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Techniques for interpreting electrochemical impedance spectroscopy of different flowing slurry electrodes configurations are presented based upon models developed for macrohomogeneous porous electrodes. These models are discussed with regards to three different slurry systems; particles in deionized water, in supporting electrolyte without redox active species (akin to electrochemical flow capacitors), and in electrolytes supporting aqueous redox couples (akin to redox flow batteries). Through investigating each of these systems, the individual properties of a slurry can be determined. It was found that traditional overpotential descriptions, (ohmic, activation, and mass transfer) were insufficient to fully describe the impedance and polarization of the slurry electrodes. An overpotential due to the distributed current distribution in the slurry electrode was considered in the frequency range of activation overpotentials that depends on the exchange current density and the ratio of the electronic and ionic conductivities. In slurry electrodes made with multi-wall carbon nanotube particles supporting the ferric/ferrous redox couple, the distributed overpotential was found to be about the same order of magnitude as the activation overpotential and the total voltaic efficiency was over 80% at 200 mA/cm 2 .

Electrochemical flow capacitors (EFCs) for grid-scale energy storage are a new technology that is beginning to receive interest. Prediction of the expected performance of such systems is important as modeling can be a useful avenue in the search for design improvements. Models based off of circuit analogues exist to predict EFC performance, but these suffer from deficiencies (e.g. a multitude of fitting constants that are required and the ability to analyze only one spatial direction at a time). In this paper mathematical models based off of three-dimensional macroscopic balances (similar to models for porous electrodes) are reported. Unlike existing three-dimensional porous electrode-based approaches for modeling slurry electrodes, advection (i.e., transport associated with bulk fluid motion) of the overpotential is included in order to account for the surface charge at the interface between flowing particles and the electrolyte. Doing so leads to the presence of overpotential boundary layers that control the performance of EFCs. These models were used to predict the charging behavior of an EFC under both flowing and non-flowing conditions. Agreement with experimental data was good, including proper prediction of the steady-state current that is achieved during charging of a flowing EFC. Electrochemical flow capacitors are a recently introduced technology that has gained considerable interest for grid-scale energy applications.1,2 These devices work by charging and discharging the double layers that exist at the interfaces between immersed electronically conducting particles and the electrolyte solution in a flowable slurry electrode. After having their surfaces charged, these particles are then subsequently stored in external tanks where they are available to be pumped back through the cell during discharge. External storage of the charged slurry allows for decoupling of power and energy -tanks can be independently scaled to be as large as desired for a particular application.A schematic of an EFC is shown in Figure 1. The design consists of two half cells and their respective positive and negative current collectors. A membrane between the two half-cells prevents electronic charge transfer between the respective negative and positive halves but permits the exchange of ionic current. During charging, slurry is continuously pumped from separate tanks of uncharged particles through the positive and negative half cells. As the separate slurry streams flow through the cells, the double layer capacitances that exist at the interfaces between the particles and the solution are charged. The now-charged slurry particles are then directed into storage tanks where the charge can be maintained for later use during discharge.In general, EFCs have so far been limited to low current density operations (<10 mA/cm 2 ); design improvements must therefore be sought. This paper reports on a mathematical model with the goal of achieving design improvements. So far, mathematical models for electrochemical flow capacitors have been...

Electrochemical flow capacitors (EFCs) are a recently developed energy storage technology. One of the principal performance metrics of an EFC is the steady-state electrical current density that it can accept or deliver. Numerical models exist to predict this performance for specific cases, but here we present a study of how the current varies with respect to the applied cell voltage, flow rate, cell dimensions, and slurry properties using scaling laws. The scaling relationships are confirmed by numerical simulations and then subsequently by comparison to results from symmetric cell EFC experiments. This modeling approach permits the delimitation of three distinct operational regimes dependent on the values of two nondimensional combinations of the pertinent variables (specifically, a capacitive Graetz number and a conductivity ratio). Lastly, the models and nondimensional numbers are used to provide design guidance in terms of criteria for proper EFC operation. The electrochemical flow capacitor is a new energy storage technology that has gained interest for grid-scale applications.1-4 EFCs store energy by charging the double layers that exist at the interfaces between the particles and an electrolyte solution in a flowable slurry electrode. The slurry particles with their charged surfaces are then subsequently transferred to external tanks for energy storage. The stored energy can be recovered by pumping these particles back through the cell during discharge. As is the case for flow batteries, external storage of the charged slurry allows for decoupling of power and energy capacity.A schematic of a four-tank EFC is shown in Figure 1. This design consists of two half cells separated by a membrane. The membrane prevents electronic charge transfer between the negative and positive half-cells but permits the exchange of ions. During charging, slurry is pumped from tanks of uncharged particles through the cell in order to be charged; after passing through the cell this slurry is then stored in a separate set of tanks for charged particles.For this four-tank implementation, discharge then requires reversal of the pumps to redirect the charged particles back into the cell. This approach requires the double layer capacity of the entire slurry flow to be charged as fully as possible upon leaving the cell (i.e. the slurry needs to be fully utilized such that all of the available surfaces are charged to half of the voltage applied across the entire EFC cell). This four-tank approach allows immediate extraction of energy at the charging potential as all of the stored slurry at any point in time is fully charged. However, the necessity of fully charging the entire slurry stream can place severe restrictions on the maximum achievable current density. An alternative two-tank approach, 5 foregoes the separate storage tanks for the charged and uncharged slurries and instead operates in a continuous mode. This approach is similar to the charging/discharging of conventional (non-flowing) capacitors. When operating in this mode la...

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