Modeling of flowable slurry electrodes with combined faradaic and nonfaradaic currents

Flowable slurry electrodes have received increased interest recently for use in electrochemical energy storage and water treatment systems. In an electrochemical cell these flowing electrodes can simultaneously support both faradaic currents (through reactions occurring at the slurry/solution interface) and nonfaradaic currents (through charging of the double layer capacitance of each slurry particle as it passes through the cell). In this paper, a model based on a three-dimensional set of macrohomogeneous equations that combines the effects of both types of current is developed. The model equations are applicable to flow battery, electrochemical flow capacitor, and flow-electrode capacitive deionization systems. Using this modeling approach, the performance of slurry electrodes in symmetric electrochemical cells is examined. Scaling techniques are applied to the equations in order to permit the prediction of the steady-state current that can be achieved from a slurry electrode as a function of cell dimensions, slurry properties, flow rate, reaction kinetics, and the potential applied across the cell. Depending on the values of four dimensionless combinations of the pertinent variables (the capacitive Graetz number, the nondimensional exchange current density, the conductivity ratio, and the flow behavior index) slurry electrodes are then shown to operate in one of four distinct operational regimes. Lastly, the variation of the physical extent of the reaction zone (i.e. electroactive zone extension) with respect to the relative magnitude of advection is characterized.