Pattern formation in the flow of thin films down an incline: Constant flux configuration

We present fully nonlinear time-dependent simulations of a thin liquid film flowing down an inclined plane. Within the lubrication approximation, and assuming complete wetting, we find that varying the inclination angle considerably modifies the shape of the emerging patterns: Finger-shaped patterns result for the flow down a vertical plane, while saw-tooth patterns develop for the flows down an inclined plane. However, in all of our simulations, the roots always move, indicating that the shape of the patterns is not necessarily related to the surface coverage, a technologically important feature of the flow. Furthermore, we find that triangular steady-state patterns may be produced for the flow down an incline, while the fingers typically grow in length for all explored times. We find quantitative agreement with reported experiments, and suggest new ones.