Dynamics of electrochemical cells in the thin-Debye-layer limit

Abstract

We analyse ion transport in a prototypical electrochemical cell consisting of a binary asymmetric electrolyte confined between planar electrodes that sustain Faradaic cation reactions described by Butler–Volmer kinetics. Ion transport is governed by the Poisson–Nernst–Planck (PNP) equations, which are analysed in the thin-Debye-layer limit using matched asymptotic expansions. This procedure replaces explicit resolution of the interfacial double layers with effective boundary conditions, yielding a closed set of nonlinear equations for the bulk ion concentrations and electrostatic potential under a time-dependent current, from which the cell voltage is obtained. Comparisons with full numerical PNP simulations show excellent agreement across a wide range of regimes. For suddenly applied DC currents, the model captures both diffusion- and kinetics-limited responses, including large overpotentials and the influence of ionic diffusivity mismatch on concentration polarization. Under sinusoidal forcing, it reproduces linear behaviour at small amplitudes and nonlinear dynamics at larger amplitudes, including waveform distortion and higher harmonics. Deviations are limited to short times associated with rapid double-layer charging, demonstrating that the macroscale model provides a compact, predictive alternative to direct PNP simulations while retaining the essential physics of time-dependent electrochemical processes.