Principles and Selected Applications

1st Edition - January 1, 1991

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  • Authors: Sangtae Kim, Seppo J. Karrila
  • eBook ISBN: 9781483161242

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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



    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


    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


    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


    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



    III Hydrodynamic Interactions

    7 General Formulation of Resistance and Mobility Relations

    7.1 Introduction

    7.2 Resistance and Mobility Relations


    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


    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


    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


    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


    13 Boundary-Multipole Collocation

    13.1 Introduction

    13.2 Two-Sphere Problems

    13.3 Error Analysis for Spheres

    13.4 Error Analysis for Spheroids



    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


    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


    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


    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


    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


    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





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

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