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Multipole expansion calculation of slow viscous flow about spheroids of different sizes

Published online by Cambridge University Press:  19 April 2006

Wei-Hsi Liao  and
David A. Krueger
Wei-Hsi Liao
Affiliation:
Department of Physics, Colorado State University, Fort Collins, Colorado 80523
David A. Krueger
Affiliation:
Department of Physics, Colorado State University, Fort Collins, Colorado 80523
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Abstract

The multipole representation technique of Gluckman, Pfeffer & Weinbaum for slow, viscous, axisymmetric motion has been applied to a system of two spheroids. The two particles may have different shapes and volumes. The limitations of this method have been studied through calculations of the drag forces and velocities of particles with aspect ratios from 0·1 to 10 and relative volumes V from 1 to 103. The multipole-expansion convergence is quite slow for large relative volumes and requires on the order of $4 \times V^{\frac{1}{3}}$ multipoles. Wild fluctuations in the drag as the number of multipoles increases were found for large oblate spheroids. Relative velocities are given quite accurately for separations of the centres greater than 1·02 times the minimum separation. Comparisons are made with previous results and approximate theories for two spheres, for non-identical particles at large separation, and for a sphere near a large spheroid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 96 , Issue 2 , 29 January 1980 , pp. 223 - 241
Copyright
© 1980 Cambridge University Press

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