Impact of Faradaic Reactions on the Charging Dynamics of the Electrical Double Layers

Electrical double layers (EDLs) and faradaic reactions are commonly observed in electrochemical systems such as batteries, fuel cells and hybrid capacitors. However, the impact of faradaic reactions on the structure of EDLs is typically neglected, making it harder to accurately predict the concentration, charge, and current profiles. Here, we propose a time-dependent perturbation expansion model in the thin EDL limit that accounts for a constant faradaic flux at the Stern layer/diffuse layer boundary. Our analysis yields two main conclusions: (i) Faradaic reactions impact the definition of the Boltzmann distribution, and thus the widely utilized Gouy-Chapman-Stern model needs to be appropriately modified; (ii) The current due to double layer charging dominates at shorter time scales whereas the current from the faradaic reaction dominates at longer timescales. We validate our perturbation expansion model through direct numerical simulations of the Poisson-Nernst-Planck equations. Overall, our analysis enables us to connect the micro-scale transport problem near the electrical double layer with the macro-scale bulk transport problem and allows us to qualitatively predict the current evolution for electrochemical systems.