Transition in flows driven by converging currents

The liquid metal battery is a promising technology especially suited to grid-scale storage. It comprises two liquid metal electrodes and a molten salt electrolyte that are stably stratified with density. We experimentally studied the flow in the positive electrode using a cylindrical apparatus with a layer of liquid gallium subject to converging current that interacts with the Earth's ambient magnetic field. At a Shercliff number S ≳ 123300, we observed electro-vortex flow (EVF) which is a poloidal flow generated by the interaction of the current with its own magnetic field, and a swirling flow which is generated by the interaction of the current with the ambient axial field, consistent with previous research. However, when we forced the flow at lower current S<123300, we observed a poloidal flow in the opposite direction to EVF. The mechanism of the latter flow is Ekman pumping, where a local fast swirl close to the thin electrode pushes fluid horizontally outward, falling along the side of the vessel and rising at the center. We also present a non-dimensional parameter, β, which is the ratio of the external field to induced field scaled by the ratio of wire radius to vessel radius, that captures the transition between these two motions. This non-dimensional number successfully predicts the transition in previous experiments in the literature.