Jou / Lebon / Casas-Vázquez Extended Irreversible Thermodynamics

4th Auflage 2010
ISBN: 978-90-481-3074-0
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 483 Seiten

The fast progress in many areas of research related to non-equilibrium ther- dynamics has prompted us to write a fourth edition of this book. Like in the previous editions, our main concern is to open the subject to the widest au- ence, including students, teachers, and researchers in physics, chemistry, engine- ing, biology, and materials sciences. Our objective is to present a general view on several open problems arising in non-equilibrium situations, and to afford a wide perspective of applications illustrating their practical outcomes and con- quences. A better comprehension of the foundations is generally correlated to an increase of the range of applications, implying mutual feedback and cross fert- ization. Truly, thermodynamic methods are widely used in many areas of science but, surprisingly, the active dynamism of thermodynamics as a ?eld on its own is not suf?ciently perceived outside a relatively reduced number of specialized researchers. Extended irreversible thermodynamics (EIT) goes beyond the classical f- malisms based on the local equilibrium hypothesis; it was also referred to in an earlier publication by the authors (Lebon et al. 1992) as a thermodynamics of the third type, as it provides a bridge between classical irreversible thermodynamics and rational thermodynamics, enlarging at the same time their respective range of application. The salient feature of the theory is that the ?uxes are incorporated into the set of basic variables.

Autoren/Hrsg.

