Flow of Soap Films on Inclined Plane

In this paper a mathematical model is constructed to describe a two dimensional flow for an inclined films with an inclination angle to the horizontal that is drainage under the action of gravity. An asymptotic analysis is employed with the use of lubrication approximation. The film is assumed to be supported by wire frame elements at the ends. We apply the Navier–Stokes equations for flow of an incompressible fluid in two dimensions with specified boundary conditions. We obtain the equations representing the film thickness, the surface concentration, and the surface velocity. We obtain the similarity solutions for extensional flow of the simplified forms of these equations by using Lagrangian coordinate and then we approximate this equation by using Taylor series to obtain another similarity equation that can be used for different values of time.