Vibrations of a diamagnetically levitated water droplet

TL;DR

This study measures and analyzes the vibrational eigenfrequencies of a water droplet levitated by magnetic fields, considering the effects of the trap's shape and forces on oscillation frequencies.

Contribution

It derives theoretical eigenfrequencies for a magnetically levitated droplet and compares them with experimental data, accounting for trap shape effects.

Findings

Eigenfrequencies increase due to the trap's restoring forces.

Theoretical predictions match experimental measurements within uncertainties.

Shape of the potential trap influences oscillation frequencies.

Abstract

We measure the frequencies of small-amplitude shape oscillations of a magnetically-levitated water droplet. The droplet levitates in a magnetogravitational potential trap. The restoring forces of the trap, acting on the droplet's surface in addition to the surface tension, increase the frequency of the oscillations. We derive the eigenfrequencies of the normal mode vibrations of a spherical droplet in the trap and compare them with our experimental measurements. We also consider the effect of the shape of the potential trap on the eigenfrequencies.