On non-linear effects in unsteady flows through porous media

Abstract

The question of the non-linear effects on the unsteady flows of non-Newtonian fluids through porous media is addressed. The slightly compressible fluids of power law behavior are considered. The exact self-similar solutions in a closed form of the non-linear equations governing the flow, for the first boundary value problem, are presented. The implications of the non-linear effects on the propagation mechanism of pressure disturbances in a non-Newtonian fluid, flowing through a porous medium, are discussed. It is shown that these disturbances propagate with finite velocity, which is a monotonically decreasing function of time, due to the existence of a moving pressure front. This relevant result is obtained from exact analytical solutions which exhibit traveling wave characteristics in a shear thinning fluid.