Abstract

The Long-Wave Theory is applied to investigate the dynamic stability of free thin fluid films flowing down an inclined plane. We assume that thin supported films have a thickness of 𝐻̅ and less than or equal to one hundred nm. Equations of Navier and Stokes, continuity-equation, and related boundary conditions are used to represent a two-dimensional stream demonstrated as a continuum. Under long-wave approximation, the governing equations for the film interface have been rescaled and simplified to obtain a highly non-linear condition of development for the film interface. A procedure for evaluating the magnitude of the effects of the high-order effects is also used to formulate simplified governing equations. In the future, we can study this problem by adding heat transfer over the stretching plate. In addition, we can also study the stability analysis to two-dimension flow of a viscous liquid within a horizontal thin liquid film with neglecting the inertia terms of Navier-Stokes equations.