Theories of Fluids with Microstructure

1 Kinematics of Flow.- 1.1 Introduction.- 1.2 Velocity Gradient Tensor.- 1.3 Rate of Deformation Tensor.- 1.4 Analysis of Strain Rates.- 1.5 Spin Tensor.- 1.6 Curvature-Twist Rate Tensor.- 1.7 Objective Tensors.- 1.8 Balance of Mass.- 1.9 Concluding Remarks.- 1.10 References.- 2 Field Equations.- 2.1 Introduction.- 2.2 Measures for Mechanical Interactions.- 2.3 Euler's Laws of Motion.- 2.4 Stress and Couple Stress Vectors.- 2.5 Stress and Couple Stress Tensors.- 2.6 Cauchy's Laws of Motion.- 2.7 Analysis of Stress.- 2.8 Energy Balance Equation.- 2.9 Entropy Inequality.- 2.10 Concluding Remarks.- 2.11 References.- 3 Couple Stresses in Fluids.- 3.1 Introduction.- 3.2 Constitutive Equations.- 3.3 Equations of Motion.- 3.4 Boundary Conditions.- 3.5 Steady Flow Between Parallel Plates.- 3.6 Steady Tangential Flow Between Two Coaxial Cylinders.- 3.7 Poiseuille Flow Through Circular Pipes.- 3.8 Creeping Flow Past a Sphere.- 3.9 Some Time-Dependent Flows.- 3.10 Stability of Plane Poiseuille Flow.- 3.11 Hydromagnetic Channel Flows.- 3.12 Some Effects on Heat Transfer.- 3.13 Concluding Remarks.- 3.14 References.- 4 Anisotropic Fluids.- 4.1 Introduction.- 4.2 Balance Laws.- 4.3 Microstructure of a Dumbbell-Shaped Particle.- 4.4 Field Equations.- 4.5 Constitutive Equations.- 4.6 Implications of the Second Law of Thermodynamics.- 4.7 Incompressible Fluids.- 4.8 Simple Shearing Motion.- 4.9 Orientation Induced by Flow.- 4.10 Poiseuille Flow Through Circular Pipes.- 4.11 Cylindrical Couette Flow.- 4.12 Concluding Remarks.- 4.13 References.- 5 Micro Fluids.- 5.1 Introduction.- 5.2 Description of Micromotion.- 5.3 Kinematics of Deformation.- 5.4 Conservation of Mass.- 5.5 Balance of Momenta.- 5.6 Microinertia Moments.- 5.7 Balance of Energy.- 5.8 Entropy Inequality.- 5.9Constitutive Equations for Micro Fluids.- 5.10 Linear Theory of Micro Fluids.- 5.11 Equations of Motion.- 5.12 Concluding Remarks.- 5.13 References.- 6 Micropolar Fluids.- 6.1 Introduction.- 6.2 Skew-Symmetry of the Gyration Tensor and Microisotropy.- 6.3 Micropolar Fluids.- 6.4 Thermodynamics of Micropolar Fluids.- 6.5 Equations of Motion.- 6.6 Boundary and Initial Conditions.- 6.7 Two Limiting Cases.- 6.8 Steady Flow Between Parallel Plates.- 6.9 Steady Couette Flow Between Two Coaxial Cylinders.- 6.10 Pipe Poiseuille Flow.- 6.11 Micropolar Fluids with Stretch.- 6.12 Concluding Remarks.- 6.13 References.- Notation.