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Fluid-structure interactions in Low-Reynolds-number flows
(Professor of Mechanical and Aerospace Engineering)
Fluid-structure interactions have been well studied over the years but most of the focus has been on high Reynolds number flows, inertially dominated flows where the drag force from the fluid typically varies as the square of the local fluid speed. There are though a large number of fluid-structure interaction problems at low values of the Reynolds number, where the fluid effects are dominated by viscosity and the drag force from the fluid typically varies linearly with the local fluid speed, which are applicable to many current research areas including hydrodynamics, microfluidics and hemodynamics. Edited by experts in complex fluids, Fluid-Structure Interactions in Low-Reynolds-Number Flows is the first book to bring together topics on this subject including elasticity of beams, flow in tubes, mechanical instabilities induced by complex liquids drying, blood flow, theoretical models for low-Reynolds number locomotion and capsules in flow. The book includes introductory chapters highlighting important background ideas about low Reynolds number flows and elasticity to make the subject matter more approachable to those new to the area across engineering, physics, chemistry and biology.
Cover; Fluid-Structure Interactions in Low-Reynolds-Number Flows; Preface; References; Nomenclature; Quantities; Acronyms; Operators; Contents; Chapter 1 -- Introduction to the Elasticity of Rods; 1.1 Discrete Setting: A Periodic Truss Network; 1.1.1 Geometric Description of a Single Cell; 1.1.2 Small-Displacement Approximation, Modes of Deformation; 1.1.3 Scaling and Symmetry Analysis of the Energy of the Cells; 1.1.4 Elongation of Springs; 1.1.5 Energy of a Single Cell; 1.1.6 Assembling the Periodic Truss; 1.2 Continuous Limit: String, 2D Elastica etc.; 1.2.1 A Generic Continuous Model.
1.2.2 The String Model1.2.3 The 2D Elastica Model; 1.2.4 Scaling Analysis: Bending Versus Stretching; 1.2.5 Other Rod Models are Possible; 1.3 Equilibrium of a 2D Elastica; 1.3.1 Derivation of the Equilibrium Equations; 1.3.2 Analogy with the Nonlinear Pendulum and 2D Drops; 1.4 Solving the Linear 2D Elastica; 1.4.1 Clamped-Free Cantilever Beam; 1.4.2 Stretched String; 1.5 The Elastica in Three Dimensions: Helical Buckling; References; Chapter 2 -- Low-Reynolds-Number Flows; 2.1 Introduction; 2.2 Equations of Motion; 2.2.1 The Reynolds Number; 2.2.2 Stokes Equations; 2.3 Elementary Flows.
2.3.1 Channel Flows2.3.2 Darcy's Approximation: Description of Porous Media; 2.3.3 Flow Through a Hole in a Wall: Sampson's Solution; 2.4 Kinematic Reversibility; 2.4.1 Observations; 2.4.2 Mathematical Reasons for Kinematic Reversibility; 2.4.3 Examples of Kinematic Reversibility; 2.5 Mathematical Features; 2.5.1 The Lorentz Reciprocal Theorem; 2.5.2 A Point Source: An Idea Illustrated with the Laplace Equation; 2.5.3 Far-Field Decay of the Stokes Equations; 2.5.4 The Point-Force Solution to the Stokes Equations.
2.5.5 An Integral Equation Representation of the Solution to the Stokes Equations2.6 General Features Related to the Motions of Objects in Viscous Flows; 2.6.1 Decomposing an External Flow into Simpler Problems; 2.6.2 Generalized Forces and Velocities: Forces, Torques, and the Stresslet Tensor; 2.6.3 ming Motions Produced by a Velocity Distribution on the Particle Surface; 2.6.4 Flow Fields Due to Forces; 2.7 Translation and Rotation of Spheres; 2.7.1 Field Around a Translating Sphere in an Unbounded Fluid; 2.7.2 Sedimentation; 2.7.3 Some Historical Uses of the Stokes Drag Formula.
2.7.4 Representation of the Solution with Vectors2.7.5 The Limit of a Point Force: A Stokeslet; 2.7.6 A Rotating Sphere and a Point Torque: The Rotlet; 2.7.7 Resistance to Rate of Deformation: The Stresslet; 2.7.8 Other Shapes; 2.8 Slender-Body Theory; 2.8.1 Resistive Force Theory: Brief Summary; 2.8.2 Resistive Force Theory: Derivation; 2.8.3 Transport and Sedimentation of Slender Objects; 2.9 Jeffery Orbits of an Elongated Particle; 2.9.1 Particle Rotation in the Plane of a Simple Shear Flow; 2.9.2 Three-Dimensional Particle Rotation in a Simple Shear Flow.
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Includes bibliographical references and index.
[Cambridge] : Royal Society of Chemistry, [2015]