Note: Intro -- Preface -- Fluid and Thermodynamics -- Fluid and Thermodynamics -- Contents -- 11 Creeping Motion Around Spheres at Rest in a Newtonian Fluid -- 11.1 Motivation -- 11.2 Mathematical Preliminaries -- 11.3 Stokes Flow Around a Stagnant Sphere -- 11.3.1 Rigid Sphere and No-Slip Condition on the Surface of the Sphere -- 11.3.2 Cunningham's Correction -- 11.3.3 Rigid Infinitely Thin Spherical Shell Filled with a Fluid of Different Viscosity -- 11.4 Oseen's TheoryFor a brief biography of Carl Wilhelm Oseen, see Fig. 11.8. -- 11.4.1 Governing Equations of the Oseen Theory -- 11.4.2 Construction of a Particular Integral of (11.58) -- 11.4.3 `Stokes-Lets' and `Oseen-Lets' -- 11.5 Theory of Lagerstöm and Kaplun -- 11.5.1 Motivation -- 11.5.2 Stokes Expansion -- 11.5.3 Oseen Expansion -- 11.5.4 Matching Procedure -- 11.6 Homotopy Analysis Method---The Viscous Drag Coefficient Computed for Arbitrary Reynolds Numbers -- 11.6.1 The Mathematical Concept -- 11.6.2 Selection of ψ0, mathcalH, hbar and Approximate Solution -- 11.7 Conclusions and Discussion -- References -- 12 Three-Dimensional Creeping Flow--- Systematic Derivation of the Shallow Flow Approximations -- 12.1 Introductory Motivation -- 12.2 Model Equations -- 12.2.1 Field Equations -- 12.2.2 Boundary Conditions -- 12.3 Scaling Procedure -- 12.4 Lowest Order Model Equations for Flow Down Steep Slopes (Strong Steep Slope Shallow Flow Approximation) -- 12.5 A Slightly More General Steep Slope Shallow Flow Approximation (Weak Steep Slope Shallow Flow Approximation) -- 12.6 Phenomenological Expressions for Creeping Glacier Ice -- 12.7 Applications to Downhill Creeping Flows -- 12.7.1 Computational Procedure -- 12.7.2 Profiles and Flows for Isothermal Conditions -- 12.7.3 Remarks for Use of the Shallow Flow Approximation for Alpine Glaciers. , 12.8 Free-Surface Gravity-Driven Creep Flow of a Very Viscous Body with Strong Thermomechanical Coupling---A Rigorous Derivation of the Shallow Ice Approximation -- 12.8.1 The Classical Shallow Flow Approximation -- 12.8.2 Applications -- 12.9 Discussion and Conclusions -- References -- 13 Shallow Rapid Granular Avalanches -- 13.1 Introduction -- 13.2 Distinctive Properties of Granular Materials -- 13.2.1 Dilatancy -- 13.2.2 Cohesion -- 13.2.3 Lubrication -- 13.2.4 Liquefaction -- 13.2.5 Segregation, Inverse Grading, Brazil Nut Effect -- 13.3 Shallow Flow Avalanche Modeling -- 13.3.1 Voellmy's Avalanche Model -- 13.3.2 The SH Model, Reduced to Its Essentials -- 13.4 A Three-Dimensional Granular Avalanche Model -- 13.4.1 Field Equations -- 13.4.2 Curvilinear CoordinatesIn this section and henceforth knowledge of the basic elements of tensor calculus are supposed known. There is a great number of books on this e.g. R. Bowenaut]Bowen and C.C. Wangaut]Wang [7], I.S. Sokolnikoffaut]Sokolnikoff [76], E. Klingbeilaut]Klingbeil [48], L. Brillouinaut]Brillouin [8]. -- 13.4.3 Equations in Dimensionless Form -- 13.4.4 Kinematic Boundary Conditions -- 13.4.5 Traction Free Condition at the Free Surface -- 13.4.6 Coulomb Sliding Law at the Base -- 13.4.7 Depth Integration -- 13.4.8 Ordering Relations -- 13.4.9 Closure Property -- 13.4.10 Nearly Uniform Flow Profile -- 13.4.11 Summary of the Two-Dimensional SH Equations -- 13.4.12 Standard Form of the Differential Equations -- 13.5 Avalanche Simulation and Verification with Experimental Laboratory Data -- 13.5.1 Introduction -- 13.5.2 Classical and High Resolution Shock Capturing Numerical Methods -- 13.6 Attempts of Model Validation and Verification of Earthquake and Typhoon Induced Landslides -- References -- 14 Uniqueness and Stability -- 14.1 Introduction -- 14.2 Kinetic Energy of the Difference Motion. , 14.3 Uniqueness -- 14.4 Stability -- 14.5 Energy Stability of the Laminar Channel Flow -- 14.6 Linear Stability Analysis of Laminar Channel Flow -- 14.6.1 Basic Concepts -- 14.6.2 The Orr--Sommerfeld and the Rayleigh Equations -- 14.6.3 The Eigenvalue Problem -- References -- 15 Turbulent Modeling -- 15.1 A Primer on Turbulent Motions -- 15.1.1 Averages and Fluctuations -- 15.1.2 Filters -- 15.1.3 Reynolds Versus Favre Averages -- 15.2 Balance Equations for the Averaged Fields -- 15.3 Turbulent Closure Relations -- 15.3.1 Reynolds Stress Hypothesis and Turbulent Dissipation Rate -- 15.3.2 Averaged Density Field ρ -- 15.3.3 Turbulent Heat Flux qt and Turbulent Species Mass Flux jt -- 15.3.4 One- and Two-Equation Models -- 15.4 k-ε Model for Density Preserving and Boussinesq Fluids -- 15.4.1 The Balance Equations -- 15.4.2 Boussinesq Fluid Referred to a Non-inertial Frame -- 15.4.3 Summary of the k - ε Equations -- 15.4.4 Boundary Conditions -- 15.4.5 Closing Remarks -- References -- 16 Turbulent Mixing Length Models and Their Applications to Elementary Flow Configurations -- 16.1 Motivation/Introduction -- 16.2 The Turbulent Plane Wake -- 16.3 The Axisymmetric Isothermal Steady Jet -- 16.4 Turbulent Round Jet in a Parallel Co-flow -- 16.5 A Study of Turbulent Plane Poiseuille Flow -- 16.6 Discussion -- References -- 17 Thermodynamics---Fundamentals -- 17.1 Concepts and Some Historical Remarks -- 17.2 General Notions and Definitions -- 17.2.1 Thermodynamic System -- 17.2.2 Thermodynamic States, Thermodynamic Processes -- 17.2.3 Extensive, Intensive, Specific and Molar State Variables -- 17.2.4 Adiabatic and Diathermic Walls -- 17.2.5 Empirical Temperature, Gas Temperature and Temperature Scales -- 17.3 Thermal Equations of State -- 17.3.1 Ideal Gas -- 17.3.2 Real Gases -- 17.3.3 The Phenomenological Model of van der Waals. , 17.4 Reversible and Irreversible Thermodynamic Processes -- 17.4.1 Diffusion -- 17.4.2 Reversible Expansion and Compaction of a Gas -- 17.5 First Law of Thermodynamics -- 17.5.1 Mechanical Energies -- 17.5.2 Definitions, Important for the First Law -- 17.5.3 Caloric Equations of State for Fluids and Gases -- 17.5.4 Simple Applications of the First Law -- 17.5.5 Specific Heats of Real Gases -- 17.6 The Second Law of Thermodynamics---Principle of Irreversibility -- 17.6.1 Preamble -- 17.6.2 The Second Law for Simple Adiabatic Systems -- 17.6.3 Generalizations for Non-adiabatic Systems -- 17.7 First Applications of the Second Law of Thermodynamics -- References -- 18 Thermodynamics---Field Formulation -- 18.1 The Second Law of Thermodynamics for Continuous Systems -- 18.2 Two Popular Forms of the Entropy Principle -- 18.2.1 Entropy Principle 1: Clausius--Duhem Inequality -- 18.2.2 Entropy Principle of Ingo MüllerIngo Müller ( ast1936), a physicist- engineer with doctorate (1966) and habilitation (1971) from the Technische Hochschule Aachen, is among the rational thermodynamicists, who was chiefly involved in research to generalize the entropy principle, to make it more flexible and better apt for thermodynamic processes than the Clausius--Duhem inequality with its absolute temperature and the a priori estimate of the entropy flux asq/T. This is seen already in his -- 18.3 Thermal and Caloric Equations