Analysis of the Reactive CO 2 Surface Flux in Electrocatalytic Aqueous Flow Reactors
We study how the mass transfer of a chemical species in shear flow is suppressed by the production of a second species that partially reacts away the first species. The second species is produced at the surface with the first species as a reactant. Our work is directly motivated by electrochemical CO 2 reduction in aqueous flow reactors, where OH– molecules generated by the CO evolution reaction react away CO 2 molecules, ultimately inhibiting the mass transfer of CO 2 to the cathode surface. We derive a simple approximation of the Sherwood number, a dimensionless measure of the mass flux into the surface, as a function of the Péclet number, surface Damköhler number, and bulk Damköhler number, and we compare our approximation to numerical solutions of the governing equations. We find that in the diffusion-limited regime, the Sherwood number is well described by the classical Graetz-Lévêque result reduced by a reaction factor due to the competing bulk reaction; with the stoichiometry relevant to electrochemical CO 2 reduction, this reaction factor is 1/2. While the model problem we solve provides insight into how OH– production affects CO 2 mass transfer, experimental systems often involve more complex chemistry. We thus also show how a common buffered electrolyte, KHCO 3 , affects our results.