Hydrodynamics of a bounded vertical film with nonlinear surface properties
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Updated: Aug 14, 2026

Film Control to Study Contributions of Waves to Droplet Impact Dynamics on Thin Flowing Liquid Films
Published on: August 18, 2018
A Homayoun Heidari1, Richard J Braun, Amir H Hirsa
1Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
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 the resulting differential algebraic system is solved. 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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