Charging of flowable electrodes with bimodal distribution of carbon particles

Carbon slurries as "flowable electrodes" have been used recently in a few electrochemical systems, e.g., electrochemical flow capacitors (EFCs) for energy storage and flow-electrode capacitive deionization (FCDI) for water treatment. These slurries typically have three parts: activated carbon particles, a conductive additive such as carbon black, and an aqueous electrolyte solution. Previously, a particle-based computational model that employs Stokesian dynamics was developed to describe the particle motion and interaction, while simultaneously solving for the charge transfer inside an electrical network of moving particles. In this work, we develop a unified expression of the dynamically varying electrical network. Furthermore, we incorporate a group of smaller particles as the conductive additive, whose effect on the charge transfer of the slurry is studied. The results suggest that at lower concentrations, the small particles may enhance charge transfer by filling interstitial spaces and bridging contacts of large particles; however, at higher concentrations, the benefits are not as clear since direct contacts of the large particles play the dominant role in charge transfer.