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Mathematical analysis of a thermodynamically consistent reduced model for iron corrosion

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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.

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Acknowledgements

The authors warmly thank Christian Bataillon for his kind feedback on the model. This Project has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No 847593 (WP DONUT), and was further supported by Labex CEMPI (ANR-11-LABX-0007-01). C. Cancès also acknowledges support from the COMODO Project (ANR-19-CE46-0002) and C. Chainais-Hillairet from the MOHYCON Project (ANR-17-CE40-0027-01). J. Venel warmly thanks the Inria research center of the University of Lille for its hospitality.

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Authors and Affiliations

  1. Inria, Univ. Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé, 59000, Lille, France

    Clément Cancès

  2. Univ. Lille, CNRS, Inria, UMR 8524 - Laboratoire Paul Painlevé, 59000, Lille, France

    Claire Chainais-Hillairet & Benoît Merlet

  3. Department of Mathematics, Università di Salerno, 84084, Fisciano, SA, Italy

    Federica Raimondi

  4. CERAMATHS, FR CNRS 2037, Univ. Polytechnique Hauts-de-France, 59313, Valenciennes, France

    Juliette Venel

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  1. Clément Cancès
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  2. Claire Chainais-Hillairet
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  4. Federica Raimondi
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Correspondence to Clément Cancès.

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Cancès, C., Chainais-Hillairet, C., Merlet, B. et al. Mathematical analysis of a thermodynamically consistent reduced model for iron corrosion. Z. Angew. Math. Phys. 74, 96 (2023). https://doi.org/10.1007/s00033-023-01970-6

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  • DOI: https://doi.org/10.1007/s00033-023-01970-6

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