Chemical etching of disordered solids

This study has been inspired to some experimental results about the slow chemical etching of thin (almost 2d) aluminum films immerged in a finite volume of a corrosive solution. The experiments consisted in monitoring the evolution of the corrosion front. One observes that this evolution is very rapid at an early stage and then slow down up to stop in a static situation. In this state the chemical concentration of the etchant in the solution is significative and the final corrosion front is fractal up to a characteristic scale with fractal dimension D~1.33. Our theoretical study consisted in the mathematical and numerical analysis of a dynamical model for this chemical etching of thin films of a disordered solid by a finite volume of a corrosive solution [24][32]. The results of this model agree very well with both the dynamical evolution and the fractal geometrical properties of the final corrosion front observed in the experiments. Furthermore we have shown, through a random field theory approach to this dynamical model, that it belongs to the random percolation universality class and in particular to the one of gradient percolation [28][49]. Finally, we have used this model to study the statistics of the chemical fracture events of these systems. To this aim we have followed a combined approach of percolation theory and probability theory of extremal events finding a good theoretical prediction for the probability law of failure events [37].