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Numerical solution of Hele-Shaw flows driven by a quadrupole

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

A blob of viscous Newtonian fluid is surrounded by inviscid fluid and sandwiched in the narrow gap between two plane parallel surfaces, so that initially its plan view occupies a simply connected domain. Recently Entov, Etingoff & Kleinbock (1993) produced some steady-state solutions for the blob placed in a quadrupole driven flow, and including the effects of surface tension. Here a numerical solution of the time-dependent problem using a Boundary Integral algorithm finds that for low values of the flow rate there exist two solutions. We find that one, which is close in shape to a circle, is stable, while the other, more deformed equilibrium, is unstable. The analysis also reveals that for certain flow strengths stable non-convex shapes also exist. If the flow strength is too large no stable equilibrium is possible.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 8 , Issue 6 , December 1997 , pp. 551 - 566
Copyright
1997 Cambridge University Press

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