Magnetohydrodynamic instability with bichromatic perturbations in aluminum reduction cells

What is it about?

A new dispersion relation is developed, which includes the effects of Lorentz force, friction, interfacial tension, and gravity. The conclusions of the study obtained from analyzing the dispersion relation in the context of aluminum reduction cells are summarized as follows: • The instability is primarily driven by the interaction of the longitudinal magnetic field and transverse current density when the solid–liquid interface (such as electrode–electrolyte) offers insignificant friction to the flow of electrolyte (liquid above interface). This is a new observation since the effect of horizontal magnetic field components is believed to be largely negligible in the published literature. • Furthermore, the transverse field interacts with the longitudinal current density to destabilize the higher modes. However, the interaction between vertical current density and horizontal magnetic field components counters the destabilizing forces involving the horizontal magnetic field. If the solid–liquid interface offers friction to resist the flow of the electrolyte (liquid above interface), the destabilizing effect of Bx, By, and perturbed current density is negligible. Under such circumstances, the instability of the liquid–liquid interface is governed by the horizontal current density and vertical magnetic field. • While Bz is predicted to be mainly responsible for the instability of lower modes at the interface, Bx and By destabilize all the modes. • The ACD at neutral stability for a few of the modes reduces to insignificantly lower values under the conditions when (i) the ratio of the modes along cell length to the width is equal to the cell aspect ratio (cell length to width), and (ii) the ratio of the magnetic field along horizontal directions is equal to the ratio of wavenumbers along cell length and width.

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Photo by Susan Wilkinson on Unsplash

Photo by Susan Wilkinson on Unsplash

Why is it important?

MHD instability of the liquid–liquid interface of a simplistic finite rectangular domain is investigated considering a bichromatic perturbation (independent wavenumbers along length and width). The destabilizing effect of individual magnetic field components along the three directions is discussed. It is primarily believed that destabilizing effect of the horizontal magnetic field is negligible. Unlike most reported works, here we discuss the destabilizing effect, conditions, and mechanism while considering the horizontal magnetic field.

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