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. (c) 2007 The Electrochemical Society.