Instability of a thin viscous film flowing under an inclined substrate: steady patterns. (10th September 2020)

• Record Type: Journal Article
• Authors: Lerisson, Gaétan; Ledda, Pier Giuseppe; Balestra, Gioele; Gallaire, François
• Is Part Of: Journal of fluid mechanics. Volume 898(2020)
• Publication Date: 2020-09-10
• Subjects: absolute/convective instability, -- nonlinear instability, -- thin films; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.396
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : 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.