Jou, David

Lebon, Georgy

Casas-Vázquez, José

Inhaltsverzeichnis

1;Preface to the Fourth Edition;5
2;Preface to the Third Edition;7
3;Preface to the First Edition;9
4;Contents;12
5;Part I General Theory;18
5.1;1 Classical, Rational and Hamiltonian Formulations of Non-equilibrium Thermodynamics;19
5.1.1;1.1 The General Balance Laws of Continuum Physics;20
5.1.1.1;1.1.1 The One-Component System;21
5.1.1.2;1.1.2 The Multicomponent Mixture;24
5.1.1.3;1.1.3 Charged Systems;26
5.1.2;1.2 The Law of Balance of Entropy;29
5.1.3;1.3 Classical Irreversible Thermodynamics;30
5.1.3.1;1.3.1 The Local-Equilibrium Hypothesis;30
5.1.3.2;1.3.2 Entropy Production and Entropy Flux;31
5.1.3.3;1.3.3 Linear Constitutive Equations;33
5.1.3.4;1.3.4 Constraints on the Phenomenological Coefficients;36
5.1.3.5;1.3.5 The Onsager–Casimir Reciprocal Relations;36
5.1.3.6;1.3.6 Limitations;38
5.1.4;1.4 Rational Thermodynamics;39
5.1.4.1;1.4.1 The Basic Axioms of Rational Thermodynamics;40
5.1.4.1.1;1.4.1.1 The Principle of Equipresence;40
5.1.4.1.2;1.4.1.2 The Principle of Memory or Heredity;41
5.1.4.1.3;1.4.1.3 The Principle of Local Action;41
5.1.4.1.4;1.4.1.4 The Principle of Material Frame-Indifference;41
5.1.4.2;1.4.2 Constitutive Equations;44
5.1.4.3;1.4.3 Critical Remarks;46
5.1.5;1.5 A Hamiltonian Formulation: the generic Formalism;48
5.1.6;1.6 Problems;51
5.2;2 Extended Irreversible Thermodynamics: Evolution Equations;57
5.2.1;2.1 Heat Conduction in Rigid Solids;58
5.2.1.1;2.1.1 Motivations;58
5.2.1.2;2.1.2 The Generalised Gibbs Equation;64
5.2.2;2.3 One-Component Viscous Fluid;69
5.2.3;2.4 The Generalised Entropy Flux and Entropy Production;71
5.2.4;2.5 Linearized Evolution Equations of the Fluxes;73
5.2.5;2.6 Rational Extended Thermodynamics;75
5.2.5.1;2.6.1 Heat Conduction;75
5.2.5.2;2.6.2 Viscous Fluids;79
5.2.6;2.7 Some Comments and Perspectives;80
5.2.7;2.8 Problems;83
5.3;3 Extended Irreversible Thermodynamics: Non-equilibrium Equations of State;87
5.3.1;3.1 Physical Interpretation of the Non-equilibrium Entropy;87
5.3.2;3.2 Non-equilibrium Equations of State: Temperature;90
5.3.2.1;3.2.1 Zeroth Law, Second Law, and Temperature;91
5.3.2.2;3.2.2 Evaluation of in Some Special Situations;95
5.3.2.3;3.2.3 Alternative Definitions of Generalised Temperature;95
5.3.2.4;3.2.4 Experimental Hints for the Non-equilibrium Temperature;97
5.3.3;3.3 Non-equilibrium Equations of State: Thermodynamic Pressure;98
5.3.4;3.4 Concavity Requirements and Stability;101
5.3.4.1;3.4.1 Heat Conduction in a Rigid Solid;102
5.3.4.2;3.4.2 Heat Conduction in Ideal Gases;103
5.3.4.3;3.4.3 Shear Viscous Pressure in Viscous Fluids;104
5.3.5;3.5 Problems;105
6;Part II Microscopic Foundations;106
6.1;4 The Kinetic Theory of Gases;107
6.1.1;4.1 The Basic Concepts of Kinetic Theory;107
6.1.1.1;4.1.1 Balance Equations;109
6.1.1.2;4.1.2 The H-Theorem and the Second Law;110
6.1.2;4.2 Non-equilibrium Entropy and the Entropy Flux;112
6.1.3;4.3 Grad's Solution;113
6.1.4;4.4 The Relaxation-Time Approximation;118
6.1.5;4.5 Dilute Non-ideal Gases;120
6.1.5.1;4.5.1 Entropy and Evolution Equations;121
6.1.5.2;4.5.2 Microscopic Identification of Coefficients;123
6.1.6;4.6 Non-linear Transport;124
6.1.7;4.7 Beyond the Thirteen-Moment Approximation;128
6.1.8;4.8 Problems;133
6.2;5 Fluctuation Theory;136
6.2.1;5.1 Einstein's Formula: Second Moments of Equilibrium Fluctuations;136
6.2.2;5.2 Ideal Gases;141
6.2.3;5.3 Fluctuations and Hydrodynamic Stochastic Noise;144
6.2.4;5.4 The Entropy Flux;144
6.2.5;5.5 Application to a Radiative Gas;146
6.2.6;5.6 Onsager's Relations;148
