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Gravitational Drainage of a Tangentially-Immobile Thick Film

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Abstract

We use lubrication theory to derive an evolution equation for the free surface of a draining thick free film with a zero tangential velocity component along the free surface. The films are “thick” because effects that are important in very thin films, such as intermolecular forces, do not play a role in the situation of interest. The evolution equation results from the balance of surface tension, gravity, and dynamic viscosity. Subregions of the film appear and they involve balancing these effects pairwise. Computations are performed on the full evolution equation and for various boundary conditions corresponding to different parts of the film. Matched asymptotics are developed that predict the behavior as the film enters the bath and these agree very well with the computed results. Comparison with experiment is favorable for the rate of decrease of the film thickness.

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