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Two-dimensional slow viscous flows with time-dependent free boundaries driven by surface tension

Published online by Cambridge University Press:  16 July 2009

S. Richardson
S. Richardson
Affiliation:
Department of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland
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Abstract

We consider the two-dimensional quasi-steady Stokes flow of an incompressible Newtonian fluid occupying a time-dependent simply-connected region bounded by a free surface. The motion is driven by a constant surface tension acting at the free boundary so that, with the effects of gravity ignored, one expects the boundary to approach a circular form as time evolves. It is shown that, if at some initial instant the region occupied by the fluid is given by a rational conformal map of the unit disc, then it must retain this property as long as the region remains simply-connected. Moreover, its evolution may be described analytically; in simple cases this description is explicit, but in more complicated problems the numerical integration of a system of first order differential equations may be required.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 3 , Issue 3 , September 1992 , pp. 193 - 207
Copyright
Copyright © Cambridge University Press 1992

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