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When a finite volume of etching solution is in contact with a disordered solid, complex dynamics of the solid-solution interface develop. If the etchant is consumed in the chemical reaction, the dynamics stop spontaneously on a self-similar fractal surface. As only the weakest sites are corroded, the solid surface gets progressively harder and harder. At the same time, it becomes rougher and rougher uncovering the critical spatial correlations typical of percolation. From this, the chemical process reveals the latent percolation criticality hidden in any random system. Recently, a simple minimal model was introduced by Sapoval et al. to describe this phenomenon. Through analytic and numerical study, we obtain a detailed description of the process. The time evolution of the solution corroding power and of the distribution of resistance of surface sites is studied in detail. This study explains the progressive hardening of the solid surface. Finally, this dynamical model appears to belong to the universality class of gradient percolation.

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