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We present porous electrode theory for capacitive deionization (CDI) withelectrodes containing nanoparticles that consist of a redox-activeintercalation material. A geometry of a desalination cell is considered whichconsists of two porous electrodes, two flow channels and an anion-exchangemembrane, and we use Nernst-Planck theory to describe ion transport in theaqueous phase in all these layers. A single-salt solution is considered, withunequal diffusion coefficients for anions and cations. Similar to previousmodels for CDI and electrodialysis, we solve the dynamic two-dimensionalequations by assuming that flow of water, and thus the advection of ions, iszero in the electrode, and in the flow channel only occurs in the directionalong the electrode and membrane. In all layers, diffusion and migration areonly considered in the direction perpendicular to the flow of water. Electronicas well as ionic transport limitations within the nanoparticles are neglected,and instead the Frumkin isotherm (or regular solution model) is used todescribe local chemical equilibrium of cations between the nanoparticles andthe adjacent electrolyte, as a function of the electrode potential. Our modeldescribes the dynamics of key parameters of the CDI process with intercalationelectrodes, such as effluent salt concentration, the distribution ofintercalated ions, cell voltage, and energy consumption.

Theory of water desalination with intercalation materials