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The general solution for an ellipsoid in low-Reynolds-number flow

Published online by Cambridge University Press:  21 April 2006

Sangtae Kim  and
P. V. Arunachalam
Sangtae Kim
Affiliation:
Department of Chemical Engineering, University of Wisconsin, 1415 Johnson Drive, Madison, WI 53706, USA
P. V. Arunachalam
Affiliation:
Mathematics Research Center, University of Wisconsin, 610 Walnut Street, Madison, WI 53705, USA Permanent address: Department of Mathematics, Sri Venkateswara University, Tirupati 517502, India.
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Abstract

The general solution for low-Reynolds-number flow about an ellipsoid is derived by the singularity method and by representation in ellipsoidal harmonics. It is shown that, as in potential flow, the focal ellipse is the image system for the ellipsoid. A simple transformation which resembles a step in the derivation of the Dirichlet potential is introduced and its implications are explored. This transformation converts the velocity representation for an nth-order ambient field into that for the (n + 1)th-order field. The method furnishes an explanation for the invariance of the domain of the singularity distribution (the focal ellipse) with respect to the ambient field. Faxén relations for all multipole moments for arbitrary Stokes flow are derived in both integral and symbolic operator forms.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 178 , May 1987 , pp. 535 - 547
Copyright
© 1987 Cambridge University Press

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