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.