Thermodynamics of Flowing Systems

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