Nonequilibrium Statistical Mechanics of Heterogeneous Fluid Systems

by Bashkirov; Andrei G.

• ISBN13: 9780849328602
• ISBN10: 0849328608
• Format: Hardcover
• Copyright: 1995-03-09
• Publisher: CRC Press

Summary

There is a wide variety of heterogeneous fluid systems that possess interphase surfaces. This monograph is devoted to pioneering studies in nonequilibrium statistical mechanics of such systems. Starting from the Liouville equation, the equations of surface hydrodynamics are derived with allowance for discontinuities of thermodynamic parameters of interphase boundaries. Brownian motion of a large solid particle in a fluid and nucleation are treated as results of fluctuations of flows across particle surfaces. With the use of the Gibbs method, a shock wave in a gas is considered as a sort of an interphase surface, and the surface tension of a shock front is introduced for the first time.

Table of Contents

Preface

Zubarev Method of Nonequilibrium Statistical Operator

Contracted Description of a Statistical System

Quasiequilibrium Distribution Function

Nonequilibrium Distribution Function

Transport Phenomena at Interfaces and the Problem of Boundary Conditions in Hydrodynamics

Introduction

Geometric Description of the Surface

Local Equilibrium Distribution

Gibbs Adsorption Equation

Conservation Laws

Equations of Ideal Hydrodynamics

Nonequilibrium Distribution Function

Transport Equations for Surface Films

Motion Equations for Excess Quantities

The Problem of Boundary Conditions in Hydrodynamics

Theory of Capillary Waves Damping

Shock Waves in Gases as Interface Surfaces

Introduction

The Jump Conditions on Curved Discontinuities

Estimation of the Surface Tension Coefficient

Equations for Small Disturbances

Shock Wave Stability Analysis

Nucleation Theory: Fluctuations of Diffusion Flow across the Interface Boundary

Introduction

Total Nonequilibrium Distribution Function

Nucleation Kinetic Equation

Nucleation Coefficient

Entropy Production

Second Quantization Approach

Nonisothermal Nucleation Theory

The Model Example

Brownian Motion: Momentum Flow Fluctuations on Interphase Boundary

Introduction

Microscopic Description of the System of Brownian Particle and Fluid

Derivation of the Kinetic Equation

Boundary Conditions on the Surface of the Large Particle

Calculation of the Average Force and the Drag Coefficient

Brownian Diffusion of Large Particle in Inhomogeneous Fluid

On a Limitation of the Theory

Derivation of the Fokker-Planck Equation for the Point Brownian Particle

Kirkwood Friction Coefficient

Diffusion of the Point Particle

Brownian Motion of N Spheres in Inhomogeneous Fluids

Introduction

The N-Particle Fokker-Planck Equation

The Smoluchowski Equation

Brownian Diffusion of Suspended Particles

Convective Diffusion of Particles in Fixed Dispersed Layers

Stochastization of the Diffusion Equation

Renormalized Diffusion Coefficient

Vector and Tensor Divergencies in Curvilinear Coordinates

Mechanical Definition of Surface Tension

Exclusion of Time-Derivatives of Parameters

Bibliography

Index