Statistical Microhydrodynamics

by Sinaiski, Emmanuil G.; Zaichik, Leonid I.

• ISBN13: 9783527406562
• ISBN10: 3527406565
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-03-03
• Publisher: Wiley-VCH

Summary

Written by experienced practitioners and teachers, this concise and comprehensive treatment on particulate flow covers both the theory as well as applications and examples from the oil and chemical industry.Following a look at the basic concepts of probability theory, the authors goe on to examine the elements of microhydrodynamics, Brownian motion, and real liquids in turbulent flow.Of interest for lecturers in physics, theoretical physicists and chemists, as well as chemical engineers.

Author Biography

Emmanuil G. Sinaiski completed the Lomonossow-State University, Moscow, Russia, where he obtained his PhD in physics and mathematics. He received a Dr Eng. Sci. degree in petroleum engineering from Gubkin-State University of Oil&Gas, Moscow, Russia where he was later appointed to a full professorship. Professor Sinaiski published numerous books and scientific articles, among them 'Separation of Mulitphase, Mulitcomponent Systems' published in 2007 by Wiley-VCH. His fields of interest are applied mathematics, fluid mechanics, physicochemical hydrodynamics, chemical and petroleum engineering.

Leonid I. Zaichik studied at the Moscow Power Engineering Institute, Russia and graduated with a Diploma of Higher Education in Thermophysics in 1971. He received his PhD in Engineering Sciences from the Krzhihanovsky Power Engineering Institute, Moscow, Russia, in 1986. He has been working as an Engineer for the All Union Institute for Current Sources and as Senior Researcher and Head of Laboratory at the Krzhizhanovsky Power Engineering Institute in Moscow. Since 1996 he is Head of the Laboratory of Mathematical Modelling at the Institute for High Temperatures of the Russian Academy of Sciences. Dr. Zaichik is author of two books and more than 300 research papers.

Table of Contents

Preface

Nomenclature

Basic Concepts of the Probability Theory

Events, Set of Events, and Probability

Random Variables, Probability Distribution Function, Average Value, and Variance

Generalized Functions

Methods of Averaging

Characteristic Functions

Moments and Cumulants of Random Variables

Correlation Functions

Bernoulli, Poisson, and Gaussian Distributions

Stationary Random Functions, Homogeneous Random Fields

Isotropic Random Fields

Spectral Representation

Stochastic Processes

Markovian Processes

The Chapman-Kolmogorov Integral Equation

The Chapman-Kolmogorov, Chapman-Feller, Fokker-Planck, and Liouville Differential Equations

Derivation of the Differential Chapman-Kolmogorov Equation

Discontinuous ("Jump") Processes

The Kolmogorov-Feller Equation

Diffusion Processes

The Fokker-Planck Equation

Deterministic Processes

The Liouville Equation

Stochastic Differential Equations

The Langevin Equation

The Langevin Equation

The Diffusion Equation

The Diffusion Equation with Chemical Reactions Taken into Account

Strownian Motion of a Particle in a Hydrodynamic Medium

Variational (Functional) Derivatives

The Characteristic Functional

Elements of Microhydrodynamics

Motion of an Isolated Particle in a Quiescent Fluid

Motion of an Isolated Particle in a Moving Fluid

Motion of Two Particles in a Fluid

Fluid is at Rest at the Infinity

Fluid is Moving at the Infinity

Multi-Particle Motion

Flow of a Fluid Through a Random Bed of Particles

Brownian Motion of Particles

Random Walk of an Isolated Particle

Isotropic Distribution

Gaussian Distribution

An Arbitrary Distribution in the Limiting Case N 1

Random Walk of an Ensemble of Particles

Brownian Motion of a Free Particle in a Quiescent Fluid

Brownian Motion of a Particle in an External Force Field

The Smoluchowski Equation

Brownian Motion of a Particle in a Moving Fluid

Brownian Diffusion with Hydrodynamic Interactions

Brownian Diffusion with Hydrodynamic Interactions and External Forces

High Peclet Numbers: Peij 1

Small Peclet Numbers, Peij 1

Particle Sedimentation in a Monodisperse Dilute Suspension

Particle Sedimentation in a Polydisperse Dilute Suspension, with Hydrodynamic and Molecular Interactions and Brownian Motion of Particles

Transport Coefficients in Disperse Media

Infinitely Dilute Suspension with Non-interacting Particles

The Influence of Particle Interactions on Transport Coefficients

Concentrated Disperse Media

Turbulent Flow of Fluids

General Information on Laminar and Turbulent Flows

The Momentum Equation for Viscous Incompressible Fluids

The Equations of Heat Inflow, Heat Conduction and Diffusion

The Conditions for the Beginning of Turbulence

Hydrodynamic Instability

The Reynolds Equations

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