Journal of Fluid Mechanics

Oscillations of magnetically levitated aspherical droplets

D. L.  Cummings a1 and D. A.  Blackburn a1
a1 The Open University, Oxford Research Unit, Berkeley Road, Boars Hill, Oxford, OX1 5HR, UK

Article author query
cummings dl   [Google Scholar] 
blackburn da   [Google Scholar] 


In experiments to measure the surface energy of a magnetically levitated molten metal droplet by observation of its oscillation frequencies, Rayleigh's equation is usually used. This assumes that the equilibrium shape is a sphere, and the surface restoring force is due only to surface tension. This work investigates how the vibrations of a non-rotating liquid droplet are affected by the asphericity and additional restoring forces that the levitating field introduces. The calculations show that the expected single frequency of the fundamental mode is split into either three, when there is an axis of rotational symmetry, or five unequally spaced bands. Frequencies, on average, are higher than those of an unconstrained droplet; the surface tension appears to be increased over its normal value. This requires a small correction to be made in all analyses of surface energy. A frequency sum rule is derived from a simplified model of the magnetic field which allows the corresponding Rayleigh frequency to be evaluated from the observed frequencies of the fundamental and translational modes. A more detailed analysis shows a similar correction but one that is also sensitive to the position of the droplet in the field.

(Published Online April 26 2006)
(Received December 5 1989)