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Similarity solutions to some gravity flows of non-Newtonian fluids through a porous medium. (English) Zbl 0776.76009

Summary: The nonlinear rheological effects of non-Newtonian fluids on the steady and unsteady gravity flows through a porous medium are addressed. The governing equations are derived and some similarity solutions, determining the shape of the free surface, are obtained. These show the existence of travelling-wave characteristics for a shear thinning fluid. The behavior of the solutions indicates that the disturbances of the free surface propagate with finite velocity, which is a monotonically decreasing function of time.

MSC:

76A05 Non-Newtonian fluids
76S05 Flows in porous media; filtration; seepage
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