Chemical etching of a disordered solid: from experiments to field theory

We present a two-dimensional theoretical model for the slow chemical corrosion of a thin film of a disordered solid by suitable etching solutions. This model explains different experimental results showing that the corrosion stops spontaneously in a situation in which the concentration of the etchant is still finite while the corrosion surface develops clear fractal features. We show that these properties are strictly related to the percolation theory, and in particular to its behavior around the critical point. This task is accomplished both by a direct analysis in terms of a self-organized version of the gradient percolation model and by field theoretical arguments.