Resonant oscillations of inviscid charged drops

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Abstract
Moderate-amplitude axisymmetric oscillations of charged inviscid drops held together by surface tension are calculated by a multiple-timescale expansion. The corrections to the drop shape and velocity caused by mode coupling at second order in amplitude are predicted for two-, three- and four-lobed motions of drops with net charge up to the Rayleigh limit Qc ≡ 4π½. Resonant oscillations between four- and six-lobed motions occur for total charge values near and are analysed. Both frequency and amplitude modulation of the oscillation are predicted for drop motions starting from general initial deformations.

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