Power exponential velocity distributions in disordered porous media

TL;DR

This paper investigates velocity distribution functions in disordered porous media, revealing they follow a power exponential law with parameters depending on porosity, and identifies a universal exponent at the percolation threshold.

Contribution

It introduces a power exponential law model for velocity distributions in porous media and analyzes how its parameters vary with porosity, including a universal exponent at the threshold.

Findings

Velocity distributions follow a power exponential law controlled by parameters.

The exponent $$ is universal at the percolation threshold.

The exponent $$ increases with porosity but remains below 2.

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.