Oscillation of a Rotating Levitated Droplet: Analysis with a Mechanical Model

TL;DR

This paper introduces a mechanical model for analyzing the oscillation of levitated rotating droplets, aiming to improve surface tension measurement accuracy by correlating oscillation frequency with rotation speed.

Contribution

A novel single-mode mechanical model for ellipsoidal deformation of levitated droplets, validated against experimental data, enhancing surface tension measurement techniques.

Findings

Oscillation frequency depends on rotational speed.

Model predictions align with experimental observations.

Surface tension measurement accuracy can be improved.

Abstract

A droplet of millimeter-to-centimeter scale can exhibit electrostatic levitation, and such levitated droplets can be used for the measurement of the surface tension of the liquids by observing the characteristic frequency of oscillatory deformation. In the present study, a simple mechanical model is proposed by considering a single mode of oscillation in the ellipsoidal deformation of a levitated rotating droplet. By measuring the oscillation frequency with respect to the rotational speed and oscillation amplitude, it is expected that the accuracy of the surface tension measurement could be improved. Using the proposed model, the dependences of the characteristic frequency of oscillatory deformation and the averaged aspect ratio are calculated with respect to the rotational angular velocity of a rotating droplet. These dependences are found to be consistent with the experimental observations.