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Stability of a liquid film flowing down an inclined anisotropic and inhomogeneous porous layer: an analytical description

Published online by Cambridge University Press:  18 October 2016

P. Deepu ,
Srinivas Kallurkar ,
Prateek Anand  and
Saptarshi Basu
P. Deepu*
Affiliation:
TIFR Centre for Interdisciplinary Sciences, Narsingi, Hyderabad 500075, India
Srinivas Kallurkar
Affiliation:
Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India
Prateek Anand
Affiliation:
Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India
Saptarshi Basu
Affiliation:
Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India
*
†Email address for correspondence: pdeepu@tifrh.res.in
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Abstract

We study the effect of anisotropy and inhomogeneity in the permeability of the porous layer on the stability of surface waves of an inclined fluid–porous double-layer system. The fluid is assumed to be Newtonian and the porous layer to be Darcian. The porous layer is saturated with the same fluid and the two layers are coupled at the interface via the Beavers–Joseph condition. Linear stability analysis is performed based on a long-wave approximation. The resulting eigenvalue problem is exactly solved up to third order in the wavenumber. The anisotropic behaviour of permeability, cross-stream component of permeability, surface tension and porosity are found to have only higher-order effects on the stability characteristics of the system. On the other hand, the inhomogeneous feature in the streamwise component of permeability play a dominant role in determining the stability of the gravity-driven surface waves; as do other system parameters such as the thickness of the fluid layer relative to that of the porous layer and the Beavers–Joseph coefficient.

JFM classification

Instability: Instability Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 807 , 25 November 2016 , pp. 135 - 154
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Copyright
© 2016 Cambridge University Press 

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