Small-amplitude oscillations of electrostatically levitated drops

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Abstract
The nature of axisymmetric oscillations of electrostatically levitated drops is examined using an analytical method of multiple-parameter perturbations. The solution for the quiescent equilibrium shape exhibits both stretching of the drop surface along the direction of the externally applied electric field and asymmetry about the drop's equatorial plane. In the presence of electric and gravitational fields, small-amplitude oscillations of charged drops differ from the linear modes first analysed by Rayleigh. The oscillatory response at each frequency consists of several Legendre polynomials rather than just one, and the characteristic frequency for each axisymmetric mode decreases from that calculated by Rayleigh as the electric field strength increases. This lowering of the characteristic frequencies is enhanced by the net electric charge required for levitation against gravity. Since the contributions of the various forces appear explicitly in the analytic solutions, physical insight is readily gained into their causative role in drop behaviour.

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