The Drainage of Thin Liquid Films on an Inclined Solid Surface

Abstract

In this paper, we consider the thinning process of an inclined thin liquid film over a solid boundary with an inclination angle to the horizontal in gravity driven flow. 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. The solution of the governing equations of the film thickness is obtained numerically by the Rung-Kutta method with the aid of Mat lab(ode45). We present here some of the theoretical aspects of the instability development in an inclined thin liquid films on a solid surface in two dimensional coordinate system with an inclination angle to the horizontal . There are different types of phenomena that can occur, such as drainage, details of rupture, non-Newtonian surface properties in moving contract lines in thin liquid films (1). These phenomena can help to describe the physical processes that occur in our real world. (2,3) have studied the case of contact line instabilities of thin liquid films but with constant flux configuration and also they considered some global models of a moving contact lines. (4) studied the thin liquid films flowing down the inverted substrate in three dimensional flow. (5) investigated the dynamics of an inclined thin liquid films of variable thickness in steady and unsteady cases and when the film is stationary and uniform. (6) considered the stability of thin liquid films and sessile droplets. The stability of the contact line of thin fluid film flows with constant flux configuration is considered by (7). (8) considered the spreading of thin liquid films with small surface tension in the case when the flow is unsteady. The Non-linear analysis of creeping flow on the inclined permeable substrate plane subjected to an electric field was considered by (9). In this paper we investigate the drainage of the inclined thin liquid films where the gravity and other forces such as viscous and surface tension forces have a significant effect on the flow of the film. We use 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. The solution of the governing equations of the liquid film thickness is obtained numerically.