# Effect of trap potential on the Rayleigh breakup of a levitated charged droplet

## TL;DR

This study investigates how trap potential influences the asymmetric Rayleigh breakup of levitated charged droplets, revealing the effects of trap parameters and droplet properties through high-speed imaging and boundary element simulations.

## Contribution

It presents the first detailed experimental and numerical analysis of asymmetric droplet breakup in a quadrupole trap, highlighting the role of trap strength and droplet position.

## Key findings

- Trap strength affects droplet deformation and breakup symmetry.
- Asymmetric breakup occurs predominantly opposite to gravity.
- Breakup characteristics are influenced more by the electric field than by field-induced effects.

## Abstract

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 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 a first of its kind of study, we capture the successive events of the droplet deformation, breakup and relaxation of the drop after jet ejection using high speed imaging at a couple of hundred thousand frames per second. A pertinent question of the effect of the electrodynamic trap parameters such as applied voltage as well as physical parameters such as the size of the drop, gravity and conductivity on the characteristics of droplet breakup is also 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 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 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.