Power exponential velocity distributions in disordered porous media

Abstract

Velocity distribution functions link the micro- and macro-level theories of fluid flow through porous media. Here we study them for the fluid absolute velocity and its longitudinal and lateral components relative to the macroscopic flow direction in a model of a random porous medium. We claim that all distributions follow the power exponential law controlled by an exponent $\gamma$ and a shift parameter $u_0$ and examine how these parameters depend on the porosity. We find that $\gamma$ has a universal value $1/2$ at the percolation threshold and grows with the porosity, but never exceeds 2.