Basic flow and its three-dimensional linear stability in a small spherical droplet spinning in an alternating magnetic field

We present a numerical analysis of the liquid metal flow and its three-dimensional linear stability in a spherical droplet spinning in an alternating magnetic field. The applied magnetic field is uniform and the droplet spins around an axis parallel to the field. The droplet is assumed to be small so that its deformation by both electromagnetic and centrifugal forces is negligible. We find that a sufficiently fast spinning suppresses and stabilizes the internal flow in the droplet. However, there is a narrow range of rotation rates corresponding to an Ekman number of E ≈ 10^-2, where the spinning can destabilize the internal flow. Our results can be useful for the assessment of melt flow conditions in certain material processing technologies using electromagnetic levitation melting techniques.