Dr. Federica Raimondi “A thermodynamically consistent model for iron corrosion”

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.