Critical fluctuations and self-organized fractality in chemical reactions: Spontaneous gradient percolation in the etching of random solids

A simple model of the chemical attack of random solids by etching solutions of finite volumes has been studied in two dimensions. The etching species are consumed in the chemical reaction and the etchant strength at any time is calculated from the varying concentration of the solution. The occupation probability of solid surface sites by the etching liquid varies in time and space along with the evolution of the process. There is then a spontaneously established gradient of the chemical potential at the moving interface. The criticality of the system has been identified by the maximum etching speed and extremal fluctuations of the length of the liquid–solid interface. This occurs when the etching strength corresponds to the percolation threshold. This is the first example of the existence of critical fluctuations in the framework of chemical reactions. The results suggest that the system belongs to the same universality class as gradient percolation. The fact that the rate of interface production is apparently maximum at criticality suggests the possible existence of an underlying variational principle linking extremal surfaces to percolation.