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We analyse small-amplitude oscillations of a weakly viscous electricallyconducting liquid drop in a strong uniform DC magnetic field. An asymptoticsolution is obtained showing that the magnetic field does not affect the shapeeigenmodes, which remain the spherical harmonics as in the non-magnetic case.Strong magnetic field, however, constrains the liquid flow associated with theoscillations and, thus, reduces the oscillation frequencies by increasingeffective inertia of the liquid. In such a field, liquid oscillates in atwo-dimensional (2D) way as solid columns aligned with the field. Two types ofoscillations are possible: longitudinal and transversal to the field. Suchoscillations are weakly damped by a strong magnetic field - the stronger thefield, the weaker the damping, except for the axisymmetric transversal andinherently 2D modes. The former are overdamped because of being incompatiblewith the incompressibility constraint, whereas the latter are not affected atall because of being naturally invariant along the field. Since the magneticdamping for all other modes decreases inversely with the square of the fieldstrength, viscous damping may become important in a sufficiently strongmagnetic field. The viscous damping is found analytically by a simple energydissipation approach which is shown for the longitudinal modes to be equivalentto a much more complicated eigenvalue perturbation technique. This studyprovides a theoretical basis for the development of new measurement methods ofsurface tension, viscosity and the electrical conductivity of liquid metalsusing the oscillating drop technique in a strong superimposed DC magneticfield.

Oscillations of weakly viscous conducting liquid drops in a strong magnetic field