Thermodynamics of Flowing Systems
with Internal Microstructure
Published on 26. May 1994
705 pages
978-0-19-534488-2 (ISBN)
Description
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.
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Antony N. Beris | Brian J. Edwards
Thermodynamics of Flowing Systems: with Internal Microstructure
Book
08/1994
Oxford University Press Inc
€405.50
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Content
- Intro
- Contents
- Chapter 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
- Chapter 2: Symplectic geometry in optics
- 2.1 Introduction
- 2.2 Theories of optics
- 2.3 Symplectic structure
- 2.4 Gaussian and linear optics
- 2.5 Geometrical optics
- 2.6 An overview of wave optics and electromagnetisrn
- Chapter 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 A historical aside on the principle of least action
- Chapter 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
- Chapter 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 Nonlinear elasticity
- 5.6 The relation between thermodynamics and hydrodynamics
- Chapter 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 of flowing systems
- 6.5 The Onsager/Casimir reciprocal relations
- 6.6 Affinities and fluxes for continua
- Chapter 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
- Chapter 8: Incompressible viscoelastic fluids
- 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
- Chapter 9: Transport phenomena in viscoelastic fluids
- 9.1 Compressible and non-isothermal viscoelastic fluid models
- 9.2 Modeling of the rheology and flow-induced concentration changes in polymer solutions
- 9.3 Surface effects on the microstructure and concentration in incompressible and isothermal viscoelastic fluid flows
- Chapter 10: Non-conventional 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
- Chapter 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 liquidcrystalline 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
- Chapter 12: Multi-fluid transport/reaction models with application in the modeling 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
- Epilogue
- Appendix A: Introduction to differential manifolds
- A.1 Differential manifolds
- A.2 Curves
- A.3 Tangent spaces
- A.4 Differential forms
- A.5 Symplectic forms and symplectic transformations
- A.6 The Lagrangian manifold
- A.7 The Hamiltoniari vector field
- A.8 The Poisson bracket
- Appendix B: The Legendre dual transformation
- Appendix C: Poisson brackets for arbitrary second-rank deformation tensors
- Appendix D: Calculations of the random-flight model
- D.1 Calculation of the end-to-end distribution function near a solid surface
- D.2 Calculation of the partition function
- Bibliography
- Author Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- R
- S
- T
- U
- V
- W
- Y
- Z
- Subject Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- V
- W
