## 3 Results and Discussion
Figure 6 compares performance and limiting current distribution as a function of flow rate when the H\({}_{2}\) solution is not mass transport limited. Figure 6a shows V-I curves (discharging) at different flow rate values. Figure 6b-d show the corresponding distributions under limiting current conditions at the end of the polarization curves. For single cell studies in RFBs, a commonly accepted practice is the setting of flow factors to high values (\(\lambda\geq 5\)). The current density recorded at this condition can be found in Figure 6c. A consistent distribution reflects that at these conditions, the electrode is being fed with sufficient electrolytes. An increase in stoichiometry has been proposed as a viable way of improving the cell performance [18]. Upon testing, a twofold increment (V\({}_{\rm{B}2}\) = 30 mL min\({}^{-1}\), equivalent to \(\lambda\geq 10\) at 10 A) resulted in a 7% extension of the limiting current density, displaying still a consistently homogeneous distribution (Figure 6b). Such supply overflows can be reasonable at the lab-scale level, but lead to considerable energy waste in the upscaling stage. It is thus interesting to investigate what is the minimum possible rate that reliably enables a satisfactory performance. The flow rate was therefore adjusted, limiting it below the original value (V\({}_{\rm{B}2}\) = 8 mL min\({}^{-1}\)). The limit in current was slightly shifted (3.8%) and the current density remained mostly unaffected. The limiting flow rate was found at V\({}_{\rm{B}2}\) = 3 mL min\({}^{-1}\), equivalent to \(\lambda\cong 1.5\) at 8 A; at this point it is possible to identify a steep shift in the graph (Figure 6a) as well as a current distribution that follows the direction of the electrolyte, with high currents at the cell inlet (bottom) that gradually decrease towards the outlet (top). This effect can be explained as a mass transport limitation, since the electrolyte utilization at the currents applied is relatively high (a cell with 50% SOC inlet, operating at 350 mA/cm\({}^{2}\) has a SOC of 75% at the outlet). Figure 5: Current density distribution at limiting conditions for V\({}_{\rm{H2}}\) = 65 mL min\({}^{-1}\) with reversed electrolyte direction (from right to left). The same effect was investigated in the charge direction. Figure 7a shows V-I curves (charging) at different flow rate values. Figure 7b-d show the corresponding distributions under limiting current conditions at the end of the polarization curves. The mass transport limitation induced by concentration changes from inlet to outlet can again be identified, but this time the maximum limiting current density reached at overflow conditions (\(V_{\text{Br2}}=30\) mL min\({}^{-1}\)) was 10% lower compared to the one obtained in the discharge direction, suggesting that additional processes take place during charging. The conductivity of the electrolytes depends primarily on the high proton concentration. As the cell charges, Br\({}^{-}\) is converted to Br\({}_{2}\) and protons are consumed in the production of H\({}_{2}\). This decreasing proton concentration is directly related to the electrolyte conductivity [12]. Figure 6: (**a**) Polarization curves (discharge) for different catholyte flow rates and corresponding current distributions at limiting conditions for (**b**) \(V_{\text{Br2}}=30\) mL min\({}^{-1}\), (**c**) \(V_{\text{Br2}}=12\) mL min\({}^{-1}\), (**d**) \(V_{\text{Br2}}=8\) mL min\({}^{-1}\), and (**e**) \(V_{\text{Br2}}=3\) mL min\({}^{-1}\). The supply of H\({}_{2}\) was fixed to \(V_{\text{H2}}=170\) mL min\({}^{-1}\).