Electrodialysis (ED) is a well-established water desalination technology, applied mainly to brackish water desalination. In ED, desalination is driven by an applied electric field, which results in salt ion electromigration through alternating cation and anion exchange membranes. Recently, classical ED cells have been modified by driving them via spontaneous redox reactions occurring at the electrodes. Such a cell is distinct from classical ED as it does not require electricity, but rather requires solely chemical energy input in the form of redox active chemicals, and outputs both desalted water and electricity simultaneously. We here extend ED theory in order to capture a cell driven by spontaneous redox half-reactions occurring at electrode surfaces. In the cell considered, an AEM and CEM are separated by a channel with flowing feedwater. On the opposite side of the AEM is an anode and flowing anolyte, while a cathode and flowing catholyte are on the opposite side of the CEM. To capture cell behavior and performance at steady state, we solve a set of equations comprising the species' NernstePlanck equation and electroneutrality, which are coupled to activation and concentration overpotential losses at planar electrodes. Our model captures the crossover of coion species through membranes as well as electric potential, counterion, and coion concentration variations within the membranes. We elucidate key predicted phenomena, including that the cell current is limited by reactant starvation at the cathode, and that current and certain ion fluxes scale as x(-1/3), where x is the coordinate in the direction of flow. Our model predicts that at steady state, the cell can achieve an order of magnitude reduction in the NaCl concentration of a 500mM feed, while generating up to similar to 42 mW/cm(2) electrical power density. Further, we determined that the main limitation of the cell as designed is a relatively high coion crossover flux through the membranes. (C) 2019 Elsevier Ltd. All rights reserved.