The uniform electrodeposition of certain materials, such as Li metal, remains elusive because the mechanisms controlling growth instability are not fully understood. To determine the conditions that lead to either stable or unstable deposition, we develop a phase-field model for the growth of multiple deposits in a binary electrolyte and examine the behavior as the kinetic parameters are varied. We find that the second Damköhler number, defined as the ratio between the reaction and the mass transfer fluxes, is an indicator of deposition instability. Our results suggest that controlling reaction kinetics and initial roughness are essential in achieving stable electrodeposition.
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