6.2.7;5.7 Experimental Observations of Fluctuations of the Fluxes and Flux Fluctuation Theorem;150
6.2.8;5.8 Problems;152
6.3;6 Information Theory;156
6.3.1;6.1 Basic Concepts;156
6.3.2;6.2 Ideal Gas Under Heat Flux and Viscous Pressure;161
6.3.3;6.3 Ideal Gas Under Shear Flow: Non-linear Analysis;163
6.3.4;6.4 Ideal Gas Submitted to a Heat Flux: Non-linear Analysis;166
6.3.5;6.5 Relativistic Ideal Gas Under an Energy Flow;167
6.3.6;6.6 Heat Flow in a Linear Harmonic Chain;170
6.3.7;6.7 Information Theory and Non-equilibrium Fluctuations;175
6.3.8;6.8 Problems;179
6.4;7 Linear Response Theory;181
6.4.1;7.1 Projection Operator Methods;181
6.4.2;7.2 Evolution Equations for Simple Fluids;187
6.4.3;7.3 Continued-Fraction Expansions;191
6.4.4;7.4 Problems;193
6.5;8 Computer Simulations;195
6.5.1;8.1 Computer Simulations of Non-equilibrium Steady States;195
6.5.2;8.2 Non-equilibrium Equations of State;197
6.5.3;8.3 Dependence of the Free Energy on the Shear Rate: Non-linear Approach;200
6.5.4;8.4 Shear-Induced Heat Flux and the Zeroth Law;202
6.5.5;8.5 Problems;204
7;Part III Selected Applications;208
7.1;9 Hyperbolic Heat Transport in Rigid Conductors;209
7.1.1;9.1 Linear Wave Propagation: Second Soundand Telegrapher Equation;210
7.1.2;9.2 Transient Heat Conduction: Parabolic VersusHyperbolic Regimes;212
7.1.2.1;9.2.1 Formulation of the Problem in Absence of Internal Source;212
7.1.2.2;9.2.2 Results for Diamond Films;214
7.1.2.3;9.2.3 Heating in Presence of Internal Energy Source: Application to Thermal Ignition;215
7.1.2.3.1;9.2.3.1 The Model;216
7.1.2.3.2;9.2.3.2 Results for Solids Propellants;217
7.1.3;9.3 Beyond the Cattaneo Equation;218
7.1.3.1;9.3.1 Guyer–Krumhansl's Model;219
7.1.3.2;9.3.2 A Generalised Guyer–Krumhansl's Model;220
7.1.3.2.1;9.3.2.1 Heat Propagation Velocity: Non-linear Acceleration Waves;225
7.1.3.2.2;9.3.2.2 Application to Dielectric Crystals at Low Temperature (<20 K);228
7.1.3.3;9.3.3 Other Examples of Flux Limiters;229
7.1.4;9.4 Phonon Hydrodynamics;232
7.1.5;9.5 Two-Temperature Models;233
7.1.6;9.6 Other Applications;234
7.1.7;9.7 Problems;235
7.2;10 Heat Transport in Micro- and Nano-systems;242
7.2.1;10.1 EIT Description of Heat Conductionat Micro- and Nano-scales;243
7.2.1.1;10.1.1 Effective Heat Conductivity;244
7.2.1.2;10.1.2 Transient Temperature Distribution in a Micro Film;248
7.2.2;10.2 The Equation of Phonon Radiative Transfer;250
7.2.3;10.3 The Ballistic Diffusion Equation;254
7.2.3.1;10.3.1 The Model Equations;255
7.2.3.2;10.3.2 Illustration: Transient Heat Transport in Thin Films;258
7.2.4;10.4 Problems;260
7.3;11 Waves in Fluids: Sound, Ultrasound, and Shock Waves;262
7.3.1;11.1 Sound Propagation in Fluids: Linear Waves;262
7.3.1.1;11.1.1 The Classical Theory;263
7.3.1.2;11.1.2 Extended Thermodynamic Theory;265
7.3.1.3;11.1.3 Particular Results for Monatomic Gases;267
7.3.2;11.2 Non-linear Acceleration Waves in Monatomic Ideal Gases;1
7.3.3;11.3 Shock Waves;273
7.3.3.1;11.3.1 The Classical Navier–Fourier–Stokes Approach;273
7.3.3.2;11.3.2 The Extended Irreversible Thermodynamics Approach;275
7.3.3.3;11.3.3 Shock Structure;278
7.3.4;11.4 Problems;280
7.4;12 Generalised Hydrodynamics;283
7.4.1;12.1 Density and Current Correlation Functions;283
7.4.2;12.2 Spectral Density Correlation;285
7.4.2.1;12.2.1 The Classical Hydrodynamical Approximation;285
7.4.2.2;12.2.2 The EIT Description;288
7.4.3;12.3 The Transverse Velocity Correlation Function:The EIT Description;290
7.4.4;12.4 The Longitudinal Velocity Correlation Function: The EIT Description;293
