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Flow separation from a stationary meniscus

Published online by Cambridge University Press:  25 August 2009

J. SÉBILLEAU ,
L. LIMAT  and
J. EGGERS
J. SÉBILLEAU
Affiliation:
Laboratoire Matière et Systèmes Complexes, UMR CNRS 7057, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France
L. LIMAT
Affiliation:
Laboratoire Matière et Systèmes Complexes, UMR CNRS 7057, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France
J. EGGERS*
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
*
†Email address for correspondence: jens.eggers@bris.ac.uk
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Abstract

We consider the steady flow near a free surface at intermediate to high Reynolds numbers, both experimentally and theoretically. In our experiment, an axisymmetric capillary meniscus is suspended from a cylindrical tube, held slightly above a horizontal water surface. A flow of dyed water is released through the tube into the reservoir, and flow lines are thus recorded. At low Reynolds numbers, flow lines follow the free surface, and injected water spreads horizontally inside the container. Increasing the Reynolds number, the injected fluid penetrates to a certain distance into the bath, but ultimately follows the free surface. Above a critical Reynolds number of approximately 60, the flow separates from the free surface in the meniscus region and a jet projects vertically into the bath. We find no indication that the flow reattaches at higher Reynolds numbers, nor are our findings sensitive to surface contamination. We show theoretically and confirm experimentally that the separating streamline forms a right angle with the free surface.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 633 , 25 August 2009 , pp. 137 - 145
Copyright
Copyright © Cambridge University Press 2009

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