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Instabilities of the upstream meniscus in directional viscous fingering

Published online by Cambridge University Press:  26 April 2006

Sylvain Michalland ,
Marc Rabaud  and
Yves Couder
Sylvain Michalland
Affiliation:
Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France Present Address: MFPM, Place des Carmes Déchaux, 63040 Clermont-Ferrand Cedex, France.
Marc Rabaud
Affiliation:
Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France Present Address: FAST, Bt. 502, 91405 Orsay Cedex, France (to where correspondence should be addressed).
Yves Couder
Affiliation:
Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
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Abstract

New instabilities affecting the meniscus of a viscous fluid are presented. They occur in an experimental set-up introduced previously by Rabaud et al. (1990) in which a small quantity of a viscous fluid is placed in the narrow gap between two rotating cylinders. In this geometry the downstream meniscus located in the region where the two solid surfaces move away from each other is known to be unstable and to exhibit directional viscous fingering. In the present article it is shown that the upstream meniscus can also be unstable. Two types of instabilities are observed. In the first supercritical transition the front becomes time-dependent with either standing or propagating waves. In a second transition, which is subcritical, parallel fingers of finite amplitude are formed. The various types of spatio-temporal dynamical behaviour are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 312 , 10 April 1996 , pp. 125 - 148
Copyright
© 1996 Cambridge University Press

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