Low Reynolds number hydrodynamics

1. Introduction.- 1-1 Definition and purpose, 1. 1-2 Historical review, 8. 1-3 Application in science and technology, 13..- 2. The Behavior of Fluids in Slow Motion.- 2-1 The equations of change for a viscous fluid, 23. 2-2 Mechanical energy dissipation in a viscous fluid, 29. 2-3 Force and couple acting on a body moving in a viscous fluid, 30. 2-4 Exact solutions of the equations of motion for a viscous fluid, 31. 2-5 Laminar flow in ducts, 33. 2-6 Simplifications of the Navier-Stokes equations, especially for slow motion, 40. 2-7 Paradoxes in the solution of the creeping motion equations, 47. 2-8 Molecular effects in fluid dynamics, 49. 2-9 Non-newtonian flow, 51. 2-10 Unsteady creeping flows, 52..- 3. Some General Solutions and Theorems Pertaining to the Creeping Motion Equations.- 3-1 Introduction, 58. 3-2 Spherical coordinates, 62. 3-3 Cylindrical coordinates, 71. 3-4 Integral representations, 79. 3-5 Generalized reciprocal theorem, 85. 3-6 Energy dissipation, 88..- 4. Axisymmetrical Flow.- 4-1 Introduction, 96. 4-2 Stream function, 96. 4-3 Relation between stream function and local velocity, 98. 4-4 Stream function in various coordinate systems, 99. 4-5 Intrinsic coordinates, 100. 4-6 Properties of the stream function, 102. 4-7 Dynamic equation satisfied by the stream function, 103. 4-8 Uniform flow, 106. 4-9 Point source or sink, 106. 4-10 Source and sink of equal strength, 107. 4-11 Finite line source, 108. 4-12 Point force, 110. 4-13 Boundary conditions satisfied by the stream function, 111. 4-14 Drag on a body, 113. 4-15 Pressure, 116. 4-16 Separable coordinate systems, 117. 4-17 Translation of a sphere, 119. 4-18 Flow past a sphere, 123. 4-19 Terminal settling velocity, 124. 4-20 Slip at the surface of a sphere, 125. 4-21 Fluid sphere, 127. 4-22 Concentric spheres, 130. 4-23 General solution in spherical coordinates, 133. 4-24 Flow through a conical diffuser, 138. 4-25 Flow past an approximate sphere, 141. 4-26 Oblate spheroid, 145. 4-27 Circular disk, 149. 4-28 Flow in a venturi tube, 150. 4-29 Flow through a circular aperture, 153. 4-30 Prolate spheroid, 154. 4-31 Elongated rod, 156. 4-32 Axisymmetric flow past a spherical cap, 157..- 5. The Motion of a Rigid Particle of Arbitrary Shape in an Unbounded Fluid.- 5-1. Introduction, 159. 5-2 Translational motions, 163. 5-3 Rotational motions, 169. 5-4 Combined translation and rotation, 173. 5-5 Symmetrical particles, 183. 5-6 Nonskew bodies, 192. 5-7 Terminal settling velocity of an arbitrary particle, 197. 5-8 Average resistance to translation, 205. 5-9 The resistance of a slightly deformed sphere, 207. 5-10 The settling of spherically isotropic bodies, 219. 5-11 The settling of orthotopic bodies, 220..- 6. Interaction between Two or More Particles.- 6-1 Introduction, 235. 6-2 Two widely spaced spherically isotropic particles, 240: 6-3 Two spheres by the method of reflections and similar techniques, 249. 6-4 Exact solution for two spheres falling along their line of centers, 270. 6-5 Comparison of theories with experimental data for two spheres, 273. 6-6 More than two spheres, 276. 6-7 Two spheroids in a viscous liquid, 278. 6-8 Limitations of creeping motion equations, 281..- 7. Wall Effects on the Motion of a Single Particle.- 7-1 Introduction, 286. 7-2 The translation of a particle in proximity to container walls, 288. 7-3 Sphere moving in an axial direction in a circular cylindrical tube, 298. 7-4 Sphere moving relative to plane walls, 322. 7-5 Spheroid moving relative to cylindrical and plane walls, 331. 7-6 k-coefficients for typical boundaries, 340. 7-7 One- and two-dimensional problems, 341. 7-8 Solid of revolution rotating symmetrically in a bounded fluid, 346. 7-9 Unsteady motion of a sphere in the presence of a plane wall, 354..- 8. Flow Relative to Assemblages of Particles.- 8-1 Introduction, 358. 8-2 Dilute systems-no interaction effects, 360. 8-3 Dilute systems-first-order interaction effects, 371. 8-4 Concentrated systems, 387. 8-5 Systems with complex geometry, 400. 8-6 Particulate suspensions, 410. 8-7 Packed beds, 417. 8-8 Fluidization, 422..- 9. The Viscosity of Particulate Systems.- 9-1 Introduction, 431. 9-2 Dilute systems of spheres-no interaction effects, 438. 9-3 Dilute systems-first-order interaction effects, 443. 9-4 Concentrated systems, 448. 9-5 Nonspherical and nonrigid particles, 456. 9-6 Comparison with data, 462. 9-7 Non-newtonian behavior, 469..- Appendix A. Orthogonal Curvilinear Coordinate Systems.- A-l Curvilinear coordinates, 474. A-2 Orthogonal curvilinear coordinates, 477. A-3 Geometrical properties, 480. A-4 Differentiation of unit vectors, 481. A-5 Vector differential invariants, 483. A-6 Relations between cartesian and orthogonal curvilinear coordinates, 486. A-7 Dyadics in orthogonal curvilinear coordinates, 488. A-8 Cylindrical coordinate systems, 490. A-9 Circular cylindrical coordinates, 490. A-10 Conjugate cylindrical coordinate systems, 494. A-ll Elliptic cylinder coordinates, 495. A-12 Bipolar cylinder coordinates, 497. A-l3 Parabolic cylinder coordinates, 500. A-14 Coordinate systems of revolution, 501. A-l5 Spherical Coordinates, 504. A-l6 Conjugate coordinate systems of revolution, 508. A-17 Prolate spheroidal coordinates, 509. A-18 Oblate spheroidal coordinates, 512. A-19 Bipolar coordinates, 516. A-20 Toroidal coordinates, 519. A-21 Paraboloidal Coordinates, 521..- Appendix B. Summary of Notation and Brief Review of Polyadic Algebra.- Name Index.