Shape Oscillations and Stability of Charged Microdroplets

Classical Rayleigh theory predicts an instability of a surface charged liquid sphere, when the Coulomb energy $E_C$ exceeds twice the surface energy $E_S$. Previously, electrified liquid droplets have been found to disintegrate at a fissility $X=E_C/2E_S$ well below one, however. We determine the stability of charged droplets in an electrodynamic levitator by observing the amplitude and phase of their quadrupolar shape oscillations as a function of the fissility. With this novel approach, which does not rely on an independent determination of the charge and surface tension of the droplets, we are able to confirm for the first time the Rayleigh limit of stability at $X=1$ for micrometer sized droplets of ethylene glycol.