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Numerical simulations of sink flow in the Hele-Shaw cell with small surface tension

Published online by Cambridge University Press:  01 December 1997

E. D. KELLY  and
E. J. HINCH
E. D. KELLY
Affiliation:
DAMTP, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
E. J. HINCH
Affiliation:
DAMTP, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

The motion of an initially circular drop of viscous fluid surrounded by inviscid fluid in a Hele-Shaw cell withdrawn from an eccentric point sink is considered. Using a numerical algorithm based on a boundary integral equation, the solution for small, finite surface tension is observed. It is found that the zero-surface-tension formation of a cusp is avoided, and instead a narrow finger of inviscid fluid forms, which then rapidly propagates towards the sink. The scaling of the finger in the sink vicinity is determined.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 8 , Issue 6 , December 1997 , pp. 533 - 550
Copyright
1997 Cambridge University Press

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