Gravity-driven flow of a shear-thinning power-law fluid over a permeable plane

The flow of a thin layer of power-law fluid on a porous inclined plane is considered. The unsteady equations of motion are depth-integrated according to the von Karman momentum integral method. The variation of the velocity distribution with the depth is accounted for, and it is furthermore assumed that the flow through the porous medium is governed by the modified Darcy’s law. The stability condition is deduced considering the hierarchy of kinematic and gravity waves. The response of the linearized model to a Dirac-delta disturbance in unbounded domain is analytically deduced, in both stable and unstable conditions 1624 C. Di Cristo, M. Iervolino and A. Vacca of flow. The influence of the effect of power-law exponent and bottom permeability on the disturbance propagation is finally analyzed, suggesting indications about the choice of the bottom permeability in order to improve the performance of industrial processes.

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