A phase-field model of electrochemical interface dynamics is developed to study cathode shape and topology change in transport-limited electrolysis in two and three dimensions under conditions of rapid charge redistribution. A case study for the binary model is carried out for an Fe–FeO system. Stability behavior of the model is in good agreement with linear stability theory for small amplitude sinusoidal perturbation in electrodeposition. When there is no convection, a high electric field and low surface tension cause the cathode interface to be unstable, leading to growth of dendrites which break into powders. When the electrodes and electrolyte are low-viscosity fluids, flow provides an additional mechanism for stabilizing the interface. A new stability criterion for this liquid situation based on the Schmidt number is derived from dimensional analysis and model results. For an unstable cathode interface, a streamer morphology (liquid dendrites) is observed in two and three dimensions. This binary model is extended to a ternary system and a representative case is carried out for the Ti–Mg–Cl system. One- and two-dimensional ternary simulations show qualitatively correct interface motion and electrical potential behavior.