analysis for Spheroids Exercises References IV Foundations of Parallel Computational Microhydrodynamics 14 The Boundary Integral Equations for Stokes Flow 14.1 The Setting for Computational Microhydrodynamics 14.2 Integral Operators and Integral Equations 14.3 Notation and Definitions 14.4 The Boundary Integral Equation in the Primary Variables 14.