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Note on the direct calculation of mobility functions for two equal-sized spheres in Stokes flow

Published online by Cambridge University Press:  21 April 2006

Byung Jun Yoon  and
Sangtae Kim
Byung Jun Yoon
Affiliation:
Department of Chemical Engineering, University of Wisconsin, Madison, WI 53706, USA
Sangtae Kim
Affiliation:
Department of Chemical Engineering, University of Wisconsin, Madison, WI 53706, USA
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Abstract

A simple, direct method is presented for the calculation of mobility functions for the translational and rotational velocities and stresslets of two equal-sized spheres in unbounded low-Reynolds-number flow when the ambient velocity field is a superposition of a uniform stream, a vorticity and a rate-of-strain field. Our numerical procedure furnishes accurate values for touching spheres and coefficients for the near-field asymptotic expansions. The singular behaviour of the mobility functions is clarified. These results have been used to determine accurately the coefficient of the O(c2) term in the expression for the bulk stress in a suspension of spheres (6.95c2 instead of 7.6c2).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 185 , December 1987 , pp. 437 - 446
Copyright
© 1987 Cambridge University Press

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