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Intro; Preface; Fluid and Thermodynamics-Volume 1: Basic Fluid Mechanics; Fluid and Thermodynamics-Volume 2: Advanced Fluid Mechanics and Thermodynamic Fundamentals; Fluid and Thermodynamics-Volume 3: Structured and Multiphase Fluids; Contents; 21 Balance Laws of Continuous System; 21.1 Classification of Continuous Systems; 21.1.1 Balance Laws; 21.1.2 Single Constituent Systems; 21.1.3 Multiphase Continua and Mixtures; 21.1.4 Boltzmann and Polar Continua; 21.2 General Balance Laws for the Constituents; 21.3 Balance Laws for the Mixture as a Whole; 21.4 Summary; 21.5 Discussion; References
22 Kinematics of Classical and Cosserat Continua22.1 Preamble; 22.2 Classical Motion; 22.3 Classical Deformation Measures; 22.4 Micromotion; 22.5 Extended Deformation Measures; 22.6 Curvature Tensors; 22.7 Velocity Gradient and Gyration Tensor; 22.8 Natural Basis System; 22.9 Deformation Measures Referred to the Natural Basis; 22.10 Cosserat Deformation Tensors and Natural Bases; 22.11 Balance of Micro-Inertia; 22.12 Cosserats Book of 1909, Its Reception and Influence on the 20th Century and Beyond; References; 23 Thermodynamics of Class I and Class II Classical Mixtures
23.1 General Introduction23.2 Diffusion of Tracers in a Classical Fluid; 23.2.1 Basic Assumptions; 23.2.2 Material Theory for Diffusion Processes; 23.3 Saturated Mixture of Nonpolar Solid and Fluid Constituents; 23.3.1 Motivation; 23.3.2 Choice of the Material Class and Material Theory; 23.3.3 Some Properties of Differential (Pfaffian) Forms; 23.3.4 The Differential of the Entropy; 23.3.5 Thermodynamic Equilibrium; 23.3.6 Extension to Nonequilibrium States; 23.4 Discussion; References; 24 Thermodynamics of Binary Solid-Fluid Cosserat Mixtures; 24.1 Introductory Remarks
24.2 Thermodynamics of an Elastic Solid Plus a Viscoelastic Fluid24.3 Evolution Equations for the Volume Fractions; 24.4 Process Variables and Constitutive Functions; 24.5 Handling of the Entropy Inequality; 24.6 Detailed Exploitation of (24.23)-(24.43); 24.7 Behavior at and Near Thermodynamic Equilibrium; 24.7.1 Equilibrium Helmholtz Free Energies; 24.7.2 Equilibrium Implications; 24.7.3 Exploitation of the Entropy Inequality in the Neighborhood of the Equilibrium; 24.8 On Classes of Alternative Models; 24.8.1 The Hybrid Model I (HMI); 24.8.2 The Hybrid Model II (HMII)
24.8.3 The Incompressible Model (IM)24.9 Specification of the Material Behavior; 24.9.1 Rules of Aequipresence and Phase Separation and Their Approximate use for a Binary Mixture; 24.9.2 A Linear Model of Thermoelasticity of a Cosserat Single-Constituent Body; 24.9.3 Elastic Energies for Isotropic Solid Boltzmann Bodies; References; 25 A Continuum Approach to Liquid Crystals-The Ericksen-Leslie-Parody Formulation; 25.1 A Phenomenological View of Liquid Crystals; 25.2 A Continuum Formulation of Nematic Liquid Crystals; 25.2.1 General Physical Conservation Laws
22 Kinematics of Classical and Cosserat Continua22.1 Preamble; 22.2 Classical Motion; 22.3 Classical Deformation Measures; 22.4 Micromotion; 22.5 Extended Deformation Measures; 22.6 Curvature Tensors; 22.7 Velocity Gradient and Gyration Tensor; 22.8 Natural Basis System; 22.9 Deformation Measures Referred to the Natural Basis; 22.10 Cosserat Deformation Tensors and Natural Bases; 22.11 Balance of Micro-Inertia; 22.12 Cosserats Book of 1909, Its Reception and Influence on the 20th Century and Beyond; References; 23 Thermodynamics of Class I and Class II Classical Mixtures
23.1 General Introduction23.2 Diffusion of Tracers in a Classical Fluid; 23.2.1 Basic Assumptions; 23.2.2 Material Theory for Diffusion Processes; 23.3 Saturated Mixture of Nonpolar Solid and Fluid Constituents; 23.3.1 Motivation; 23.3.2 Choice of the Material Class and Material Theory; 23.3.3 Some Properties of Differential (Pfaffian) Forms; 23.3.4 The Differential of the Entropy; 23.3.5 Thermodynamic Equilibrium; 23.3.6 Extension to Nonequilibrium States; 23.4 Discussion; References; 24 Thermodynamics of Binary Solid-Fluid Cosserat Mixtures; 24.1 Introductory Remarks
24.2 Thermodynamics of an Elastic Solid Plus a Viscoelastic Fluid24.3 Evolution Equations for the Volume Fractions; 24.4 Process Variables and Constitutive Functions; 24.5 Handling of the Entropy Inequality; 24.6 Detailed Exploitation of (24.23)-(24.43); 24.7 Behavior at and Near Thermodynamic Equilibrium; 24.7.1 Equilibrium Helmholtz Free Energies; 24.7.2 Equilibrium Implications; 24.7.3 Exploitation of the Entropy Inequality in the Neighborhood of the Equilibrium; 24.8 On Classes of Alternative Models; 24.8.1 The Hybrid Model I (HMI); 24.8.2 The Hybrid Model II (HMII)
24.8.3 The Incompressible Model (IM)24.9 Specification of the Material Behavior; 24.9.1 Rules of Aequipresence and Phase Separation and Their Approximate use for a Binary Mixture; 24.9.2 A Linear Model of Thermoelasticity of a Cosserat Single-Constituent Body; 24.9.3 Elastic Energies for Isotropic Solid Boltzmann Bodies; References; 25 A Continuum Approach to Liquid Crystals-The Ericksen-Leslie-Parody Formulation; 25.1 A Phenomenological View of Liquid Crystals; 25.2 A Continuum Formulation of Nematic Liquid Crystals; 25.2.1 General Physical Conservation Laws