of State -- 18.3.1 Canonical Equations of State -- 18.3.2 Specific Heats and Other Thermodynamic Quantities -- 18.3.3 Application to Ideal Gases -- 18.3.4 Isentropic Processes in Caloric Ideal Gases -- 18.4 Thermodynamics of an Inviscid, Heat Conducting -- 18.4.1 The Coleman-Noll Approach -- 18.4.2 The Rational Thermodynamics of Ingo Müller -- References -- 19 Gas Dynamics -- 19.1 Introductory Remarks. , 19.2 Propagation of Small Perturbations in a Gas -- 19.2.1 Fundamental Equations -- 19.2.2 Plane and Spherical Waves -- 19.2.3 Eigen Oscillations Determined with Bernoulli's Method -- 19.3 Steady, Isentropic Stream Filament Theory -- 19.4 Theory of Shocks -- 19.4.1 General Concepts -- 19.4.2 Jump Conditions -- 19.4.3 Stationary Shocks in Simple Fluids Under Adiabatic Conditions -- 19.5 Final Remarks -- References -- 20 Dimensional Analysis, Similitude and Physical Experiments at Laboratory Scale -- 20.1 Introductory MotivationThe topic presented here in this chapter is a popular theme in fluid mechanics and is the subject of several books, e.g., G.I. Barenblattaut]Barenblatt [1], Henry Görtleraut]Gortler@Görtler [17], H.L. Langhaaraut]Langhaar [26], Joseph Spurkaut]Spurk [40], K. Hutteraut]Hutter and K. Jöhnkaut]Johnk@Jöhnk [20] and others. A mathematical theory, based on a system of axioms with an extensive list of related references is given by D.E. Carlsonaut]Carlson [13, 14]. -- 20.1.1 Dimensional Analysis -- 20.1.2 Similitude and Model ExperimentsFrom K. Hutteraut]Hutter et al.: Physics of Lakes, Vol. 3 [21], pp. 313--314. -- 20.1.3 Systems of Physical Entities -- 20.2 Theory of Dimensional Equations -- 20.2.1 Dimensional Homogeneity -- 20.2.2 Buckingham's Theorem -- 20.2.3 A Set of Examples from Fluid Mechanics -- 20.3 Theory of Physical Models -- 20.3.1 Analysis of the Downscaling of Physical Processes -- 20.3.2 Applications -- 20.4 Model Theory and Differential Equations -- 20.4.1 Avalanching Motions down Curved and Inclined Surfaces -- 20.4.2 Navier--Stokes--Fourier--Fick Equations -- 20.4.3 Non-dimensionalization of the NSFF Equations -- 20.5 Discussion and Conclusions -- References -- List of Biographies -- Name Index -- Subject Index.

Note: Intro -- Preface -- Fluid and Thermodynamics -- Fluid and Thermodynamics -- Contents -- 1 Introduction -- 1.1 Historical Notes and Definition of the Subject Field -- 1.2 Properties of Liquids -- References -- 2 Hydrostatics -- 2.1 Some Basic Concepts -- 2.2 Fluid Pressure -- 2.3 Fundamental Equation of Hydrostatics -- 2.4 Pressure Distribution in a Density Preserving Heavy Fluid -- 2.5 Hydrostatic Buoyancy of Floating Bodies -- 2.6 Hydrostatics in an Accelerated Reference System -- 2.7 Pressure Distribution in the Still Atmosphere -- Reference -- 3 Hydrodynamics of Ideal Liquids -- 3.1 Basic Kinematic Concepts -- 3.1.1 Motion, Velocity -- 3.1.2 Streamlines, Trajectories, Streaklines -- 3.2 Mass Balance, Continuity -- 3.3 Balance of Linear Momentum -- 3.4 Bernoulli's Equation -- 3.5 Simple Applications of the Bernoulli Equation -- 3.6 Global Formulation of the Momentum Equation -- 3.7 Applications of the Balance Law of Momentum in Integrated Form -- 3.7.1 Reaction Forces Due to Fluid Flow Through Pipes -- 3.7.2 Borda Exit Orifice -- 3.7.3 Impact of a Free Jet on a Wall -- 3.7.4 Mixing Processes -- 3.7.5 Hydraulic Jump -- 3.8 Plane Flow Around Infinitely Long Wings -- 3.8.1 Flow Through a Periodic Grid of Wings -- 3.8.2 Flow Around a Single Wing -- 3.9 Balance of Moment of Momentum -- 3.10 Applications of the Balance of Angular Momentum -- 3.10.1 Segner's Water Wheel -- 3.10.2 Euler's Turbine Equation -- References -- 4 Conservation of Angular Momentum---Vorticity -- 4.1 Circulation -- 4.2 Simple Vorticity Theorems -- 4.3 Helmholtz Vorticity Theorem -- 4.4 Potential Vorticity Theorem -- References -- 5 An Almanac of Simple Flow Problems of Ideal Fluids -- 5.1 General Concepts -- 5.1.1 A Primer on Vector Analysis -- 5.1.2 Determination of a Vector Field from Its Sources and Vortices -- 5.2 Vortex-Free Flow Fields. , 5.2.1 Mathematical Preliminaries -- 5.2.2 Potential Fields -- 5.3 Motion-Induced Force on a Body in Potential Flow. The Virtual Mass Concept -- 5.3.1 Force on a Sphere -- 5.3.2 Force on a Body of Arbitrary Geometry -- 5.4 Plane Flow Configuration -- 5.4.1 Stream Function -- 5.4.2 Simple Plane Flows of Ideal Fluids -- References -- 6 Function-Theoretical Methods Applied to Plane Potential Flows -- 6.1 General Principles -- 6.1.1 Some Notation and Mathematical Properties of Complex Functions -- 6.1.2 Examples -- 6.1.3 Steady Flow Around an Arbitrary Cylinder at Rest -- 6.1.4 The Kutta-Joukowski Mapping -- 6.2 Applications -- 6.2.1 Flow Over a Plane Plate -- 6.2.2 Potential Flow Over a Circular Segment -- 6.2.3 Realistic Air-Wings with Finite Thickness -- 6.3 The Circle Theorem of Milne-Thomson -- 6.4 Laminar Free Jets -- 6.4.1 Flow Through a Slit Orifice in a Vertical Wall -- 6.4.2 Potential Flow Through a Periodic Arrangement of Slits -- 6.5 Schwarz-Christoffel Transformation -- 6.5.1 Build-up of the General Schwarz-Christoffel Transformation -- 6.5.2 Examples of Schwarz-Christoffel Transformations -- References -- 7 Viscous Fluids -- 7.1 Fundamental Dynamical Equations of Viscous Fluids -- 7.1.1 Newtonian Fluids -- 7.1.2 Dilatant and Pseudoplastic Density Preserving Fluids -- 7.2 Plane Wall Bounded Shear Flows -- 7.3 Applications -- 7.3.1 Couette Viscometer -- 7.3.2 Cone Plate Viscometer -- 7.3.3 Hover Craft or Oil Pressure Cushion -- 7.3.4 Flows of Liquid Films -- 7.3.5 Influence of the Weight of a Fluid in Plane Poiseuille Flow -- 7.3.6 Slide Bearing Theory -- 7.4 Three-Dimensional Creeping Flow of a Pseudoplastic Fluid with Free Surface -- References -- 8 Simple Two- and Three-Dimensional Flow Problems of the Navier-Stokes Equations -- 8.1 Introductory Review -- 8.2 Steady State Layer Flows -- 8.2.1 Hagen-Poiseuille Flow. , 8.2.2 Ekman Theory and Its Extensions -- 8.3 Simple Unsteady Flows -- 8.3.1 Oscillating Wall -- 8.3.2 Adjustment of a Velocity Jump -- 8.4 Stationary Axisymmetric Laminar Jet -- 8.5 Viscous Flow in a Converging Two-Dimensional Channel -- 8.6 Closing Remarks -- References -- 9 Simple Solutions of Boundary Layer Equations -- 9.1 Preview -- 9.2 Two-Dimensional Boundary Layer Flow in the Vicinity of a Stagnation Point -- 9.3 Three-Dimensional Boundary Layer Flow in the Vicinity of a Stagnation Point -- 9.4 Boundary Layer Flows Around Wedges -- 9.4.1 Boundary Layer Equations -- 9.4.2 Flow Along Sidewalls of Wedges -- 9.4.3 Rotating Disk of Infinite Extent -- 9.5 The Blasius Boundary Layer -- 9.6 Round Laminar Jet---A Not So Simple Boundary Layer Problem -- 9.7 Boundary Layers of theaut]Navier Navier-Stokes aut]Stokes Equations Treated by Matched Asymptotic Expansions -- 9.7.1 A Simple Introductory Example -- 9.7.2 The Blasius Boundary Layer -- 9.8 Global Laws of the Steady Boundary Layer Theory -- 9.8.1 Global Mass and Momentum Balances -- 9.8.2 Holstein-Bohlen Procedure -- 