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Free surface flows with large slopes: beyond lubrication theory

Jacco H. Snoeijer
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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.

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Jacco H. Snoeijer. 2006-03-31. Free surface flows with large slopes: beyond lubrication theory. https://doi.org/10.1063/1.2171190

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