(536b) Dynamics of Electrochemical Cells in the Thin-Debye-Layer Limit

Traditionally, electrochemical cells have been modeled using equivalent circuits, which precludes an understanding of the micro-scale ion dynamics within the cell. Here, we develop a macro-scale electrokinetic model in the thin-Debye-layer limit through a perturbation analysis, starting from the electrokinetic equations, i.e. Poisson and Nernst-Planck equations for a binary asymmetric electrolyte, and a single electron transfer Faradaic reaction of cations following Butler-Volmer kinetics on the electrodes. We obtain an analytical expression for the voltage and electric field as a function of a general time-dependent input current. We validate our macro-scale model for the case of a steady current, recovering the results from Bazant et al., 2005, Siam J. Appl. Math, for a symmetric electrolyte. For the case of an input AC current, we find a rectified electric field caused by the reactions on the electrodes, even in the case of electrolytes with equal anion and cation diffusivities. Lastly, the nonlinear impedance response of the cell to an ac voltage shows a sensitivity to charge-transfer asymmetry, not present in the linear response when a small current is used. The results presented here further advance the theoretical understanding of electrolyte transport in electrochemical devices.