Fluid motions induced by a periodic magnetic field in and about a liquid drop

In this paper we consider the flow field induced by a periodic magnetic field in and about a conducting liquid drop immersed in an incompressible insulating fluid. It is assumed that at infinity the magnetic field varies with time t as cos ωt, where ω is a constant. This magnetic field is associated with a periodic electric field which produces a net electric stress, dependent on the spatial variables, normal to the drop surface. This stress sets up a flow field, in and about the liquid drop, that creates an appropriate viscous stress so that there is stress balance at the drop surface. The flow field is periodic with angular frequency 2ω. For small drop deformations the drop shape at any instant is a spheroid. It is shown that for large ω the amplitude of the velocity field for a conducting drop is approximately independent of ω and for a non-conducting drop it is proportional to ω. The larger velocity amplitude for a non-conducting drop is probably due to the fact that in this case there is no dissipation of electromagnetic energy. The electric stress over the drop surface increases with ω and it is suggested that the drop will burst at large ω unless the amplitude of the applied magnetic field is suitably decreased.