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Falling film on an anisotropic porous medium

Published online by Cambridge University Press:  25 August 2022

Sanghasri Mukhopadhyay Open the ORCID record for Sanghasri Mukhopadhyay [Opens in a new window] ,
Nicolas Cellier Open the ORCID record for Nicolas Cellier [Opens in a new window] ,
Usha R Open the ORCID record for Usha R [Opens in a new window] ,
Marx Chhay Open the ORCID record for Marx Chhay [Opens in a new window]  and
Christian Ruyer-Quil Open the ORCID record for Christian Ruyer-Quil [Opens in a new window]
Sanghasri Mukhopadhyay
Affiliation:
Université Savoie Mont Blanc, CNRS, LOCIE, 73000 Chambéry, France
Nicolas Cellier
Affiliation:
Université Savoie Mont Blanc, CNRS, LOCIE, 73000 Chambéry, France
Usha R
Affiliation:
Department of Mathematics, IIT Madras, Chennai, 600036 Tamil Nadu, India
Marx Chhay
Affiliation:
Université Savoie Mont Blanc, CNRS, LOCIE, 73000 Chambéry, France
Christian Ruyer-Quil*
Affiliation:
Université Savoie Mont Blanc, CNRS, LOCIE, 73000 Chambéry, France
*
†Email address for correspondence: christian.ruyer-quil@univ-smb.fr
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Abstract

The stability and dynamics of a falling liquid film over an anisotropic porous medium are studied using a one-domain approach. Our stability analysis shows a significant departure from the effective no-slip boundary condition in the isotropic case. Anisotropy does not affect the threshold of linear instability. However, a non-trivial dual effect of anisotropy on the film stability is observed depending on the permeability of the porous medium. This dual effect results from the net balance of the enhancement of viscous diffusion at the top Brinkman sublayer and the mitigation of viscous damping in the core Darcy sublayer. Three-equation models have been derived from the lubrication theory approximation in terms of the exact mass balance and averaged momentum balances in the porous and liquid layers. In the nonlinear regime, anisotropy has a dual effect by damping capillary waves at large permeabilities and enhancing them at low permeabilities. Anisotropy also affects wave speeds and shapes, modifies travelling-wave branches of solutions, affects the development of a time-periodic wavetrain by inlet forcing and alters the noise-driven dynamics of the flow. These effects result from the mitigation of mass exchange at the liquid–porous interface and the contribution of the cross-stream permeability in the Brinkman top sublayer to the viscous diffusion.

JFM classification

Interfacial Flows (free surface): Thin films Low-Reynolds-number flows: Lubrication theory

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JFM Papers
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Journal of Fluid Mechanics , Volume 947 , 25 September 2022 , A26
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© The Author(s), 2022. Published by Cambridge University Press

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References

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