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Viscous flows with time-dependent free boundaries in a non-planar Hele–Shaw cell

Published online by Cambridge University Press:  01 February 1997

VLADIMIR M. ENTOV  and
PAVEL I. ETINGOF
VLADIMIR M. ENTOV
Affiliation:
Institute for Problems in Mechanics, Russian Academy of Sciences, prosp. Vernadskogo, 101, Moscow, Russia
PAVEL I. ETINGOF
Affiliation:
Harvard University, Department of Mathematics, Cambridge, MA 02138, USA (Email: [email protected])
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Abstract

The dynamics of blobs of viscous fluid in a non-planar Hele–Shaw cell is considered. The general approach developed by Richardson and some of the resulting analytic techniques are extended to flows in non-planar cells, including cells shaped as surfaces of revolution and helical surfaces. An example related to the development and coalescence of two initially separated blobs in a cell on a spherical surface is presented. Some applications to mathematically equivalent problems dealing with planar Hele–Shaw cells with a non-uniform gap and flows through porous media are also discussed.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 8 , Issue 1 , February 1997 , pp. 23 - 35
Copyright
1997 Cambridge University Press

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