7.4.5;12.5 Influence of Higher-Order Fluxes;296
7.4.6;12.6 Problems;297
7.5;13 Non-classical Diffusion, Thermo-diffusion and Suspensions;299
7.5.1;13.1 Molecular Diffusion in Perfect Fluid Mixtures;300
7.5.2;13.2 Telegrapher's Equation and Stochastic Processes;305
7.5.2.1;13.2.1 Correlated Random Walk;306
7.5.2.2;13.2.2 H–Theorem for Telegrapher Type Equation;307
7.5.3;13.3 Non-Fickian Diffusion in Polymers;309
7.5.4;13.4 Hyperbolic Reaction–Diffusion Systems;314
7.5.5;13.5 Thermo-diffusion in Binary Mixtures;316
7.5.6;13.6 Suspensions of Solid Particles in Fluids;319
7.5.6.1;13.6.1 Suspensions Versus Molecular Diffusion;320
7.5.6.2;13.6.2 EIT Description of Suspensions;321
7.5.6.3;13.6.3 Comparison with Other Models;324
7.5.6.3.1;13.6.3.1 Internal Variables Theory;324
7.5.6.3.2;13.6.3.2 The Two-Fluid Model;325
7.5.7;13.7 Microstructure in Rapid Solidification of Binary Alloys;326
7.5.8;13.8 Problems;329
7.6;14 Electrical Systems and Micro-devices Modelization;334
7.6.1;14.1 Electrical Systems: Evolution Equations;334
7.6.2;14.2 Cross Terms in Constitutive Equations: Onsager's Relations;338
7.6.3;14.3 Hydrodynamical Models of Transport in Semiconductors and Plasmas;341
7.6.3.1;14.3.1 Transport in Semiconductors;341
7.6.3.2;14.3.2 Transport in Plasmas;345
7.6.4;14.4 Dielectric Relaxation of Polar Liquids;347
7.6.5;14.5 Problems;350
7.7;15 From Thermoelastic Solids to Rheological Materials;354
7.7.1;15.1 Thermoelasticity;355
7.7.2;15.2 Viscoelasticity;358
7.7.3;15.3 Plasticity;361
7.7.4;15.4 Relation of EIT to Kinetic Polymer Models;366
7.7.4.1;15.4.1 The Rouse and Zimm Models;366
7.7.4.2;15.4.2 EIT Description of the Rouse and Zimm Models;367
7.7.4.3;15.4.3 Kinetic Justification of the EIT Results;368
7.7.5;15.5 Non-Newtonian Fluids;372
7.7.5.1;15.5.1 General Considerations;372
7.7.5.2;15.5.2 EIT Description of Second-Order Non-Newtonian Fluids;376
7.7.5.2.1;15.5.2.1 A Three-Parameter Model;376
7.7.5.2.2;15.5.2.2 Giesekus Four-Parameter Model;382
7.7.6;15.6 Problems;383
7.8;16 Thermodynamics of Polymer Solutions Under Shear Flow;389
7.8.1;16.1 The Chemical Potential Under Shear;390
7.8.2;16.2 Explicit Solution for the Rouse–Zimm Model;394
7.8.3;16.2 Chemical Reactions Under Flow;399
7.8.3.1;16.2.1 Shear-Induced Effect on the Affinity;399
7.8.3.2;16.2.2 Illustration: Polymer Degradation Under Flow;400
7.8.4;16.4 Dynamical Approach;403
7.8.5;16.5 Shear-Induced Migration of Polymers;405
7.8.6;16.6 Problems;409
7.9;17 Relativistic Formulation;413
7.9.1;17.1 The Macroscopic Theory;414
7.9.2;17.2 Characteristic Speeds;417
7.9.3;17.3 Relativistic Kinetic Theory;420
7.9.4;17.4 Nuclear Matter and Relativistic Ion Collisions;423
7.9.5;17.5 Problems;425
7.10;18 Viscous Cosmological Models and Cosmological Horizons;428
7.10.1;18.1 Viscous Cosmological Models and Accelerated Expansion;429
7.10.2;18.2 Particle Production and Effective Bulk Viscosity;435
7.10.3;18.3 Extended Thermodynamics and Cosmological Horizons;437
7.10.4;18.4 Astrophysical Problems: Gravitational Collapse;440
7.10.5;18.5 Problems;441
8;A Summary of Vector and Tensor Notation;444
8.1;A.1 Symmetric and Antisymmetric Tensors;444
8.2;A.2 Decomposition of a Tensor;444
8.3;A.3 Scalar (or Dot) and Tensorial (Inner) Products;445
8.4;A.4 (Inner) Tensorial Product (also Named Dyadic Product);446
8.5;A.5 Cross Multiplication Between Two Vectors and Between a Tensor and a Vector;446
8.6;A.6 Differentiation;446
8.7;A.7 Tensor Invariants;447
9;B Useful Integrals in the Kinetic Theory of Gases;448
10;C Some Physical Constants;449
11;References;450
12;Author Index;471
13;Subject Index;478