Steady and traveling flows of a power-law liquid over an incline

The slow flow of thin liquid films on solid surfaces is an important phenomenon in nature and in industrial processes, and an intensive effort has been made to investigate it. So far research has been focused mainly on Newtonian fluids, notwithstanding that often in the real situations as well as in the experiments, the rheology of the involved liquid is non-Newtonian. In this paper we investigate within the lubrication approximation the family of traveling wave solutions describing the flow of a power-law liquid on an incline. We derive general formulae for the traveling waves, that can be of several kinds according to the value of the propagation velocity c and of an integration constant j 0 related to the difference between c and the averaged velocity of the fluid u. There are exactly 17 different kinds of solutions. Five of them are the steady solutions ( c=0). In addition there are eight solutions that correspond to different downslope traveling waves, and four that describe waves traveling upslope.