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Inertial effects on Saffman–Taylor viscous fingering

Published online by Cambridge University Press:  29 March 2006

CHRISTOPHE CHEVALIER
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes, UMR 7636 CNRS, Université Paris 6, Ecole Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, 75231 Paris cedex 05, France Ecole Nationale des Ponts et Chaussées, 6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne-la-Vallée cedex 2, France
MARTINE BEN AMAR
Affiliation:
Laboratoire de Physique Statistique, UMR 8550 CNRS, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris cedex 05, France
DANIEL BONN
Affiliation:
Laboratoire de Physique Statistique, UMR 8550 CNRS, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris cedex 05, France Van der Waals-Zeeman Institute, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, the Netherlands
ANKE LINDNER
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes, UMR 7636 CNRS, Université Paris 6, Ecole Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, 75231 Paris cedex 05, France

Abstract

For the Saffman–Taylor instability, the inertia of the fluid may become important for high finger speeds. We investigate the effects of inertia on the width of the viscous fingers experimentally. We find that, due to inertia, the finger width can increase with increasing speed, contrary to what happens at small Reynolds number Re. We find that inertial effects need to be considered above a critical Weber number We. In this case it can be shown that the finger width is governed by a balance between viscous forces and inertia. This allows us to define a modified control parameter $1/B'$, which takes the corrections due to inertia into account; on rescaling the experimental data with $1/B'$, they all collapse onto the universal curve for the classical Saffman–Taylor instability. Subsequently, we try to rationalize our observations. Numerical simulations, taking into account a modification of Darcy's law to include inertia, are found to only qualitatively reproduce the experimental findings, pointing to the importance of three-dimensional effects.

Type
Papers
Copyright
© 2006 Cambridge University Press

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