Inertial model of flow through porous media

This paper demonstrates that pressure gradients which are observed in flow through porous media can be attributed to inertia forces due to changes in flow direction inherent to flow through porous media, Moreover, the paper shows that the magnitude of these pressure gradients, inertial in origin, are comparable with those empirically observed even in the case where dissipative forces are assumed to be negligible. It does this by presenting a mathematical model which includes higher-order derivatives of velocity which are usually neglected in equations of motion. These additional acceleration terms are analysed numerically on simple porous-media models. These models are constructed by placing, first, a single obstacle-sphere into a uniform flow and then by building a porous medium by adding to the number of spheres obstructing the flow. The pressure drop across the barrier of spheres is calculated numerically and compared with experimental findings.