Slow Motion of a General Axisymmetric Slip Particle Along Its Axis of Revolution and Normal to One or Two Plane Walls
Huan J. Keh; and Yu C. Chang;

doi:10.3970/cmes.2010.062.225
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 62, No. 3, pp. 225-254, 2010
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Keywords Creeping flow, Axisymmetric particle, Prolate and oblate spheroids, Slip-flow surface, Boundary effect, Hydrodynamic drag force, Singularity method, Boundary collocation technique
Abstract A theoretical study of the Stokes flow caused by a rigid particle of revolution translating axisymmetrically perpendicular to two parallel plane walls at an arbitrary position between them in a viscous fluid, which may slip at the particle surface, is presented. A method of distribution of a set of spherical singularities along the axis of revolution within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solution of the fluid velocity field that satisfies the boundary conditions at the plane walls and at infinity. The slip condition on the particle surface is then satisfied by applying a boundary collocation technique to this general solution to determine the unknown constants. The drag force acting on the particle by the fluid is calculated with good convergence behavior for various cases. For the motion of a slip sphere perpendicular to two plane walls, our drag results agree very well with the numerical solutions previously obtained. For the translation of a no-slip prolate or oblate spheroid along its axis of revolution normal to a single plane wall, the agreement between our results and the available solutions in the literature is also excellent. It is found that for a spheroid with specified aspect ratio and particle-to-wall spacings, its boundary-corrected drag force in general decreases with an increase in its slip coefficient. For given wall-to-wall spacings, the hydrodynamic drag force is minimal when the particle is situated midway between the two plane walls and increases monotonically when it approaches either of the walls. For fixed separation and slip parameters, the normalized drag force increases with a decrease in its axial-to-radial aspect ratio, and the boundary effect on the motion of an oblate spheroid can be very significant.
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