Surface hardening and self-organized fractality through etching of random solids

When a finite volume of etching solution is in contact with a disordered so lid, complex dynamics of the solid-solution interface develop. If the etcha nt is consumed in the chemical reaction, the dynamics stop spontaneously on a self-similar fractal surface. As only the weakest sites are corroded, th e solid surface gets progressively harder and harder. At the same time, it becomes rougher and rougher uncovering the critical spatial correlations ty pical of percolation. From this, the chemical process reveals the latent pe rcolation criticality hidden in any random system. Recently, a simple minim al model was introduced by Sapoval et al. to describe this phenomenon. Thro ugh analytic and numerical study, we obtain a detailed description of the p rocess. The time evolution of the solution corroding power and of the distr ibution of resistance of surface Sites is studied in detail. This study exp lains the progressive hardening of the solid surface. Finally, this dynamic al model appears to belong to the universality class of gradient percolatio n.