Free surface flows with large slopes: beyond lubrication theory

Abstract

The description of free surface flows can often be simplified to thin film (or lubrication) equations, when the slopes of the liquid-gas interface are small. Here we present a long wavelength theory that remains fully quantitative for steep interface slopes, by expanding about Stokes flow in a wedge. For small capillary numbers, the variations of the interface slope are slow and can be treated perturbatively. This geometry occurs naturally for flows with contact lines: we quantify the difference with ordinary lubrication theory through a numerical example and analytically recover the full Cox-Voinov asymptotic solution.

4 pages, 3 figures

References in corpus (3)

• Disjoining Potential and Spreading of Thin Liquid Layers in the Diffuse Interface Model Coupled to Hydrodynamics
• Scaling at the selective withdrawal transition
• Toward a description of contact line motion at higher capillary numbers

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