Translation-deformation coupling effects on the Rayleigh instability of an electrodynamically levitated charged droplet
The breakup pathway of the Rayleigh fission process observed experimentally using high-speed imaging of a charged drop levitated in an AC quadrupole trap is shown to undergo asymmetric breakup by ejecting a jet in the upward direction ((i.e., opposite to the direction of gravity)). To explain this typical experimental observation, we carry out numerical calculations based on the boundary element method considering inertial droplets levitated electrodynamically using quadrupole electric fields. The simulations show that the gravity-induced downward shift in the equilibrium position of the drop in the trap causes significant, large-amplitude shape oscillations superimposed over the center-of-mass oscillations of the drop. An important observation here is that the shape oscillations due to the applied quadrupole fields, result in sufficient deformations that act as triggers for the onset of the instability below the Rayleigh limit, thereby admitting a sub-critical instability. The center-of-mass oscillations of the droplet within the trap, which follow the applied frequency, are out of phase with the applied AC signal. Thus the combined effect of shape deformations and dynamic position of the drop leads to an asymmetric breakup such that the Rayleigh fission occurs upwards via the ejection of a jet at the north-pole of the deformed drop.