Open Access

ARTICLE

Slow Rotation of an Axially Symmetric Particle about Its Axis of Revolution Normal to One or Two Plane Walls

Yi W. Wan¹, Huan J. Keh²

1 Department of Chemical Engineering, National Taiwan University, Taipei, 10617, Taiwan, ROC
2 Corresponding Author: Department of Chemical Engineering, National Taiwan University, Taipei, 10617, Taiwan, ROC. E-mail: huan@ntu.edu.tw

Computer Modeling in Engineering & Sciences 2011, 74(2), 109-138. https://doi.org/10.3970/cmes.2011.074.109

Abstract

The steady rotation of an axially symmetric particle about its axis of revolution normal to two plane walls at an arbitrary position between them in a viscous fluid is studied theoretically in the limit of small Reynolds number. The fluid is allowed to slip at the surface of the particle. A method of distribution of a set of spherical singularities along the axis of revolution inside a prolate particle or on the fundamental disk within an oblate particle is used to find the general solution for the fluid velocity distribution that satisfies the boundary conditions at the confining walls and at infinity. The slip condition at the particle surface is then satisfied by applying a boundary collocation technique to this general solution to numerically determine the unknown constants. The torque exerted on the particle by the fluid is calculated with good convergence behavior for various cases. For the rotation of a confined no-slip sphere, our torque results agree excellently with the available solutions in the literature. It is found that, for a spheroid with specified aspect ratio and particle-to-wall spacings, its boundary-corrected hydrodynamic torque decreases monotonically with an increase in its slip coefficient. For given wall-to-wall spacings, the hydrodynamic torque 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 torque increases with a decrease in its axial-to-radial aspect ratio, and the boundary effect on the rotation of an oblate spheroid can be very significant.

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