9.9 Non-stationary Boundary Layers -- 9.9.1 Impulsive Start from Rest -- 9.9.2 Boundary Layer Formed at the Boundary of an Oscillating Body -- 9.9.3 Oscillation-Induced Drift Current -- 9.9.4 Non-Stationary Plate Boundary Layer -- References -- 10 Pipe Flows -- 10.1 Introductory Remarks -- 10.2 Laminar Pipe Flow -- 10.2.1 The Law of Hagen-Poiseuille -- 10.2.2 Laminar Flow in Cylindrical Pipes of Arbitrary Cross-Section -- 10.2.3 Flow Out of a Vessel -- 10.2.4 Influence of the Wall Drag of a Pipe to the Exit Flow from a Vessel -- 10.3 Turbulent Flows in Pipes -- 10.3.1 Coefficient of Resistance -- 10.3.2 Plane Turbulent Flow According to Prandtl and von Kármán. , 10.3.3 Calculation of Pressure Loss in Pipe FlowsThis subsection illustrates how pressure losses in a sequential arrangement of pipe segments are technically performed in the context of the Prandtl-von Kármán turbulence model. Conceptual thoughts on its theoretical limitation are given in the subsequent subsection. -- 10.3.4 Questioning the Prandtl-von Kármán Logarithmic Velocity ProfileWe follow in this subsection closely Chap. 30 in Physics of Lakes, Vol. 3 [9]. -- 10.4 Concluding Remarks -- References -- List of Biographies -- Name Index -- Subject Index.

Note: 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 Continua -- 22.1 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 Introduction -- 23.2 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 Fluid -- 24.3 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 -- 25.2.2 Hydrostatics of Nematic Liquid Crystals -- 25.2.3 Hydrodynamics of Nematic Liquid Crystals -- 25.3 A Thermodynamic Theory for Nematic Liquid Crystals -- 25.3.1 Kinematics -- 25.3.2 Conservation Laws and Entropy Inequality -- 25.3.3 Constitutive Relations and Exploitation of the Entropy Principle -- 25.4 Thermodynamics of an Incompressible Liquid … -- 25.5 Explicit Constitutive Parameterizations -- 25.5.1 Frank's Parameterization of the Free Energy -- 25.5.2 Parameterization of the Nonequilibrium Stress, Intrinsic Director Body Force, and Heat Flux Vector -- 25.5.3 Parodi Relation for a Nematic Liquid Crystal -- 25.6 Solutions for Simple Flow Problems -- 25.6.1 Shear Flows. , 25.7 Discussion -- References -- 26 Nematic Liquid Crystals with Tensorial Order Parameters -- 26.1 Nematic Liquid Crystals with Tensorial Order Variables -- 26.1.1 Motivation and Literature Review -- 26.1.2 Variational Principle -- 26.1.3 Liquid Crystals with Tensorial Order Parameters and Dissipative Microstructure -- 26.2 Uniaxial Nematic Crystals -- 26.2.1 Introductory Note -- 26.2.2 Uniaxial Nematics with Constant Order Parameter -- 26.2.3 Leslie's Alternative Formulation for Uniaxial Nematics -- 26.2.4 Uniaxial Nematics with Variable Scalar Order Parameter -- 26.3 Nematic Liquid Crystals Based on a Rank-2 Alignment Tensor -- 26.3.1 Motivation -- 26.3.2 Lagrange-Rayleigh Theory of the Alignment Tensor -- 26.4 Discussion and Conclusions -- 26.4.1 Pereira Borgmeyer-Hess Theory -- 26.4.2 Elastic and Viscous Contributions -- 26.4.3 The Role of the Inertia of the Microrotation -- 26.A.1 Constraints of Coordinates -- 26.A.2 Generalized Coordinates -- 26.A.3 d'Alembert's Principle, Principle of Virtual Work -- 26.A.4 Derivation of the Lagrange Equations -- References -- 27 Multiphase Flows with Moving Interfaces and Contact Line-Balance Laws -- 27.1 Introduction -- 27.2 General Balance Equations for Physical Bulk, Surface, and Line Quantities -- 27.2.1 Integral Form of