Thermodynamics of flowing systems : with internal microstructure

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Thermodynamics of flowing systems : with internal microstructure / Antony N. Beris, Brian J. Edwards

資料種別:

図書

出版情報:

New York : Oxford University Press, 1994

形態:

xx, 683 p. ; 24 cm

シリーズ名:

The Oxford engineering science series ; 36 <BA0001711X>

著者名:

ISBN:

9780195076943 [019507694X]

書誌ID:

BA22913725

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references and index

主題:

Hamiltonian systems; Microstructures--Mathematical models; Poisson brackets; Thermodynamics--Mathematical models; Transport theory--Mathematical models; Viscoelasticity

言語:

英語

目次情報:

Theory / Part I：

Introduction / Chapter 1：

Overview / 1.1：

The challenge of multiple time and length scales / 1.2：

The energy as the fundamental quantity / 1.3：

The generalized bracket approach / 1.4：

A simple application: The damped oscillator / 1.5：

Symplectic geometry in optics / Chapter 2：

Theories of optics / 2.1：

Symplectic structure / 2.3：

The symplectic vector space / 2.3.1：

The symplectic transformation / 2.3.2：

Gaussian and linear optics / 2.4：

Gaussian optics / 2.4.1：

Linear optics / 2.4.2：

Geometrical optics / 2.5：

The symplectic structure of geometrical optics / 2.5.1：

Fermat's principle / 2.5.2：

An overview of wave optics and electromagnetism / 2.6：

Hamiltonian mechanics of discrete particle systems / Chapter 3：

The calculus of variations / 3.1：

Hamilton's principle of least action / 3.2：

The Poisson bracket description of Hamilton's equations of motion / 3.3：

Properties of the Poisson bracket / 3.4：

The Liouville equation / 3.5：

The optical/mechanical analogy / 3.6：

A historical aside on the principle of least action / 3.7：

Fermat's reception / 3.7.1：

Maupertuis' contribution / 3.7.2：

Hamilton on the principle of least action / 3.7.3：

Equilibrium thermodynamics / Chapter 4：

The fundamental equation of thermodynamics / 4.1：

Other fundamental relationships of thermodynamics / 4.2：

The fundamental equation for a multicomponent system / 4.3：

Extensive variable formulation / 4.3.1：

Specific variable formulation / 4.3.2：

Density variable formulation / 4.3.3：

Equilibrium thermodynamics of a material with internal microstructure / 4.4：

Additivity in compound systems / 4.5：

Poisson brackets in continuous media / Chapter 5：

The material description of ideal fluid flow / 5.1：

The canonical Poisson bracket for ideal fluid flow / 5.2：

The calculus of functionals / 5.2.1：

The continuum Poisson bracket / 5.2.2：

The spatial description of ideal fluid flow / 5.3：

Ideal fluid flow with constraints: The incompressible fluid / 5.4：

Nonlinear elasticity / 5.5：

The material description of nonlinear elasticity / 5.5.1：

Spatial bracket derivation / 5.5.2：

Spatial bracket in terms of a tensor with unit trace / 5.5.3：

The relation between thermodynamics and hydrodynamics / 5.6：

The global system / 5.6.1：

The compound system / 5.6.2：

Non-equilibrium thermodynamics / Chapter 6：

Irreversibility and stability / 6.1：

Systems with internal variables / 6.2：

The Clausius inequality / 6.3：

Non-equilibrium thermodynamics of flowing systems / 6.4：

The entropy balance equation / 6.4.1：

The linear phenomenological relations / 6.4.2：

Frame indifference and material invariance / 6.4.3：

The principle of microscopic reversibility / 6.4.4：

The nature of affinities and fluxes / 6.4.5：

The Onsager/Casimir reciprocal relations / 6.5：

Einstein's fluctuation theory / 6.5.1：

Transformation properties of the reciprocal relations / 6.5.2：

Affinities and fluxes for continua / 6.6：

Density description of the entropy production rate / 6.6.1：

Description of the entropy production rate in terms of fluxes / 6.6.2：

The dissipation bracket / Chapter 7：

The general dissipation bracket / 7.1：

Definition and properties of the dissipation bracket / 7.1.1：

Equivalence of the energetic and entropic formalisms / 7.1.2：

The hydrodynamic equations for a single-component system / 7.2：

The general isotropic fluid / 7.2.1：

The incompressible Navier/Stokes equations / 7.2.2：

The hydrodynamic equations for a polar fluid / 7.2.3：

The hydrodynamic equations for a multicomponent fluid / 7.3：

Applications / Part II：

Incompressible viscoelastic fluids / Chapter 8：

Incompressible and isothermal viscoelastic fluid models in terms of a single conformation tensor / 8.1：

Simple phenomenological spring/dashpot-type models / 8.1.1：

Elastic dumbbell models of dilute polymer solutions arising through kinetic theory / 8.1.2：

