Vibrational frequency of a nonconducting charged liquid drop

The vibration of a nonconducting liquid drop endowed with a surface charge is considered, in supplement to the well-known case of a conducting liquid drop studied by Lord Rayleigh in the last century. It is assumed that there is no charge conduction except by hydrodynamical transport due to the flow motion. It is found that the surface flow is of such a form that the charge again maintains an electrostatic equipotential at the surface of the drop at all instants of the vibrational motion, and the same Rayleigh result is obtained. The Rayleigh result is applicable to more general classes of liquid drops, irrespective of the conductivity of the liquid in these two limits.