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Highlights • A two-dimensional model for the design of flow fields in VRFBs is reported. • Uniformity of vanadium ion distribution is evaluated by uniformity factors. • Pressure drop is accurately captured in interdigitated and serpentine flow fields. • Performance of several design of flow fields for a large cell is studied. Abstract In this work, we report a two-dimensional mathematical model for the design of flow fields in vanadium redox flow batteries (VRFBs). The model is validated by calculating the pressure drop, distribution uniformity of vanadium ions in an interdigitated flow field and a serpentine flow field for a 9-cm2 cell. The model is then used to simulate interdigitated and a series of parallel serpentine design of flow fields in a 410-cm2 cell. It is demonstrated that with an increase in the number of parallel serpentine channels, the pumping power decreases while the distribution of vanadium ions becomes less uniform. Among the design of flow fields studied in this work, the interdigitated design performs the lowest pumping power and the most uniform distributions of vanadium ions. [ABSTRACT FROM AUTHOR]

• A transient VRFB model with anion exchange membrane (AEM) is proposed. • AEM parameters are brought into the description of charge and mass transfer. • Current density in AEM is carried by both H+ and HSO 4 − ions. • Suggestion for optimizing AEM parameters to improve VRFB performance is given. Vanadium redox flow batteries (VRFBs) with anion exchange membranes (AEMs) exhibit a high columbic efficiency and slow capacity decay due to the reduced crossover rate of vanadium ions. Modeling of this promising type of flow battery is challenging because of the difficulty in the description of charge and mass transfer through AEMs. In this work, we propose a transient model for VRFBs with AEM, which incorporates the ion selective adsorption to overcome the inaccurate description of ion distributions in AEM, and improves the transport coefficients to avoid their changes with different electrolytes, thereby introducing AEM parameters such as porosity and fixed charges into the description of charge and mass transfer. It shows that the simulation results of ion selective adsorption are highly consistent with the experiment; the effects of AEM parameters on transport processes and battery performance are well captured. Interestingly, it is found that the current density in AEM is carried by both H+ and HSO 4 − ions, and the proportion of H+ ions is quite large. At high current densities, an increase in AEM porosity greatly improve the voltage efficiency while maintaining a high coulombic efficiency. Meanwhile, small capacity decay rate can be obtained by adjusting fixed concentration. [ABSTRACT FROM AUTHOR]