Surface oscillations of a sub-Rayleigh charged drop levitated in a quadrupole trap

A conducting charged drop, when subjected to a small amplitude perturbation, becomes unstable when the surface charge exceeds its Rayleigh limit. On the other hand, a drop with a charge in the sub-Rayleigh limit exhibits capillary oscillations whose amplitude and frequency depend upon the amount of the charge. In experiments, such systems are studied by levitating them in a quadrupole potential. The oscillations of a sub-Rayleigh charged drop in such setups now also depend upon the strength of the quadrupole potential. We conduct the first of its kind of experiments which indicate that a highly charged drop (but in the sub-Rayleigh limit) undergoes several cycles of prolate and oblate shape deformations. The surface oscillations of the levitated charged drop are observed to follow the frequency of the applied alternate current electric field, and the magnitude of prolate deformations is higher than the oblate deformation. To explain this, we provide a theory in the viscous potential flow limit that assumes axisymmetric shape oscillations of a perfectly conducting charged drop levitated in a quadrupole electric field. The analysis indicates that the experimental results can be explained only if a positional shift of the drop in the quadrupole field is assumed, thereby demonstrating the role of the local electric field.A conducting charged drop, when subjected to a small amplitude perturbation, becomes unstable when the surface charge exceeds its Rayleigh limit. On the other hand, a drop with a charge in the sub-Rayleigh limit exhibits capillary oscillations whose amplitude and frequency depend upon the amount of the charge. In experiments, such systems are studied by levitating them in a quadrupole potential. The oscillations of a sub-Rayleigh charged drop in such setups now also depend upon the strength of the quadrupole potential. We conduct the first of its kind of experiments which indicate that a highly charged drop (but in the sub-Rayleigh limit) undergoes several cycles of prolate and oblate shape deformations. The surface oscillations of the levitated charged drop are observed to follow the frequency of the applied alternate current electric field, and the magnitude of prolate deformations is higher than the oblate deformation. To explain this, we provide a theory in the viscous potential flow limit that assume...