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A slow motion of viscous liquid caused by a slowly moving solid sphere: an addendum

Published online by Cambridge University Press:  26 February 2010

M. E. O'Neill
M. E. O'Neill
Affiliation:
Department of Mathematics, University College London, Gower Street, London, W.C.1
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Extract

In the author's paper [1] in which an exact solution is given to the Stokes equations for the steady motion without rotation of a rigid sphere through a viscous fluid in a direction parallel to and at an arbitrary distance d from a fixed plane, expressions were obtained for the forces and couples which are exerted on the sphere and the plane by the fluid. The forces were shown to be equal and opposite. The couple acting on the sphere was found to have Cartesian components (0, Gy, 0), when moments of the surface stress are taken about the centre of the sphere, where

and the couple acting on the plane was found to be (0, Gy′, 0) where

The notation of (1) and (2) follows that as explained in [1] but a misplaced minus sign is corrected.

Type
Research Article
Information
Mathematika , Volume 14 , Issue 2 , December 1967 , pp. 170 - 172
Copyright
Copyright © University College London 1967

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References

1.O'Neill, M. E., Mathematika, 11 (1964), 67–74.CrossRefGoogle Scholar
2.Dean, W. R. and O'Neill, M. E., Mathematika, 10 (1963), 13–24.CrossRefGoogle Scholar
3.O'Neill, M. E. and Stewartson, K., J. Fluid Mech., 27 (1967), 705–724.CrossRefGoogle Scholar