# Influence of the trap potential waveform on surface oscillation and breakup of a levitated charged drop

## TL;DR

This study investigates how different trap waveforms influence surface oscillations and breakup of levitated charged droplets, revealing that waveform type affects oscillation modes and harmonic responses but not breakup thresholds.

## Contribution

It provides new insights into the effects of waveform shape on droplet oscillation modes and harmonic content, validated through experiments, theory, and simulations.

## Key findings

- Droplet oscillates mainly in SPSO mode depending on forces and trap position.
- Oscillation frequency matches the forced frequency regardless of waveform.
- Breakup characteristics are unaffected by waveform type.

## Abstract

A charged droplet can be electrodynamically levitated in the air using a quadrupole trap by typically applying a sinusoidal electric field. When a charged drop is levitated it exhibits surface oscillations simultaneously building charge density due to continuous evaporation and subsequently undergoes breakup due to Rayleigh instability. In this work, we examined large-amplitude surface oscillations of a sub-Rayleigh charged drop and its subsequent breakup, levitated by various applied signals such as sine, square and ramp waveform at various imposed frequencies, using high-speed imaging (recorded at 100-130 thousand Frames Per Second (fps)). It is observed that the drop surface oscillates in sphere-prolate-sphere-oblate (SPSO) mode and seldom in the sphere-prolate-sphere (SPS) mode depending on the intricate interplay of various forces due to charge(q), the intensity of applied field ($\Lambda$) and shift of the droplet from the geometric center of the trap ($z_{shift}$). The Fast Fourier Transformation (FFT) analysis shows that the droplet oscillates with the forced frequency irrespective of the type of the applied waveform. While in the sinusoidal case, the nonlinearities are significant, in the square and ramp potentials, there is an admittance of all the harmonic frequencies of the applied potential. Interestingly, the breakup characteristics of a critically charged droplet is found to be unaffected by the type of the applied waveform. The experimental observations are validated with an analytical theory as well as with the Boundary Integral (BI) simulations in the potential flow limit and the results are found to be in a reasonable agreement.