Range of Validity of a Simplified Model for Diffuse Charge Dynamics


The modelling of electrochemical processes often requires the solution of the Poisson-Nernst-Planck (PNP) equations. In complex geometries, such as porous electrodes, that is challenging due to the presence of disparate length scales, ranging from the Debye screening length (∼nm) to the device length scale (∼cm). To overcome this difficulty, one often assumes that the electric double layer (EDL) is at quasi-equilibrium to construct a simplified model that accounts for ion diffusion in the electro-neutral bulk of the electrolyte while replacing the EDLs with appropriate boundary conditions. Various researchers have demonstrated that such an approach is valid in the asymptotic limit of a thin EDL and moderate electrode potentials. In this note, we explore the range of validity of this approximation by considering a one-dimensional electrolytic cell with blocking electrodes subjected to a step change and time-periodic alternations in the electrodes’ potentials by calculating the errors associated with the approximate approach as functions of the EDL thickness and electric field frequency and intensity. Additionally, we delineate numerical instabilities associated with the numerical solutions of the bulk equations with the nonlinear boundary condition peculiar to this problem.