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A falling film on a porous medium

Published online by Cambridge University Press:  25 January 2013

A. Samanta ,
B. Goyeau  and
C. Ruyer-Quil
A. Samanta
Affiliation:
Laboratoire FAST, UPMC Univ. Paris 06, Univ. Paris-Sud, CNRS, UMR CNRS 7608, Bat. 502, Campus Universitaire, F-91405 Orsay, France
B. Goyeau
Affiliation:
Laboratoire EM2C, UPR CNRS 288, Ecole Central Paris, Grande Voie des Vignes, F-92295 Châtenay-Malabry CEDEX, France
C. Ruyer-Quil*
Affiliation:
Laboratoire FAST, UPMC Univ. Paris 06, Univ. Paris-Sud, CNRS, UMR CNRS 7608, Bat. 502, Campus Universitaire, F-91405 Orsay, France
*
†Email address for correspondence: ruyer@fast.u-psud.fr
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Abstract

A gravity-driven falling film on a saturated porous inclined plane is studied via a continuum approach, where the liquid and porous layers are considered as a single composite layer. Using a weighted residual technique, a two-equation model is derived in terms of the local flow rate $q(x, t)$ and the entire layer thickness $H(x, t)$. Its linear stability analysis has been satisfactorily compared to the results of the Orr–Sommerfeld problem. The principal effect of the porous substrate on the film flow is to displace the liquid–porous interface to an effective liquid–solid interface located at the lower boundary of the upper momentum boundary layer in the porous medium. The stability and dynamics of the film is thus only weakly affected by the presence of a permeable substrate. In both the linear and the nonlinear regimes, the spatial response of a falling film on a porous medium is not very different from that observed on an impermeable inclined wall. However, the wavy motion of the film triggers a significant exchange of mass at the liquid–porous interface.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Geophysical and Geological Flows: Shallow water flows Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 716 , 10 February 2013 , pp. 414 - 444
Copyright
©2013 Cambridge University Press

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