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E-raamat: Thermodynamics of Flowing Systems: with Internal Microstructure

(Associate Professor, Department of Chemical Engineering, University of Illinois at Urbana-Champaign), (Postdoctoral Associate, Department of Chemical Engineering, University of Illinois at Urbana-Champaign)
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Thermodynamics of Flowing Systems: with Internal MicrostructureSuurem pilt
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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 copyright Book News, Inc. Portland, Or.

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.

Arvustused

"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 "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


PART I: THEORY
1. Introduction
1.1. Overview
1.2. The Challenge of Multiple Time and Length Scales
1.3. The Energy as the Fundamental Quantity
1.4. The Generalized Bracket Approach
1.5. A Simple Application: The Damped Oscillator
2. Symplectic Geometry in Optics
2.1. Introduction
2.2. Theories of Space
2.3. Symplectic Structure
2.4. Gaussian and Linear Optics
2.5. Geometrical Optics
2.6. An Overview of Wave Optics and Electromagnetism
3. Hamiltonian Mechanics of Discrete Particle Systems
3.1. The Calculus of Variations
3.2. Hamilton's Principle of Least Action
3.3. The Poisson Bracket Description of Hamilton's Equations of Motion
3.4. Properties of the Poisson Bracket
3.5. The Liouville Equation
3.6. The Optical/Mechanical Analogy
3.7. The Historical Aside on the Principle of Least Action
4. Equilibrium Thermodynamics
4.1. The Fundamental Equation of Thermodynamics
4.2. Other Fundamental Relationships of Thermodynamics
4.3. The Fundamental Equation for a Multicomponent System
4.4. Equilibrium Thermodynamics of a Material with Internal Microstructure
4.5. Additivity in Compound Systems
5. Poisson Brackets in Continuous Media
5.1. The Material Description of Ideal Fluid Flow
5.2. The Canonical Poisson Bracket for Ideal Fluid Flow
5.3. The Spatial Description of Ideal Fluid Flow
5.4. Ideal Fluid Flow with Constraints: The Incompressible Fluid
5.5. Non-Linear Elasticity
5.6. The Relation between Thermodynamics and Hydrodynamics
6. Non-Equilibrium Thermodynamics
6.1. Irreversibility and Stability
6.2. Systems with Internal Variables
6.3. The Clausius Inequality
6.4. Non-Equilibrium Thermodynamics
6.5. The Onsager/Casimir Reciprocal Relations
6.6. Affinities and Fluxes for Continua
7. The Dissipation Bracket
7.1. The General Dissipation Bracket
7.2. The Hydrodynamic Equations for a Single Component System
7.3. The Hydrodynamic Equations for a Multicomponent Fluid
PART II: APPLICATIONS
8. Incompressible Viscoelastic Flows
8.1. Incompressible and Isothermal Viscoelastic Fluid Models in Terms of a Single Conformation Tensor
8.2. Incompressible Viscoelastic Fluid Models in Terms of Multiple Conformation Tensors
9. Transport Phenomena in Viscoelastic Fluids
9.1. Compressible and Non-Isothermal Viscoelastic Fluid Models
9.2. Modelling of the Rheology and Flow-Induced Concentration Changes in Polymer Solution
9.3. Surface/Microstructure Interactions in Incompressible and Isothermal Viscoelastic Fluid Flows
10. Non-Standard Transport Phenomena
10.1. Relaxational Phenomena in Heat and Mass Transfer
10.2. Phase Transitions in Inhomogeneous Media
10.3. The Inertial Description of Incompressible Viscoelastic Fluids
11. The Dynamical Theory of Liquid Crystals
11.1. Introduction to Liquid Crystals
11.2. Thermodynamics of Liquid Crystals under Static Conditions
11.3. The LE and Doi Models for Flowing Liquid-Crystalline Systems
11.4. The Bracket Description of the LE Theory
11.5. The Conformation Tensor Theory
11.6. Comparison of the Conformation Tensor Theory to Previous Theories
11.7. Concluding Remarks
12. Multi-Fluid Transport/Reaction Models with Application in the Modelling of Weakly-Ionized Plasma Dynamics
12.1. Introduction
12.2. The Non-Dissipative Multi-Fluid System
12.3. The Dissipative Multi-Fluid System
12.4. Chemical Reactions in a Multicomponent Single-Fluid System
12.5. Chemical Reactions in Multi-fluid Systems
12.6. Weakly-Ionized Plasma Model
12.7. Conclusions
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