# Stability of electrodynamically levitated one or many charged droplets in the presence of noise

## TL;DR

This paper investigates how external noise affects the stability and arrangement of charged droplets levitated in an electrodynamic balance, combining theoretical analysis with numerical simulations to understand transitions from ordered to disordered states.

## Contribution

It introduces a classical pseudo-potential approach to analyze stability under noise and validates it with numerical simulations solving the modified Mathieu equation for multiple droplets.

## Key findings

- Transition from Coulombic crystal to liquid-like structure above a threshold noise level
- Theoretical predictions are in fair agreement with simulation results
- Stability analysis applicable to pollutant particle capture in air streams

## Abstract

The theory of the effect of external fluctuation force on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using classical pseudo-potential approach. The theory is supplemented with numerical simulations where the non-homogeneous modified Mathieu equation is solved for single droplet as well as many droplets. The transition from the well ordered Coulombic crystal to randomly distributed liquid like structure is observed above a threshold value of the order parameter. The theory and simulations are found to be in fair agreement with each other. The simulation is aimed at studying the stability of structures for capturing the pollutant particle form the air streams using contactless membrane.