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Forced dewetting on porous media

Published online by Cambridge University Press:  15 February 2007

OLIVIER DEVAUCHELLE ,
CHRISTOPHE JOSSERAND  and
STEPHANE ZALESKI
OLIVIER DEVAUCHELLE
Affiliation:
Laboratoire de Modélisation en Mécanique, CNRS-UMR 7606, Case 162, 4 place Jussieu, 75252 Paris Cédex 05, France
CHRISTOPHE JOSSERAND
Affiliation:
Laboratoire de Modélisation en Mécanique, CNRS-UMR 7606, Case 162, 4 place Jussieu, 75252 Paris Cédex 05, France
STEPHANE ZALESKI
Affiliation:
Laboratoire de Modélisation en Mécanique, CNRS-UMR 7606, Case 162, 4 place Jussieu, 75252 Paris Cédex 05, France
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Abstract

We study the dewetting of a porous plate withdrawn from a liquid bath. The contact angle is fixed to zero and the flow is assumed to be almost parallel to the plate (lubrication approximation). The ordinary differential equation involving the position of the water surface is analysed in phase space by means of numerical integration. We show the existence of a stationary moving contact line with zero contact angle below a critical value of the capillary number η U/γ. Above this value, no stationary contact line can exist. An analytical model, based on asymptotic matching is developed, which reproduces the dependence of the critical capillary number on the angle of the plate with respect to the horizontal (3/2 power law), provided the capillary length is much larger than the square root of the porous-medium permeability. In addition, it is shown that the classical lubrication equation leads not only to the well-known Landau–Levich–Derjaguin films, but also to a family of films for which thickness is not imposed by the problem parameters.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 574 , 10 March 2007 , pp. 343 - 364
Copyright
Copyright © Cambridge University Press 2007

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