A phase-field model for electrode reactions with Butler–Volmer kinetics

A novel phase-field model for electrochemical processes is formulated, in which the Butler–Volmer kinetics at the electrode/electrolyte interface is taken into account. Using the model, the kinetics and morphology of the electrode/electrolyte interface during an electrode reaction have been investigated. The numerical result satisfies the Nernst equation and Gibbs–Thomson effect at planar and curved interfaces in the equilibrium system, respectively. In addition, the Butler–Volmer relation between the growth velocity of the electrode/electrolyte interface and the overpotential during the electrode reaction is confirmed. Moreover, the morphology of the electrode/electrolyte interface is examined as a function of the applied voltage and reaction coefficient. The tip radius of the electrodeposit is proportional to the inverse of the square root of the growth velocity, which agrees with the dendrite growth theory for the solidification process.