Finite Volume model for diffusion- and activation-controlled pitting corrosion of stainless steel

Steel corrosion plays an adversary, but central role in different technological fields. Reasonable modeling of corrosion calls for a profound theoretical study of the underlying mechanisms. The present paper is concerned with mathematical modeling of (localized) pitting corrosion: We derive the mass conservation law of a dissolving body hosting a metal/solution interface which separates the solid metal electrode from the liquid electrolyte, and we complement the mass balance law by a thermally activated, potential-dependent electrochemical kinetics law for the dissolution reaction and by Fick’s law for ionic transport in the electrolyte solution. As long as the electrolyte solution adjacent to the electrode boundary does not reach its saturation level, the Arrhenius-type dissolution kinetics law governs the dissolution rate, and Fick’s law governs solely the concentration distribution in the electrolyte solution (activation-controlled corrosion mechanism). However, once the saturation level is reached at the electrode boundary, the pit depth evolution is governed by the diffusion of ions from the electrode boundary into the electrolyte-filled pit (diffusion-controlled corrosion mechanism). Corresponding mathematical solutions (time-dependent fields of concentrations) are obtained by means of the Finite Volume Method. For experimentally supported model input values (concerning dissolution activity, corrosion potential, transfer coefficient, metal charge number, ionic saturation concentration, and solid metal concentration), the influence of the overpotential on the corrosion characteristics (pit depth and shape evolution, current density, ionic concentrations in electrolyte) is shown by means of 1D and 2D simulations.