Momentum jump condition at the boundary between a porous medium and a homogeneous fluid: inertial effects

The momentum transfer condition that applies at the boundary between a porous medium and a homogeneous fluid when inertial effects are important is developed as a jump condition based on the non-local form of the volume-averaged momentum equation. Outside the boundary region, this non-local form reduces to the classic transport equations, i.e., the Forchheimer equation with the Brinkman correction and the Navier-Stokes equations. The structure of the theory is comparable to that used to develop jump conditions at phase interfaces; thus, experimental measurements are required to determine the two coefficients that appear in the jump condition. The first of these coefficients is associated with an excess viscous stress, whereas the second is related to an excess inertial stress. The theory indicates that both of these coefficients are of order 1.