Computational modeling of particle hydrodynamics and charging process for the flowable electrodes of carbon slurry

Slurry of activated carbon particles mixed with an aqueous electrolyte solution has been used as "flowable electrode" in a few recent electrochemical systems, e.g., electrochemical flow capacitors (EFCs) for energy storage, and flow-electrode capacitive deionization (FCDI) for water treatment. In these applications, the porous carbon particles with very large specific surface area adsorb ions from the electrolyte and meanwhile store electrical charges when a voltage source is added in the charging process. Under the flow condition, the motion of the particles and their mutual contact form a dynamically varying electrical network for the charge transport through the bulk material. We introduce a novel particle-based computational model using the Stokesian dynamics to simulate the hydrodynamic interaction of the carbon particles and the charge transport. An analogous electrical circuit model is developed by approximating the particles with many interconnected resistor-capacitor units, and the circuit's topology is temporally changing depending on the instantaneous particle configuration. The Stokesian model and the circuit model are solved simultaneously to study how the hydrodynamic interaction and cluster formation affect the charge transport process of the slurry. The presence of the stationary current collector can be included to incorporate the near-wall effects on particle mobility. In the simulation, we vary the particle concentration as well as the ratio of the particle charging time to the hydrodynamic interaction time. The results shows that the charge transport in the carbon slurry is enhanced by increasing the concentration of the particles and faster particle charging. In addition, cluster formation of the particles plays an important role for the electronic transport process. After scaling, the transient electrical current from the present study generally agrees with that from previous experimental and modeling studies.