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.

4 pages, 3 figures

References in corpus (3)

• Spatial Fluctuations Of Fluid Velocities In Flow Through A Three-Dimensional Porous Medium
• Percolation of overlapping squares or cubes on a lattice
• Anisotropy of flow in stochastically generated porous media

Cited by in corpus (6)

• Local pore size correlations determine flow distributions in porous media
• Electron energy partition across interplanetary shocks: I. Methodology and Data Product
• Dispersion of motile bacteria in a porous medium
• Universal Particle Kinetic Distribution in Crowded Environments
• Self-similar distributions of fluid velocity and stress heterogeneity in a dissolving porous limestone
• Self-organized homogenization of flow networks