Concentration gradient, diffusion, and flow through open porous medium near percolation threshold via computer simulations

The interacting lattice gas model is used to simulate fluid flow through an open percolating porous medium with the fluid entering at the source-end and leaving from the opposite end. The shape of the steady-state concentration profile and therefore the gradient field depends on the porosity (p). The root mean square (rms) displacements of fluid and its constituents (tracers) show a drift power-law behavior, R∝t in the asymptotic regime (t→∞). The flux current density (j) is found to scale with the porosity according to, j∝(Δp)β with Δp=p−pc and β≃1.7.