On the Modeling of Wave Phenomena in Pit Corrosion

Abstract The evolution of pit corrosion in a tank containing a biofuel solution is investigated through a phase-field model, consisting of the Allen-Cahn and Cahn-Hilliard equations. An hyperbolic quasilinear model of partial differential equations is derived on the basis of Rational Extended Thermodynamics, in order to describe some effects, such as the behavior of waves with finite propagation velocity. This model reduces to Allen Cahn and Cahn Hilliard system for small relaxation times. The evolution of discontinuity waves, a particular class of solutions, is analyzed to explore shock and simple wave formation, with a focus on their compatibility with pit corrosion kinetics.