LAUSR

Abstract Microfluidic-based membraneless redox flow batteries have been recently proposed and tested with the aim of removing one of the most expensive and problematic components of the system, the ion-exchange membrane. In this promising design, the electrolytes are allowed to flow parallel to each other along microchannels, where they remain separated thanks to the laminar flow conditions prevailing at sub-millimeter scales, which prevent the convective mixing of both streams. The lack of membrane enhances proton transfer and simplifies overall system design at the expense of larger crossover rates of vanadium ions. The aim of this work is to provide estimates for the crossover rates induced by the combined action of active species diffusion and homogeneous self-discharge reactions. As the rate of these reactions is still uncertain, two limiting cases are addressed: infinitely slow (frozen chemistry) and infinitely fast (chemical equilibrium) reactions. These two limits provide lower and upper bounds for the crossover rates in microfluidic vanadium redox flow batteries, which can be conveniently expressed in terms of analytical or semi-analytical expressions. In summary, the analysis presented herein provides design guidelines to evaluate the capacity fade resulting from the combined effect of vanadium cross-over and self-discharge reactions in these emerging systems.