Analytical modeling for redox flow battery design

Deeper market penetration of redox flow batteries requires optimization of the cell performance. Though important for performance optimization, detailed analytical solutions have not been developed for coupled electrolyte flow, mass and charge transport of ions, and reaction kinetics within redox flow batteries. To this end, this work presents analytical solutions to spatial variations of active species concentration and over-potential based on advection-diffusion transport for ions and Bulter-Volmer model for interface reaction kinetics. The solutions are validated with results from a finite element model and a calibrated zero-dimensional model. These solutions are then applied to investigate the relationship between over-potential and state of charge, current density, flow velocity, standard reaction rate constant, diffusivity, total active species concentration, and electrode structure. Explicit formulas are identified for minimum activation over-potential and limiting current density as well as their dependence on electrolyte properties, operation conditions, and electrode structure. With our new mathematical formulas, this work provides a theoretical framework for flow battery design.