Open Access

ARTICLE

Slow Rotation of an Axisymmetric Slip Particle about Its Axis of Revolution

by 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 2009, 53(1), 73-94. https://doi.org/10.3970/cmes.2009.053.073

Abstract

The problem of the rotation of a rigid particle of revolution about its axis in a viscous fluid is studied theoretically in the steady limit of low Reynolds number. The fluid is allowed to slip at the surface of the particle. A singularity method based on the principle 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 for the fluid velocity field that satisfies the boundary condition at infinity. The slip condition on the surface of the rotating particle is then satisfied by applying a boundary collocation technique to this general solution to numerically determine the unknown coefficients. The torque exerted on the particle by the fluid is evaluated with good convergence behavior for various cases. For the rotation of a slip sphere and of a no-slip prolate or oblate spheroid about its axis of symmetry, our torque results agree excellently with the corresponding exact solutions. For the rotation of a slip spheroid, the agreement between our results and the available approximate analytical solution is also very good. It is found that the hydrodynamic torque on the rotating spheroid with a given equatorial radius is a monotonically increasing function of the axial-to-radial aspect ratio of the spheroid for a no-slip or finite-slip spheroid and vanishes for a perfectly slip spheroid. For the rotation of a spheroid with a fixed aspect ratio, the hydrodynamic torque decreases monotonically with an increase in the slip coefficient of the particle.

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Keywords

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