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

Lerisson, Gaëtan (Laboratory of Fluid Mechanics and Instabilities, EPFL, Lausanne, Switzerland) ; Ledda, Giuseppe (Laboratory of Fluid Mechanics and Instabilities, EPFL, Lausanne, Switzerland) ; Balestra, Gioele (School of Engineering and Architecture (HEIA-FR), HES-SO // University of Applied Sciences Western Switzerland) ; Gallaire, François (Laboratory of Fluid Mechanics and Instabilities, EPFL, Lausanne, Switzerland)

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.


Mots-clés:
Type d'article:
scientifique
Faculté:
Ingénierie et Architecture
Ecole:
HEIA-FR
Institut:
IPRINT - Institut de printing
Date:
2020-09
Pagination:
26 p.
Publié dans:
Journal of Fluid Mechanics
Numérotation (vol. no.):
2020, vol. 898
DOI:
ISSN:
0022-1120
Le document apparaît dans:

Note: The status of this file is: restricted


 Notice créée le 2020-10-27, modifiée le 2020-11-03

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