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.
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.