Correlated response in a driven flow of self-organizing particles around a slit in porous media by interacting lattice gas

Abstract

The flow of immiscible particles (A, B) through a porous medium with a vertical slit is studied by an interacting lattice-gas computer simulation on a discrete lattice. The source of the particles is connected to the bottom and particles are driven upward by concentration gradient and a pressure bias against gravity. Distribution of flowing particles around the slit is examined as a function of the slit width and bias at high and low porosity at a steady state. At the low bias, a sharp change in the densities (high in slit to low in adjacent porous media) of both constituents occurs as expected. Onset of an undershooting in the density and mobility of particle profiles appears at the interface of slit and the porous medium on increasing the bias, an unexpected correlated response. The competition between the faster flow in the slit and slower motion of the particles in the surrounding porous medium induces stronger correlations at higher bias; as a result, a well-defined density profile emerges with higher density in the porous matrix away from the slit interface. The range of correlation and therefore the response increases on increasing the bias. Lowering the porosity to near the percolation threshold leads to the onset of oscillation in the density profile and broadening of the mobility profile, a distinct difference from the response at high porosity.

Bottom-up model of adsorption and transport in multiscale porous media

“…Our model therefore provides a theoretical framework for this empirical relation as the power law is in no way imposed. In contrast, we recall that Archie's law and its linear response to ∇P are valid for certain φ and P ranges only [55].…”