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Some Axisymmetric and Asymmetric Stokes Flows Involving Axisymmetric Bodies

Choudhury, Abdul Mukid; (1999) Some Axisymmetric and Asymmetric Stokes Flows Involving Axisymmetric Bodies. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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The effect of a layer of an adsorbed monomolecular surfactant film of fluid covering the free surface of a finite or semi-infinite volume of substrate fluid, has been investigated for motion within both surfactant and substrate fluids caused by the slow rotation of a partially submerged solid body of revolution. The resulting boundary value problem is solved for varying depths of partial submersion of the solid body by a method in which the equations governing the motion in the substrate and the surfactant boundary condition are satisfied exactly. The error in satisfying the boundary condition on the solid body surface is minimized according to a least-squares technique. A comparison is made with data available from (a) exact solution and (b) experiment when possible. Illustrations include the sphere, concentric spheres and prolate and oblate ellipsoids. Methods are presented for obtaining exact solutions in analytic form of the equations of asymmetric Stokes flow when an axisymmetric body is at rest or in motion in homogeneous viscous fluid. One method shows how the difficulty of determining three coupled quasi-harmonic functions simultaneously, which is the general problem encounted in this type of flow, may be overcome by the superposition of solutions for flows involving only two quasi-harmonic functions, with each of these functions determined sequentially. Another method considers a class of asymmetric translation problems which involve only two quasi-harmonic functions and analytical expressions are determined for the drag on the body which are compared with numerical values of the drag already available in the literature for certain body shapes.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Some Axisymmetric and Asymmetric Stokes Flows Involving Axisymmetric Bodies
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Thesis digitised by ProQuest.
URI: https://discovery.ucl.ac.uk/id/eprint/10121703
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