Hydrodynamics of Bounded Vertical Film with Nonlinear Surface Properties

Date
2001
Authors
Heidari, A.H.
Braun, Richard J.
Hirsa, A. H.
Snow, S.A.
Naire, S.
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Publisher
Department of Mathematical Sciences
Abstract
The drainage of a thin liquid film with an insoluble monolayer down a vertical wall is studied. Lubrication theory is used to develop a model where the film is pinned at the top with a given thickness and the film drains into a bath at the bottom. A nonlinear equation of state is used for the surface tension and the surface viscosity is a nonlinear function of the surfactant concentration; these are appropriate for some aqueous systems. The three partial differential equations are solved via discretization in space and then solving the resulting differential algebraic system. Results are described for a wide range of parameters, and the conditions under which the free surface is immobilized are discussed.
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