FLOW OF FLUIDS THROUGH POROUS MEDIA DUE TO HIGH PRESSURE GRADIENTS: PART 2-UNSTEADY FLOWS

An interesting class of applications concerning flow through porous media concerns flows of fluids involving very high pressures and pressure gradients in the flow domain such as the problems of enhanced oil recovery and carbon dioxide sequestration. Most porous solids are inhomogeneous and anisotropic, and the flows of fluids taking place through such porous solids are inherently unsteady. In this short paper we allow for the possibility that the flow is unsteady and that the viscosity and drag are dependent on the pressure (there is considerable experimental evidence to support the fact that the viscosity of a fluid depends on the pressure) but we assume that the solid is homogeneous and isotropic. We consider the problem wherein the fluid flow that enters a slab is pulsatile in nature, about a non-zero mean pressure. Our aim was to determine whether the pulsations would enhance the volumetric flux, a phenomenon that is observed in pulsatile flows in pipes; we however find that this is not the case, that is, pulsations in the pressure do not lead to flow enhancement, rather it diminishes the volumetric flux. To our knowledge, this is the first study wherein the unsteady flow of a fluid with pressure-dependent viscosity through a porous solid is carried out.