Stability of a liquid metal interface affected by a high-frequency magnetic field

Abstract

The stability of a free liquid metal surface influenced by an alternating magnetic field is investigated both experimentally and analytically. The experimental set-up consists of an annulus filled with liquid metal. The outer wall of the annulus is made of quartz glass to allow visualization using a high-speed camera system. The magnetic field is generated by ring-like inductor located at some distance above the free surface of the liquid metal. The inductor is supplied by an alternating current of variable frequency between 5 kHz and 50 kHz. The alternating magnetic field induces Lorentz forces within the liquid and generates an electromagnetic pressure acting on the free surface. Two different types of instabilities in the are detected. At lower inductor currents we observe sinusoidal surface waves, while at higher currents, above a critical value, an electromagnetic pinch is generated. During the experiments we measure the critical current and the amplitude of the surface waves for various frequencies. A simple analytical model has been developed in order to predict the instability of a plane liquid metal surface affected by an alternating electromagnetic field. The hydrodynamic equations are simplified by applying the Hele-Shaw approximation for a thin annulus gap. The electromagnetic equations are simplified by using the skin depth approximation. Here we exploit the fact that for high frequencies the penetration depth of the magnetic field is small compared to the liquid layer height. Within this assumption, the electromagnetic pressure on the free surface can be calculated by using the method of mirror charges. Linear stability analysis shows that the plane surface becomes unstable to perturbations of wave number k whenever the effect of the electromagnetic pressure exceeds the stabilizing effects of surface tension and gravity. The critical inductor current predicted by the model is in good agreement with the critical value of the instability observed in experiment.