This book provides an introduction to theories of fluids with microstruc ture, a subject that is still evolving, and information on which is mainly available in technical journals. Several approaches to such theories, employ ing different levels of mathematics, are now available. This book presents the subject in a connected manner, using a common notation and a uniform level of mathematics. The only prerequisite for understanding this material is an exposure to fluid mechanics using Cartesian tensors. This introductory book developed from a course of semester-length lec tures that were first given in the Department of Chemical Engineering at the University of Delaware and subsequently were given in the Department of Mechanical Engineering at the Indian Institute of Technology, Kanpur. The encouragement of Professor A. B. Metzner and the warm hospitality of the Department of Chemical Engineering, University of Delaware, where the first set of notes for this book were prepared (1970-71), are acknowledged with deep appreciation. Two friends and colleagues, Dr. Raminder Singh and Dr. Thomas F. Balsa, made helpful suggestions for the improvement of this manuscript. The financial support provided by the Education Development Centre of the Indian Institute of Technology, Kanpur, for the preparation of the manuscript is gratefully acknowledged.
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ISBN-13
978-3-540-13708-5 (9783540137085)
DOI
10.1007/978-3-642-82351-0
Schweitzer Klassifikation
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.- 5.9 Constitutive 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.
