Enhanced seepage through a soft porous material

We perform direct numerical simulations to study the flow through a model of deformable porous media. For sufficiently soft solid skeleton we find that the flow-rate ($Q$) increases with the pressure-difference ($\Delta P$) at a rate that is faster than linear. We construct a theory of this super-linear behavior by modelling the elastic properties of the solid skeleton by Winkler foundation. Our theory further predicts that the permeability is (a) an universal function of $\beta \equiv \Delta P/G$, where $G$ is the shear modulus of the solid skelton and (b) proportional to the cube porosity -- Kozeny-Carman formula in the small porosity limit. Both of these predictions are confirmed by our simulations.