8. Transport in Liquid-Phase Electrochemical Devices

Transport of reactants and products in liquid-fed electrochemical cells is critical in terms of reactant utilization, concentration polarizations, and coulombic efficiencies. Design of electrochemical flow cells can benefit from adequately detailed models that capture the locally variable impact of reactant depletion and product build-up on electrochemical reactions throughout the cell. This chapter illustrates the importance of transport modeling by presenting a finite-volume, two-dimensional (2-D) model of a liquid-phase electrochemical cell with simple cell geometry, but complex multistep chemistry at each electrode incorporating parasitic reactions and/or mixed potentials. The modeled cell involves two half-cell reactions, borohydride (\(\mathrm{BH_{4}^{-}}\)) oxidation and hydrogen peroxide (H₂O₂) reduction, in planar flow channels with electrodes separated by flowing liquid-phase electrolytes and an ion-exchange membrane. This generic cell topology is representative of many fuel cells and flow batteries. The finite-volume model solves for conservation of mass, momentum, species, and charge in both the cathode and anode flow channels for ideal, dilute, and concentrated electrolytes. The model couples the flows to complex boundary conditions at the electrochemically active electrode surfaces and the selective ion-exchange membrane. Model results show that the balance of advection, diffusion, and migration in the liquid electrolytes results in complex profiles that predict boundary layer build-up and significant advection perpendicular to the flow path. The direct borohydride-hydrogen peroxide fuel cell transport model, used to illustrate these concepts, shows how liquid-phase transport limits conversion and dictates cell voltages within the context of the competing reactions at the two electrodes. The chapter ends by demonstrating how such a model can be implemented in design studies to explore strategies for improving practical cell performance.