Translation-deformation coupling effects on the Rayleigh instability of an electrodynamically levitated charged droplet.

The breakup pathway of the Rayleigh fission process observed in the past experiments carried out using high-speed imaging of a charged drop levitated in an AC quadrupole trap has shown to exhibit several cycles of shape and center-of-mass oscillations followed by asymmetric breakup by ejecting a jet in the upward direction (i.e., opposite to the direction of gravity). We recently attempted to explain this using boundary integral simulations in the Stokes flow limit, wherein the position of the droplet and the polarity of the end cap electrodes were assigned using physical arguments, and the center-of-mass motion was not estimated consistently invoking quasi-static conditions. In this work, we explain the experimental observation of upward breakup of charged droplets in a quadrupolar field, using numerical calculations based on the boundary element method considering inviscid droplets levitated electrodynamically using quadrupole electric fields. The center-of-mass motion and the end cap are consistently calculated in the numerical scheme. 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 subcritical 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 upward via the ejection of a jet at the north pole of the deformed drop.

Subcritical asymmetric Rayleigh breakup of a charged drop induced by finite amplitude perturbations in a quadrupole trap.

The breakup pathway of Rayleigh fission of a charged drop is unequivocally demonstrated by continuous, high-speed imaging of a drop levitated in an AC quadrupole trap. The experimental observations consistently exhibited asymmetric, subcritical Rayleigh breakup with an upward (i.e., opposite to the direction of gravity) ejection of a jet from the levitated drop. These experiments supported by numerical calculations show that the gravity induced downward shift of the equilibrium position of the drop in the trap causes significant, large amplitude shape oscillations superimposed over the center-of-mass oscillations. The shape oscillations result in sufficient deformations to act as triggers for the onset of instability below the Rayleigh limit (a subcritical instability). The concurrently occurring, center-of-mass oscillations, which are out of phase with the applied voltage, are shown to lead to an asymmetric breakup such that the Rayleigh fission occurs upwards via the ejection of a jet at the pole of the deformed drop. As an important application, it follows by inference that the nanodrop generation in electrospray devices will occur, more as a rule rather than as an exception, via asymmetric, subcritical Rayleigh fission events of microdrops due to inherent directionality provided by the external electric fields.

Effect of the Quadrupolar Trap Potential on the Rayleigh Instability and Breakup of a Levitated Charged Droplet.

The experimental demonstration of Rayleigh instability that results in the breakup of a charged droplet, levitated in a quadrupole trap, has been investigated in the literature, but only scarcely. We report here the asymmetric breakup of a charged drop, levitated in a loose trap, wherein the droplet is stabilized at an off-center location in the trap. This aspect of levitation leads to an asymmetric breakup of the charged drop, predominantly in a direction opposite to that of gravity. In the present work, we report the evidence of successive events of the deformation and breakup of a charged drop and its subsequent relaxation after jet ejection using high-speed imaging at a couple of hundred thousand frames per second. Several relevant aspects of this phenomenon such as the effect of the electrodynamic (ED) trap parameters in terms of the applied potential as well as physical parameters such as the size of the drop, gravity, and conductivity on the characteristics of droplet breakup are explored. A clear effect of the trap strength on the deformation (both symmetric and asymmetric) is observed. Moreover, the cone angle at the pole undergoing asymmetric breakup is almost independent of the applied field investigated in the experiments. All of the experimental observations are compared with numerical simulations carried out using the boundary element method (BEM) in the Stokes flow limit. The BEM simulations are also extended to other experimentally achievable parameters. It is observed that the breakup in our study is mostly field-influenced and not field-induced. A plausible theory for the observations is reported, and a sensitive role of the sign of the charge on the droplet and the sign of the end-cap potential, as well as the off-center location of the droplet in the trap, is elucidated.