the General Balance Statement -- 27.2.2 Transport Theorems, Divergence Theorems, and Kinematics -- 27.2.3 Local Forms of the General Balance Statement -- 27.3 Specified Balance Equations -- 27.3.1 Conservations of Mass -- 27.3.2 Solute Transport -- 27.3.3 Balance of Linear Momentum -- 27.3.4 Balance of Angular Momentum -- 27.3.5 Conservation of Energy -- 27.3.6 Entropy Inequality -- 27.4 Implicit Representation of Phase Interfaces and Contact Line -- 27.5 One-Fluid Conservation Equations -- 27.6 Concluding Remarks -- References. , 28 Multiphase Flows with Moving Interfaces and Contact Line-Constitutive Modeling -- 28.1 Introduction -- 28.2 Thermodynamic Processes in a Boltzmann-Type Mixture -- 28.2.1 Balance Relations -- 28.2.2 Entropy Principle -- 28.3 Constitutive Relations for the Phase Interface -- 28.3.1 Constitutive Assumptions and Restrictions -- 28.3.2 Thermodynamic Equilibrium -- 28.3.3 Linear Theory for the Nonequilibrium Parts -- 28.4 Constitutive Relations for the Three-Phase Contact Line -- 28.4.1 Constitutive Assumptions and Restrictions -- 28.4.2 Thermodynamic Equilibrium -- 28.4.3 Linear Theory for the Nonequilibrium Parts -- 28.5 Constitutive Relations for Phase Interfaces with Memory -- 28.5.1 Evaluation of the Entropy Inequality -- 28.5.2 Thermodynamic Equilibrium -- 28.5.3 Isotropic Theory for the Dynamic Part -- 28.6 Closing Summary -- 28.7 Concluding Remarks -- References -- 29 A Granular Fluid as a Limit of a Binary Mixture Theory-Treated as a One-Constituent Goodman-Cowin-Type Material -- 29.1 Introduction -- 29.2 Thermodynamic Processes -- 29.2.1 Balance Relations -- 29.2.2 Entropy Inequality -- 29.3 Constitutive Relations -- 29.3.1 Constitutive Assumptions and Restrictions -- 29.3.2 Thermodynamic Equilibrium -- 29.3.3 Linear Theory for the Nonequilibrium Parts -- 29.4 Constitutive Equations for Special Granular Materials -- 29.5 Horizontal Shearing Flow Problem -- 29.5.1 Basis Equations and Boundary Conditions for Horizontal Shearing Flow -- 29.5.2 Numerical Method -- 29.5.3 Numerical Results -- 29.6 Inclined Gravity-Flow Problem -- 29.7 Vertical Channel-Flow Problems -- 29.8 Alternative Formulations -- 29.8.1 Fluid Models for Cohesionless Granular Materials with Internal Length Parameter -- 29.8.2 Application to Simple Shear, Plane Poiseuille, and Gravity-Driven Flows -- 29.9 Concluding Remarks -- References. , 30 A Granular Mixture Model with Goodman-Cowin-Type Microstructure and its Application to Shearing Flows in Binary Solid-Fluid Bodies -- 30.1 Introduction -- 30.2 Thermodynamic Considerations -- 30.2.1 Balance Relations -- 30.2.2 Entropy Principle -- 30.3 Constitutive Modeling -- 30.3.1 Constitutive Equations -- 30.3.2 Thermodynamic Equilibrium -- 30.4 Saturated Solid-Fluid Mixture with Incompressible Constituents -- 30.5 Horizontal Shearing Flow Problem -- 30.5.1 Basic Equations and Boundary Conditions for Horizontal Shearing Flows -- 30.5.2 Numerical Method -- 30.5.3 Numerical Results -- 30.6 Concluding Remarks -- References -- 31 Modeling of Turbulence in Rapid Granular Flows -- 31.1 Introduction -- 31.2 Laminar Motions -- 31.3 Turbulent Motions -- 31.4 Entropy Principle -- 31.5 Exploitation of the Entropy Inequality -- 31.6 Restriction to the Laminar Case -- 31.7 Thermodynamic Equilibrium -- 31.8 Linear Deviations from Thermodynamic Equilibrium in Dynamic Processes -- 31.9 Discussion and Conclusions -- References -- List of Biographies -- Name Index -- Subject Index.

Note: Literaturangaben