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Note on the slow rotation of a concave spherical lens or bowl in two immiscible semi-infinite viscous fluids

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

Samir R. Majumdar ,
Michael E. O'Neill  and
Howard Brenner
Samir R. Majumdar
Affiliation:
Department of Mathematics, University of CalgaryCalgary 44, Alberta, Canada
Michael E. O'Neill
Affiliation:
Department of Mathematics, University College London, London, WC1E 6BT.
Howard Brenner
Affiliation:
Department of Chemical Engineering, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213, U.S.A.
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Abstract

Using toroidal co-ordinates, an exact solution is derived for the velocity field induced in two immiscible semi-infinite viscous fluids, possessing a plane interface, by the slow rotation of a concave spherical lens, which is such that the circle of intersection of the composite spherical surfaces lies in the plane of the interface. The expression for the torque acting on the lens is derived, and this is shown to be reducible to an analytic closed form, when the lens degenerates into a spherical bowl and the fluids are identical.

MSC classification

Secondary: 76D05: Navier-Stokes equations
Type
Research Article
Information
Mathematika , Volume 21 , Issue 1 , June 1974 , pp. 147 - 154
Copyright
Copyright © University College London 1974

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References

1.Jeffery, G. B., Proc. London Math. Soc, 14 (1915), 327.CrossRefGoogle Scholar
2.Kanwal, R. P., J. Fluid Mech., 10 (1961), 17.CrossRefGoogle Scholar
3.Schneider, J. C., O'Neill, M. E. and Brenner, H., Mathematika, 20 (1973), 175.CrossRefGoogle Scholar