Stability of Hall-Heroult Cells

The motion and stability of the metal/electrolyte interface is determined by Navier-Stokes equation. The equation may be decomposed into two independent equations by taking the divergence and curl of Navier-Stokes equation. The divergence determines the motion and stability of magneto-gravitational waves. The curl of Navier-Stokes equation gives an equation containing only velocity and magnetic field, and states that the magnetic field is driving a circulation pattern in the cell, and this magneto-flow has its own stability conditions. The waves are called Alfven waves, and their stability properties are related only to magnetic field and geometry.