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Instability of a thin viscous film flowing under an inclined substrate: steady patterns

Published online by Cambridge University Press:  30 June 2020

Gaétan Lerisson ,
Pier Giuseppe Ledda ,
Gioele Balestra Open the ORCID record for Gioele Balestra [Opens in a new window]  and
François Gallaire Open the ORCID record for François Gallaire [Opens in a new window]
Gaétan Lerisson
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
Pier Giuseppe Ledda
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
Gioele Balestra
Affiliation:
iPrint Institute, University of Applied Sciences and Arts of Western Switzerland, Fribourg, CH-1700, Switzerland
François Gallaire*
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
*
†Email address for correspondence: [email protected]
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Abstract

The flow of a thin film coating the underside of an inclined substrate is studied. We measure experimentally spatial growth rates and compare them to the linear stability analysis of a flat film modelled by the lubrication equation. When forced by a stationary localized perturbation, a front develops that we predict with the group velocity of the unstable wave packet. We compare our experimental measurements with numerical solutions of the nonlinear lubrication equation with complete curvature. Streamwise structures dominate and saturate after some distance. We recover their profile with a one-dimensional lubrication equation suitably modified to ensure an invariant profile along the streamwise direction and compare them with the solution of a purely two-dimensional pendent drop, showing overall a very good agreement. Finally, those different profiles agree also with a two-dimensional simulation of the Stokes equations.

JFM classification

Instability: Absolute/convective instability Instability: Nonlinear instability Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 898 , 10 September 2020 , A6
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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