Mathematical analysis of a thermodynamically consistent reduced model for iron corrosion

TL;DR

This paper presents a thermodynamically consistent reduced model for iron corrosion, establishing global existence of solutions and providing numerical comparisons with existing models.

Contribution

It introduces a modified corrosion model that aligns with thermodynamic principles and proves global existence without parameter restrictions.

Findings

Global in time existence of solutions proven

Model aligns with thermodynamic principles

Numerical comparisons highlight differences with previous models

Abstract

We are interested in a reduced model for corrosion of iron, in which ferric cations and electrons evolve in a fixed oxide layer subject to a self-consistent electrostatic potential. Reactions at the boundaries are modeled thanks to Butler-Volmer formulas, whereas the boundary conditions on the electrostatic potential model capacitors located at the interfaces between the materials. Our model takes inspiration in existing papers, to which we bring slight modifications in order to make it consistent with thermodynamics and its second principle. Building on a free energy estimate, we establish the global in time existence of a solution to the problem without any restriction on the physical parameters, in opposition to previous works. The proof further relies on uniform estimates on the chemical potentials that are obtained thanks to Moser iterations. Numerical illustrations are finally provided to highlight the similarities and the differences between our new model and the one previously studied in the literature.