Free surface flows with large slopes: beyond lubrication theory

Details Free surface flows with large slopes: beyond lubrication theory Free surface flows with large slopes: beyond lubrication theory

2006-03-31

arxiv.org/abs/physics/0603265v1

Phys. Fluids 18, 021701 (2006)

Physics

Fluid Dynamics

4 pages, 3 figures

Scientific paper

10.1063/1.2171190

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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