Boundary Layer Analysis of Membraneless Electrochemical Cells

A mathematical theory is presented for the charging and discharging behavior of membraneless electrochemical cells that rely on slow diffusion in laminar flow to separate the half reactions. Ion transport is described by the Nernst-Planck equations for a flowing quasi-neutral electrolyte with heterogeneous Butler-Volmer kinetics. Analytical approximations for the current-voltage relation and the concentration and potential profiles are derived by boundary layer analysis (in the relevant limit of large Peclet numbers) and validated against finite-element numerical solutions. Both Poiseuille and plug flows are considered to describe channels of various geometries, with and without porous flow channels. The tradeoff between power density and reactant crossover and utilization is predicted analytically. The theory is applied to the membrane-less Hydrogen Bromine Laminar Flow Battery and found to accurately predict the experimental and simulated current-voltage data for different flow rates and reactant concentrations, during both charging and discharging. This establishes the utility of the theory to understand and optimize the performance of membrane-less electrochemical flow cells, which could also be extended to other fluidic architectures.