On modeling of corrosion and electrochemical processes: the impact of the governing equations on the potential, current density, and species distributions

The advancement of computational power and the development of commercial software that efficiently solves complex sets of partial differential equations have greatly benefited the fields of corrosion science and battery development due to the intricate sets of PDE and nonlinear boundary conditions necessary to solve electrochemical problems. Guidance on the choice of governing equations and methods to acquire adequate boundary conditions is needed to develop adequate models as the use of these finite element models becomes more popular and accessible. Different governing equations can be used to solve for the distribution of potential, current density, and dissolved species in an electrolyte. The Nernst–Planck–Poisson equations are the most general approach, but they are numerically complex and bring with them a substantial computational cost. Reduced-order models offer options in which different assumptions allow more rapid computational solutions.

In this work, the loss in accuracy of the reduced-order models is assessed by the comparison of the results obtained by these reduced-order models to those from the most general model (i.e., using the Nernst-Planck-Poisson as the governing equation) for a wide range of supporting electrolyte concentrations. In addition, a new method - a modified Laplace approach - in which the electrolyte conductivity is calculated at each position and time step, is presented. The models were performed using the governing equations available on COMSOL Multiphysics®. For electrolyte concentrations typical of most environments of interest in corrosion and electrochemistry, the reduced-order models saved substantial computational time without significant loss in accuracy. The most reduced-order modeling approach performs poorly in low supporting electrolyte to electrochemically reactive species (SER) ratios. The modified Laplace approach improved the solution, but the errors can still be significant in low SER ratios due to the absence of the diffusion potential term in the calculations. The relative impact of the migration and diffusion potential terms to solve for the potential in the electrolyte is discussed.