Single internal variable models for concentrated polymer solutions and melts / 8.1.3：

Dissipation and admissibility criteria for single-mode viscoelastic fluids / 8.1.4：

The non-negative character of the conformation tensor for single-variable viscoelastic fluids / 8.1.5：

Evolutionary character of the governing equations of single-variable viscoelastic fluids / 8.1.6：

Incompressible viscoelastic fluid models in terms of multiple conformation tensors / 8.2：

Guidelines on multiple-variable viscoelastic fluid models from the perspective of linear viscoelasticity / 8.2.1：

Phenomenological multiple-variable models / 8.2.2：

The bead/spring-chain model of kinetic theory / 8.2.3：

Transport phenomena in viscoelastic fluids / Chapter 9：

Compressible and non-isothermal viscoelastic fluid models / 9.1：

Modeling of the rheology and flow-induced concentration changes in polymer solutions / 9.2：

Single-fluid model of polymer-solution hydro-dynamics allowing for concentration variations / 9.2.1：

Two-fluid model for polymer solutions / 9.2.2：

Comparison of various theories for polymer solution hydrodynamics / 9.2.3：

Surface effects on the microstructure and concentration in incompressible and isothermal viscoelastic fluid flows / 9.3：

Derivation of the governing equations in terms of the Hamiltonian / 9.3.1：

Determination of the Hamiltonian functional / 9.3.3：

Calculations with the resulting model equations / 9.3.4：

Comparison with available experimental data and previous theoretical work / 9.3.5：

Effects of surface adsorption / 9.3.6：

Non-conventional transport phenomena / Chapter 10：

Relaxational phenomena in heat and mass transfer / 10.1：

Flux-relaxation models / 10.1.1：

The bracket formulation of relaxational phenomena in heat conduction / 10.1.2：

The bracket description of relaxational phenomena in mass diffusion / 10.1.3：

Heat and mass flux relaxation in the kinetic theory of gases / 10.1.4：

Relaxational mass transfer in polymeric systems / 10.1.5：

Phase transitions in inhomogeneous media / 10.2：

The kinetics of phase transitions / 10.2.1：

The bracket description of the kinetics of phase transitions / 10.2.2：

The inertial description of incompressible viscoelastic fluids / 10.3：

The dynamical theory of liquid crystals / Chapter 11：

Introduction to liquid crystals / 11.1：

Thermodynamics of liquid crystals under static conditions / 11.2：

Equilibrium thermodynamics of homogeneous liquid crystals / 11.2.1：

The Oseen/Frank description of non-homogeneous nematic liquid crystals / 11.2.2：

The LE and Doi models for flowing liquidcrystalline systems / 11.3：

The Leslie/Ericksen theory / 11.3.1：

The scalar/vector theory / 11.3.2：

The Doi theory / 11.3.3：

The Leslie coefficients: Implications for flow behavior and molecular determination / 11.3.4：

The bracket description of the LE theory / 11.4：

The inertial form / 11.4.1：

The non-inertial form / 11.4.2：

The conformation tensor theory / 11.5：

Comparison of the conformation tensor theory to previous theories / 11.5.1：

Reduction to the Leslie/Ericksen theory / 11.6.1：

Reduction to the scalar-vector theory / 11.6.2：

Reduction to the original Doi theory / 11.6.3：

Reduction to the extended Doi theory / 11.6.4：

Equivalent Leslie coefficients for the general conformation tensor theory / 11.6.5：

Concluding remarks / 11.7：

Multi-fluid transport/reaction models with application in the modeling of weakly ionized plasma dynamics / Chapter 12：

Elements from the modeling of weakly ionized plasma dynamics / 12.1：

Multi-fluid descriptions of nonlinear kinetics / 12.1.2：

The non-dissipative multi-fluid system / 12.2：

The dissipative multi-fluid system / 12.3：

Chemical reactions in a multicomponent single-fluid system / 12.4：

Chemical reactions in multi-fluid systems / 12.5：

Weakly ionized plasma model / 12.6：

Conclusions / 12.7：

Epilogue

Introduction to differential manifolds / Appendix A：

Differential manifolds / A.1：

Curves / A.2：

Tangent spaces / A.3：

Differential forms / A.4：

Symplectic forms and symplectic transformations / A.5：

The Lagrangian manifold / A.6：

The Hamiltonian vector field / A.7：

The Poisson bracket / A.8：

The Legendre dual transformation / Appendix B：

Poisson brackets for arbitrary second-rank deformation tensors / Appendix C：

Calculations of the random-flight model / Appendix D：

Calculation of the end-to-end distribution function near a solid surface / D.1：

Calculation of the partition function / D.2：

Bibliography

Author Index

Subject Index

Theory / Part I：

Introduction / Chapter 1：

Overview / 1.1：

The challenge of multiple time and length scales / 1.2：

The energy as the fundamental quantity / 1.3：

The generalized bracket approach / 1.4：

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