Ion transport in thin cell electrodeposition: modelling three-ion electrolytes in dense branched morphology under constant voltage and current conditions

Electrochemical deposition (ECD) and spatially coupled bipolar electrochemistry (SCBE) experiments in thin-layer cells are known to produce complex ion transport patterns concomitantly with the growth of dendrite-like structures. Here we present a macroscopic model of ECD and SCBE with a three-ion electrolyte in conditions of dense branched morphology. The model describes ion transport and deposit growth through the one-dimensional Nernst–Planck equations for ion transport, the Poisson equation for the electric field and, for ECD, a growth law for deposit evolution. We present numerical simulations for typical electrochemical deposition experiments: dense branched morphology in ECD and the incubation period in SCBE. In ECD the model predicts cation, anion and proton concentration profiles, electric field variations and deposit growth speed, that are in qualitative agreement with experiments; the predicted evolution and collision of the deposit and proton fronts reveal a time scaling close to those observed in experiments. In SCBE, the model predicts that the inverse of the incubation time scales linearly with the applied voltage. Such behaviour was observed in experiments.