An extended corrosive-passivating model with cross-diffusion for the initiation of corrosion patterns

An extended version of the Barkley model is proposed to elucidate the process of initiation of localized corrosion patterns observed on metal surfaces, in particular on the bottom of fuel tanks. The model describes the interaction between a fast activator variable, the surface concentration of the corrosive species, and a slow inhibitor, the surface concentration of the passivating one, which was assumed to be diffusionless in its original formulation. By exploiting the dichotomy between different states of the passivating species occurring at a faster time scale, the fast-reaction limit yields a novel corrosive-passivating model including a cross-diffusion term for the passivating species. When the cross-diffusion coefficient exceeds a given threshold, the cross-diffusion term so deduced allows the destabilization of the homogeneous steady-state to spatial disturbances, triggering corrosion Turing patterns. The study is complemented by numerical investigations carried out over 1D and 2D domains. These are used to corroborate analytical predictions and to provide additional insights into the morphology of the emerging corrosion patterns. Indeed, by means of a suitable choice of model parameters and initial conditions, a qualitative agreement with some experimental data showing the presence of isolated or merged corrosion “pits” is achieved. Results suggest that the extended model proposed here might be useful to improve the predictive tools currently employed in the maintenance strategies of metal surfaces.