Power-exponential velocity distributions in disordered porous media

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.