Two-Dimensional Porous Electrode Model for Capacitive Deionization

Ion transport in porous conductive materials is of great importance in a variety of electrochemical systems including batteries and supercapacitors. We here analyze the coupling of flow and charge transport and charge capacitance in capacitive deionization (CDI). In CDI, a pair of porous carbon electrodes is employed to electrostatically retain and remove ionic species from aqueous solutions. We here develop and solve a novel unsteady two-dimensional model for capturing the ion adsorption/desorption dynamics in a flow-between CDI system. We use this model to study the complex, nonlinear coupling between electromigration, diffusion, and advection of ions. We also fabricated a laboratory-scale CDI cell which we use to measure the near-equilibrium, cumulative adsorbed salt, and electric charge as a function of applied external voltage. We use these integral measures to validate and calibrate this model. We further present a detailed computational study of the spatiotemporal adsorption/desorption dynamics under constant voltage and constant flow conditions. We show results for low (20 mM KCl) and relatively high (200 mM KCl) inlet ion concentrations and identify effects of ion starvation on desalination. We show that in both cases electromigrative transport eventually becomes negligible and diffusive ion transport reduces the desalination rate.