Polygonal excitations of spinning and levitating droplets

Abstract

The shape of a weightless spinning liquid droplet is governed by the balance between the surface tension and centrifugal forces. The axisymmetric shape for slow rotation becomes unstable to a non-axisymmetric distortion above a critical angular velocity, beyond which the droplet progresses through a series of 2-lobed shapes. Theory predicts the existence of a family of 3- and 4-lobed equilibrium shapes at higher angular velocity. We investigate the formation of a triangular-shaped magnetically levitated water droplet, driven to rotate by the Lorentz force on an ionic current within the droplet. We also study equatorial traveling waves which give the droplet 3, 4 and 5-fold symmetry.

Supplementary information at http://www.nottingham.ac.uk/~ppzlev/Droplet

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• Densities of Solar System Objects from their Rotational Lightcurves
• Rayleigh-Plateau and Gregory-Laflamme instabilities of black strings
• Nonlinear Modes of Liquid Drops as Solitary Waves
• Equilibrium configurations of fluids and their stability in higher dimensions

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