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.