Efficient mixing by swirling electrovortex flows in liquid metal batteries

Using direct numerical simulations, we show that swirling electrovortex flows significantly enhance the mixing of the bottom layer alloy in liquid metal batteries during discharge. By studying the flow in various parameter regimes, we identify and explain a novel scaling law for the intensity of these swirling electrovortex flows. Using this scaling law and the model described in Herreman et al. (Phys. Rev. Fluids, vol. 5, 2020, 074501), we estimate the minimal intensity of the external magnetic field that is needed for the swirling electrovortex to enhance the mixing of the alloys in the bottom electrode of arbitrary liquid metal batteries.