Speaker
Description
We present corrosive-passivating models to describe the initiation of corrosion patterns on metal surfaces, particularly fuel tank bottoms. The classical Barkley model for excitable systems [1] has been also applied in the context of corrosion [2], modeling the interaction between corrosive and passivating species as a fast activator and a slow inhibitor, respectively. However, the original Barkley model relies on overly simplistic assumptions: the passivating species is considered diffusionless, and its reaction dynamics are restricted to linear growth and decay terms. To better capture the phenomenon of localized pitting corrosion, we propose some extensions to this model. First, we relax the diffusionless assumption by exploiting the dichotomy between different states of the passivating species occurring at a faster time scale. In the fast-reaction limit, this yields a novel model featuring a cross-diffusion term for the passivating species [3]. Second, the passivating species is assumed to follow a Leslie-Gower dynamics with a Holling-type II functional response. The resulting frameworks allow the emergence of both stationary and oscillatory corrosion patterns, enabling qualitative comparisons with experimental data. Numerical continuation, bifurcation and simulations in 1D and 2D domains complement our theoretical analysis.
Bibliography
[1] D. Barkley, A model for fast computer simulation in excitable media, Physica D 49, 61 (1991)
[2] B.C. Batista, E. Romanovskaia, V. Romanovski, M. Emmanuel, J.T. Burns, J. Ma, I.Z. Kiss, J.R. Scully, O. Steinbock, Morphogenic modeling of corrosion reveals complex effects of intermetallic particles, Adv. Sci. 11, 2404986 (2024)
[3] G. Consolo, G. Inferrera, E. Proverbio, C. Soresina, An extended corrosive-passivating model with cross-diffusion for the initiation of corrosion patterns, Physica D 483, 134986 (2025)
