Bifurcations of the shape of a magnetic fluid droplet in a rotating magnetic field

An analysis is made of the behavior of a magnetic droplet suspended in a liquid in a high-frequency uniform, rotating magnetic field. In weak fields the droplet is spheroidal while in strong fields it is disk-shaped. The observed change in the shape of the droplet as the amplitude of the field increases depends on the magnetic permeability μ of the liquid and takes place according to three scenarios: (a) for small μ the spheroidal droplet is continuously converted into a disk; (b) for intermediate μ there is a range of fields in which the droplet becomes a triaxial ellipsoid with its major axis lying in the plane of the field, and spheroid-triaxial ellipsoid-disk transitions take place as a result of a soft bifurcation; (c) at high μ both transitions are hard. Theoretical calculations are made of the stability curve for the various droplet shapes. It is predicted that a change in the types of droplet shape bifurcations will occur in strong fields. A comparison is made with the experimental data.