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 (i) the disordered geometry of the pore space, (ii) the fluid rheological properties, and (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.