Simple model of the slosh instability in aluminium reduction cells

The “slosh” instability occurs when Lorentz forces drive gravity waves by exciting coupled gravitational wave modes. This instability occurs in Hall-Heroult reduction cells which are used to manufacture aluminium. These cells consist of a horizontally large and shallow layer of molten aluminium under a layer of molten electrolyte, with both layers in between large carbon electrodes. Due to the high electrical resistivity of the electrolyte, a slight tilting of the interface between the aluminium and the electrolyte substantially redistributes the current in the cell. As a result, horizontal currents appear in the aluminum layer and interact with vertical ambient magnetic fields, giving rise to a Lorentz Force which drives the instability. Davidson and Lindsay proposed a simple mechanical analogue that captures the important physics of the instability ("Stability of Interfacial Waves in Aluminium Reduction Cells" JFM, 1998). In this talk, I will present the proposed mechanical model through discussing simplifying assumptions and deriving governing equations. I will also show numerical results illustrating instability at parameters matching the transition criterion derived in Davidson’s paper.