Non-Newtonian Fluid Film Flowing Down an Inclined Plane with a Periodic Topography

Flow of the thin layer of a nonlinearly viscous fluid subject to the gravity force down an inclined plane is considered. The capillary forces are assumed to be significant and rheology is described by the power law. The effect of a small periodic topography applied to the plane on the characteristics of steady-state flow and its stability is studied in the linear approximation; the calculations are carried out for the sinusoidal topography. It is shown that, regardless of rheology, the film on the plane with topography has the greater mean thickness as compared with the flat plane at the same flow rate, variation in the mean thickness being proportional to the second power of the topography amplitude. The variations in the increments of the normal modes and the critical Reynolds number are also proportional to the second power of the topography amplitude. The long-wave topography increases the critical Reynolds number, for dilatant fluids this effect being reached at the smaller periods than for pseudoplastic fluids.