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

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 develop...

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Bibliographic Details
Published in:Journal of fluid mechanics 2020-09, Vol.898, Article A6
Main Authors: Lerisson, Gaétan, Ledda, Pier Giuseppe, Balestra, Gioele, Gallaire, François
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Computer simulation
Contact angle
Experiments
Fluid mechanics
Group velocity
Growth rate
JFM Papers
Lubricants & lubrication
Lubrication
Measurement techniques
Perturbation
Profiles
Reynolds number
Stability
Stability analysis
Substrates
Thin film coatings
Thin films
Wave packets
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2020.396