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A falling film down a slippery inclined plane

Published online by Cambridge University Press:  07 September 2011

A. Samanta ,
C. Ruyer-Quil  and
B. Goyeau
A. Samanta
Affiliation:
Laboratoire FAST, UMR CNRS 7608, Université Pierre et Marie Curie, Campus Universitaire, 91405 Orsay, France
C. Ruyer-Quil*
Affiliation:
Laboratoire FAST, UMR CNRS 7608, Université Pierre et Marie Curie, Campus Universitaire, 91405 Orsay, France
B. Goyeau
Affiliation:
Laboratoire EM2C, UPR CNRS 288, École Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry CEDEX, France
*
†Email address for correspondence: [email protected]
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Abstract

A gravity-driven film flow on a slippery inclined plane is considered within the framework of long-wave and boundary layer approximations. Two coupled depth-averaged equations are derived in terms of the local flow rate and the film thickness . Linear stability analysis of the averaged equations shows good agreement with the Orr–Sommerfeld analysis. The effect of a slip at the wall on the primary instability has been found to be non-trivial. Close to the instability onset, the effect is destabilising whereas it becomes stabilising at larger values of the Reynolds number. Nonlinear travelling waves are amplified by the presence of the slip. Comparisons to direct numerical simulations show a remarkable agreement for all tested values of parameters. The averaged equations capture satisfactorily the speed, shape and velocity distribution in the waves. The Navier slip condition is observed to significantly enhance the backflow phenomenon in the capillary region of the solitary waves with a possible effect on heat and mass transfer.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Waves/Free-surface Flows: Solitary waves Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 684 , 10 October 2011 , pp. 353 - 383
Copyright
Copyright © Cambridge University Press 2011

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