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Two-dimensional Stokes flow with suction and small surface tension

Published online by Cambridge University Press:  01 December 1999

L. J. CUMMINGS  and
S. D. HOWISON
L. J. CUMMINGS
Affiliation:
Lab. de Phys. Stat. de l'E.N.S., 24 rue Lhomond, 75231 Paris Cedex 05, France
S. D. HOWISON
Affiliation:
Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB, UK
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Abstract

In this article the complex variable theory of two-dimensional Stokes flow as developed by Richardson [22], and modified by Howison & Richardson [16], is reviewed. The analysis of [16] is extended to a new solution driven by a point sink, which uses a cubic polynomial conformal mapping (with real coefficients) from the unit disk onto the fluid domain. This solution is analysed in the limit of small surface tension. An apparent ‘stability paradox’ (where two equivalent flow geometries are found, one of which is ‘stable’ and the other unstable) is resolved by allowing the coefficients to take complex values.

Information

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 10 , Issue 6 , December 1999 , pp. 681 - 705
Copyright
© 1999 Cambridge University Press

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