Modeling the Drainage of aVertical Thin Liquid Film

In this paper, we consider the drainage of a vertical thin liquid film and we study the case of instability in gravity driven flow of a vertical thin films. Throughout this work, we assumed that the fluid thickness is constant far behind the front and we neglect the thickness of the film at the beginning of the motion. The equation of the film thickness is obtained analytically, using the similarity method by which we can isolate the explicit time dependence and then the shape of the film will depend on one variable only.