Non-Newtonian fluid flow through three-dimensional disordered porous media

We investigate the flow of various non-Newtonian fluids through three-dimensional disordered porous media by direct numerical simulation of momentum transport and continuity equations. Remarkably, our results for power-law (PL) fluids indicate that the flow, when quantified in terms of a properly modified permeability-like index and Reynolds number, can be successfully described by a single (universal) curve over a broad range of Reynolds conditions and power-law exponents. We also study the flow behavior of Bingham fluids described in terms of the Herschel-Bulkley model. In this case, our simulations reveal that the interplay of ({\it i}) the disordered geometry of the pore space, ({\it ii}) the fluid rheological properties, and ({\it iii}) the inertial effects on the flow is responsible for a substantial enhancement of the macroscopic hydraulic conductance of the system at intermediate Reynolds conditions. This anomalous condition of ``enhanced transport'' represents a novel feature for flow in porous materials.