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Resonances of a conducting drop in an alternating electric field

Resonance phenomena of a conducting drop forced by an alternating electric field are studied by perturbation analysis. Although the motions are assumed to be irrotational, weak viscous effects are included in the boundary condition of the normal stress balance. Without an external field, the first-order expansion of the domain perturbations yields the same result as that obtained by Lamb (1932) for the viscous decay of the free oscillation modes. A primary resonance occurs in the first-order forced oscillation problem. Under strong excitation, superharmonic, sub-harmonic, and coupled resonances are revealed in the second-order solutions. Hence, large-amplitude drop oscillations may occur even if the excitation frequencies are away from the characteristic drop frequencies and the spatial forms of the excitation modes do not directly match the drop shape modes. In order to obtain comparable response amplitudes, however, the magnitudes of external forcing required to excite secondary resonances are shown to be about an order greater than that for the primary resonances.