Interfacial instabilities in aluminium reduction cells

Abstract

This paper extends the analysis of Sneyd (1985) on interfacial instabilities in aluminium reduction cells. The cell model consists of a plane fluid layer of relatively low electrical conductivity, sandwiched between an upper rigid wall and lower fluid layer, both of high conductivity. A steady current passes through the layers, and the magnetic field is assumed to be a linear function of position. The principal new effects introduced are (i) a horizontal current component in the aluminium; (ii) vertical magnetic field components, and vertical field gradients; (iii) an aluminium pool of finite depth; and (iv) uniform zeroth-order flow in the fluid layers, and mechanical dissipation. A dispersion relation for small-amplitude waves is derived and discussed. The destabilizing Kelvin—Helmholtz mechanism and electromagnetic forces compete with gravity, surface tension and mechanical dissipation. Electromagnetic destabilization is likely to occur in practice at wavelengths of 1 m or more, and becomes more intense with decreasing layer depths. The most dangerous mechanism appears to be driven by vertical gradients of the horizontal field.