Stability of a Magnetically Levitated Diamagnetic Fluid Column

The stability of a magnetically levitated nonmagnetic liquid column in a magnetic fluid and a nonuniform magnetic field is studied theoretically and experimentally. The angular velocity equation of the interfacial wave is derived by assuming that (1) the fluids are inviscid, (2) the undisturbed interface between the levitated fluid and the surrounding fluid is an infinitely long cylindrical surface, (3) the amplitudes of the disturbances are very small, and (4) the magnetic susceptibility of each fluid is much smaller than 1. The stable conditions of different modes are discussed. The experimental study is performed with two very long magnetic north poles set face to face to form the nonuniform magnetic field, using water as the levitated fluid and a diluted oil-base magnetic fluid as the surrounding fluid.