Modeling the transient effects of pore-scale convection and redox reactions in the pseudo-steady limit

We introduce theory to study the convection of active species with redox reactions at solid/solution interfaces within porous media, motivated by applications in energy storage devices where cyclic charge and discharge with recirculating flow requires the consideration of transient mass transfer. We show that under pseudo-steady conditions the coupled mass transfer problem involving redox of active species can be simplified to a linear, time-independent auxiliary problem. The proposed model is then solved numerically for porous media containing periodically spaced cylinders in crossflow. The results show three transport mechanisms depending on Péclet number Pe. Interactions between solid surfaces induced either by diffusion or advection produce spatial variation of surface flux. With Pe increasing from unity, advection initially causes diffusive flux to redistribute, causing a rise in Sherwood number Sh (non-dimensional mass transfer coefficient). The locations of flux maxima coincide with those of vorticity and strain rate for Pe above a certain “saturation” value. The variations of Sh with porosity and Pe are interpreted using a regime map that is defined based on the spatial variance of solute concentration. The auxiliary problem introduced provides a framework to predict mass transfer coefficients for arbitrary microstructures to guide the design of high-performance electrodes.