Microhydrodynamics
Principles and Selected Applications
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Microhydrodynamics: Principles and Selected Applications presents analytical and numerical methods for describing motion of small particles suspended in viscous fluids. The text first covers the fundamental principles of low-Reynolds-number flow, including the governing equations and fundamental theorems; the dynamics of a single particle in a flow field; and hydrodynamic interactions between suspended particles. Next, the book deals with the advances in the mathematical and computational aspects of viscous particulate flows that point to innovations for large-scale simulations on parallel computers. The book will be of great use to students in engineering and applied mathematics. Students and practitioners of chemistry will also benefit from this book.
Table of Contents
Preface
Organization Scheme
I 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
References
II 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
References
III 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
14.5 On Solving Problems with Velocity BCs
Exercises
15 Odqvist's Approach for a Single Particle Surface
15.1 Smoothness of the Boundary Surfaces
15.2 Single and Double Layer Potentials, and Some of Their Properties
15.3 Results for a Single Closed Surface
15.4 The Completion Method of Power and Miranda for a Single Particle
Exercises
16 Multiparticle Problems in Bounded and Unbounded Domains
16.1 The Double Layer on Multiple Surfaces
16.2 The Lyapunov-Smooth Container
16.3 The Canonical Equations
16.4 RBM-Tractions from the Riesz Representation Theorem
16.5 The Stresslet
Exercises
17 Iterative Solutions for Mobility Problems
17.1 Conditions for Successful Direct Iteration
17.2 The Spectrum of the Double Layer Operator
17.3 Wielandt's Deflation
17.4 Deflation for a Single Particle
17.5 Deflation for a Container
17.6 Multiparticle Problems in Bounded and Unbounded Domains
17.7 Iterative Solution of the Tractions for a Mobility Problem
Exercises
18 Fourier Analysis for Axisymmetric Boundaries
18.1 How the Components Separate in Wave-number
18.2 Another Symmetry Argument for the Fourier Decomposition
18.3 Analytical Fourier Decomposition of the Kernel with Toroidals
18.4 Numerical Computation of the Toroidal Functions
18.5 The Numerical Solution Procedure
18.6 Axial Torque as an Example
18.7 Transverse Force and Torque
18.8 Other Details of Implementation
18.9 Limitations of the Fourier Analysis Approach
18.10 Results from the Axisymmetric Codes
18.11 Possibilities for Improvement and Generalization
Exercises
19 Three-Dimensional Numerical Results
19.1 Discretization with Constant Elements
19.2 Resistance and Mobility of Spheres
19.3 Sedimentation of Platonic Solids
19.4 Benchmarks
19.5 CDL-BIEM and Parallel Processing
19.6 Reducing Communication between Processors
Exercises
References
Notation
Index
Product details
- No. of pages: 536
- Language: English
- Copyright: © Butterworth-Heinemann 1991
- Published: January 1, 1991
- Imprint: Butterworth-Heinemann
- eBook ISBN: 9781483161242
About the Authors
Sangtae Kim
Seppo J. Karrila
About the Editor
Howard Brenner
Affiliations and Expertise
Massachusetts Institute of Technology