摘要: 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. It is well known that the contact line of currents on an inclined surface may become unstable and then a pattern of ‘fingers’ develops that affects the quality of the coatings. This instability has been intensively studied due to its relevance for the technology of various industrial processes. So far the theoretical and numerical research has been focused on Newtonian fluids, notwithstanding that often in the real situation as well as in the experiments, the rheology of the involved liquid is non-Newtonian. Using the lubrication approximation we derive the governing equations for a current of a power law non-Newtonian fluid on an inclined plane under the action of gravity and the viscous stresses. We show that surface tension effects can be included in …