Thermodynamics of Flowing Systems with Internal Microstructure [Hardcover]

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. WithThermodynamics of Flowing Systemsin 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.

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 Relationl“.