Distributions and seeps of driven mixture around a slit in porous media - interacting lattice gas simulation

We consider a porous medium with a slit on a discrete lattice of size $L_x \times L_y \times L_z$. The porous matrix is generated by a random distribution of immobile barriers on a fraction of the lattice sites. A longitudinal slit of width $L_s$ spans from bottom to top through the center of the lattice. The source of particles specified by their molecular weight, interaction, and miscibility gap is connected to the bottom ($z=1$) of the lattice with an open top ($z=L_z$). The Metropolis algorithm is used for stochastic moves of particles with a hydrostatic pressure bias ($H$). Periodic boundary conditions are used along the transverse directions with open longitudinal ends. Particles continue to enter the lattice from the source. Particles flow from bottom to top reaching a steady-state where we examine their seeps and distributions. We find that the steady-state distributions of constituents and their local mobility in the slit and the surrounding regions depend on bias and porosity with strong correlations at high bias.