Detailed Mathematical Modeling Of Liquid Metal Streamer Formation And Breakup (Invited)

A Cahn-Hilliard phase field model is formulated to describe transport-limited electrochemical reactions coupled with fluid flow in a metal reduction cell. When the reaction is limited by mass transfer of metal ions from the electrolyte to the cathode, the metal-electrolyte interface at the cathode exhibits a Mullins-Sekerka instability, leading to the growth of dendrite-like "streamers" of liquid metal into the electrolyte, which in turn significantly enhance the apparent mass transfer coefficient there. Model results for iron reduction from ferrous oxide in slag show formation of these streamers. Although the double-layer is not included in this model, the related phenomenon of electrocapillarity can be represented by a gradient penalty term which includes the electric potential gradient, such that interfacial energy is a function of the electric field normal to the interface.