Hydrodynamics of Bounded Vertical Film with Nonlinear Surface Properties
Date
2001
Journal Title
Journal ISSN
Volume Title
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.