Diffusion, interactions and universal behavior in a corrosion growth model

The growth of a layer generated by the corrosion of a metal is investigated with a simple cellular automaton model defined at a mesoscopic scale. As the metal is corroded the corrosion products precipitate into the layer at both the metal/layer and layer/solution interfaces. There is a mass redistribution in the layer between the two interfaces simulated by a random walk that mimics a diffusion process. Because the concentration of walkers may be large a steric interaction between them is introduced by the simple exclusion rule. This steric effect reduces both the efficiency of the diffusion and the corrosion rate. The time evolution of the layer thickness and the walker distribution across the layer are investigated. The distribution of walkers shows the existence of two regimes that we cannot predict from the analysis of the mean front positions only. Beyond a given time, the growth reaches a saturation regime in which the initial chemical reaction rates become irrelevant, then a universal behavior determined by diffusion is observed. The distribution of walkers presents particular features as the existence of a fixed concentration at the initial metal/solution plane position. In the saturation regime, the simulations are in agreement with the theoretical predictions of Mott and Cabrera.