Thermodynamics of Flowing Systems: with Internal Microstructure

by Antony N. Beris, Brian J. Edwards

Overview

This much-needed monograph presents a systematic, step-by-step approach to the continuum modeling of flow phenomena exhibited within materials endowed with a complex internal microstructure, such as polymers and liquid crystals. By combining the principles of Hamiltonian mechanics with those of irreversible thermodynamics, Antony N. Beris and Brian J. Edwards, renowned authorities on the subject, expertly describe the complex interplay between conservative and dissipative processes. Throughout the book, the authors emphasize the evaluation of the free energy—largely based on ideas from statistical mechanics—and how to fit the values of the phenomenological parameters against those of microscopic models. With Thermodynamics of Flowing Systems in hand, mathematicians, engineers, and physicists involved with the theoretical study of flow behavior in structurally complex media now have a superb, self-contained theoretical framework on which to base their modeling efforts.

Product Details

ISBN-13:	9780195076943
Publisher:	Oxford University Press
Publication date:	05/26/1994
Series:	Oxford Engineering Science Series , #36
Edition description:	New Edition
Pages:	704
Product dimensions:	9.38(w) x 6.20(h) x 1.92(d)

About the Author

University of Delaware

University of Illinois, Urbana-Champaign

Table of Contents

PART I: THEORY1. Introduction1.1. Overview1.2. The Challenge of Multiple Time and Length Scales1.3. The Energy as the Fundamental Quantity1.4. The Generalized Bracket Approach1.5. A Simple Application: The Damped Oscillator2. Symplectic Geometry in Optics2.1. Introduction2.2. Theories of Space2.3. Symplectic Structure2.4. Gaussian and Linear Optics2.5. Geometrical Optics2.6. An Overview of Wave Optics and Electromagnetism3. Hamiltonian Mechanics of Discrete Particle Systems3.1. The Calculus of Variations3.2. Hamilton's Principle of Least Action3.3. The Poisson Bracket Description of Hamilton's Equations of Motion3.4. Properties of the Poisson Bracket3.5. The Liouville Equation3.6. The Optical/Mechanical Analogy3.7. The Historical Aside on the Principle of Least Action4. Equilibrium Thermodynamics4.1. The Fundamental Equation of Thermodynamics4.2. Other Fundamental Relationships of Thermodynamics4.3. The Fundamental Equation for a Multicomponent System4.4. Equilibrium Thermodynamics of a Material with Internal Microstructure4.5. Additivity in Compound Systems5. Poisson Brackets in Continuous Media5.1. The Material Description of Ideal Fluid Flow5.2. The Canonical Poisson Bracket for Ideal Fluid Flow5.3. The Spatial Description of Ideal Fluid Flow5.4. Ideal Fluid Flow with Constraints: The Incompressible Fluid5.5. Non-Linear Elasticity5.6. The Relation between Thermodynamics and Hydrodynamics6. Non-Equilibrium Thermodynamics6.1. Irreversibility and Stability6.2. Systems with Internal Variables6.3. The Clausius Inequality6.4. Non-Equilibrium Thermodynamics6.5. The Onsager/Casimir Reciprocal Relations6.6. Affinities and Fluxes for Continua7. The Dissipation Bracket7.1. The General Dissipation Bracket7.2. The Hydrodynamic Equations for a Single Component System7.3. The Hydrodynamic Equations for a Multicomponent FluidPART II: APPLICATIONS8. Incompressible Viscoelastic Flows8.1. Incompressible and Isothermal Viscoelastic Fluid Models in Terms of a Single Conformation Tensor8.2. Incompressible Viscoelastic Fluid Models in Terms of Multiple Conformation Tensors9. Transport Phenomena in Viscoelastic Fluids9.1. Compressible and Non-Isothermal Viscoelastic Fluid Models9.2. Modelling of the Rheology and Flow-Induced Concentration Changes in Polymer Solution9.3. Surface/Microstructure Interactions in Incompressible and Isothermal Viscoelastic Fluid Flows10. Non-Standard Transport Phenomena10.1. Relaxational Phenomena in Heat and Mass Transfer10.2. Phase Transitions in Inhomogeneous Media10.3. The Inertial Description of Incompressible Viscoelastic Fluids11. The Dynamical Theory of Liquid Crystals11.1. Introduction to Liquid Crystals11.2. Thermodynamics of Liquid Crystals under Static Conditions11.3. The LE and Doi Models for Flowing Liquid-Crystalline Systems11.4. The Bracket Description of the LE Theory11.5. The Conformation Tensor Theory11.6. Comparison of the Conformation Tensor Theory to Previous Theories11.7. Concluding Remarks12. Multi-Fluid Transport/Reaction Models with Application in the Modelling of Weakly-Ionized Plasma Dynamics12.1. Introduction12.2. The Non-Dissipative Multi-Fluid System12.3. The Dissipative Multi-Fluid System12.4. Chemical Reactions in a Multicomponent Single-Fluid System12.5. Chemical Reactions in Multi-fluid Systems12.6. Weakly-Ionized Plasma Model12.7. Conclusions

Editorial Reviews

"In this book, the authors attempt to provide a mechanism by which the necessary information from microscopic investigations can be transferred into a consistent description of dynamical phenomena from a macroscopic continuum perspective." —Applied Mechanics Review

"The principal objective of this book is to provide an extension of the Poisson bracket formalism that is also able to embrace dissipative processes. Thus, while Part I is intended to establish the theoretical premisses of such an extension, Part II illustrates the wealth of possible applications of this method, taken from the most diverse areas of complex materials science." —Mathematical Reviews

From the Publisher

Aims to discuss the simplest possible way to describe transport phenomena within structured media without unduly sacrificing the capability of the theoretical representation to describe the underlying physics. Contents include symplectic geometry in optics, Hamiltonian mechanics of discrete particle systems, equilibrium thermodynamics, Poisson brackets in continuous media, incompressible viscoelastic fluids, dynamical theory of liquid crystals, and multi-fluid transport. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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