Thin film flow over a bump on an inclined channel

Abstract

Abstract Lubrication theory is applied to model thin film flow on an inclined channel. The flow is uniform, but it is disturbed by a bump so that it produces a surface wave that is formulated into a single equation of the fluid thickness. Since the model is strongly non-linear, a numerical method is chosen for solving the equation. The effect of the bump can be seen by generating the wave at the surface. The wave increases the amplitude, splits, and propagates. For the long run, we obtain a steady form of the surface. The profile depends on the bump.