Mathematical Modelingof Iron Oxidation in an AqueousEnvironment: When Kinetics Meets Thermodynamics

Abstract We propose a one-dimensional model for the evolution at the mesoscopic scale of a magnetite/maghemite oxide layer at the surface of iron metal set in an aqueous environment. The model takes into account the convection and diffusion of three charge carriers─iron cations, electrons in the conduction band, and oxygen vacancies, convection being induced by a self-consistent electric field solving a Poisson equation. The geometry of the oxide evolves along with time due to iron oxidation and to oxide dissolution. New kinetic laws for oxidation and dissolution are derived based on probabilistic arguments at the subnanometric scale. We then show that our model is compatible with the second principle of thermodynamics, in the sense that entropy is produced by all the physical phenomena encoded in the model, providing control over the evolution of the Helmholtz free energy. Numerical simulations illustrate the behavior of our model, showing good agreement with the literature. Moreover, a detailed analysis of the different contributions to the entropy production is proposed, allowing for a comparison of the degree of irreversibility of each process. It shows in particular that several processes can significantly contribute to the entropy production, showing limitations for the concept of a single rate-limiting step.