A nonlinear phase-field model of corrosion with charging kinetics of electric double layer

Abstract

A nonlinear phase-field model is developed to simulate corrosion damage. The motion of the electrode$-$ electrolyte interface follows the usual kinetic rate theory for chemical reactions based on the Butler-Volmer equation. The model links the surface polarization variation associated with the charging kinetics of an electric double layer (EDL) to the mesoscale transport. The effects of the EDL are integrated as a boundary condition on the solution potential equation. The boundary condition controls the magnitude of the solution potential at the electrode-electrolyte interface. The ion concentration field outside the EDL is obtained by solving the electro-diffusion equation and Ohm's law for the solution potential. The model is validated against the classic benchmark pencil electrode test. The framework developed reproduces experimental measurements of both pit kinetics and transient current density response. The model enables more accurate information on corrosion damage, current density, and environmental response in terms of the distribution of electric potential and charged species. The sensitivity analysis for different properties of the EDL is performed to investigate their role in the electrochemical response of the system. Simulation results show that the properties of the EDL significantly influence the transport of ionic species in the electrolyte.

Figures (16)

• Figure 1: Schematic of equivalent circuit model and phase-field description of the metal and corrosive environment phases.
• Figure 2: Illustration of the experimental setup used in Ref. ERNST2002a (left) and the corresponding computational domain (right).
• Figure 3: Comparison between experimental measurements ERNST2002a, analytical solution SCHEINER2007, and phase-field predictions of (a) the evolution of pit depth and (b) current density as a function of immersion time.
• Figure 4: Equivalent circuit model parameters used in experimental studies (Dong et al. Dong2013, Krakowiak et al. KRAKOWIAK2005, Kovac et al. Kovac2012, Vogiatzis et al. Vogiatzis2016) and the present model. (a) Resistance proportionality constant $\chi$ and (b) half-time of capacitor charging $t_c$.
• Figure 5: Effect of the resistance proportionality constant $\chi$ on (a) the evolution of pit depth and (b) current density as a function of immersion time. The ECM parameter $t_c = 10$ s is kept constant.