Invasion of a sticky random solid: Self-established potential gradient, phase separation, and criticality

Abstract

Invasion of a sticky random solid by an aqueous solution is modeled through a chemical reaction. In this reaction, the solid elements dissolve in the solution and redeposit back on the rough interface. A self-established potential gradient (SEPG) in the binding energy of the solid is developed spontaneously and the system gets phase separated into “hard” and “soft” solids. The solution profile is found drifted slowly into the solid by the SEPG with a constant velocity. The system tunes itself to the percolation threshold in the steady state. In the steady state, the system is found consisting of finite clusters of solution molecules followed by a path of redeposited solid as an invasion percolation cluster. A diffusive growth of the interface and the solution inside the solid is found to occur. The nonequilibrium steady state of this dynamical system is found critical and characterized by a power-law distribution of cluster size with an exponent $\approx -2$.