Spontaneous order in ensembles of rotating magnetic droplets

TL;DR

This paper investigates the formation of rotating crystal-like structures in ensembles of magnetic droplets under a rotating magnetic field, combining experimental observations with a hydrodynamic interaction model.

Contribution

It introduces a new model accounting for hydrodynamic and magnetic interactions in droplet ensembles, explaining their collective rotating behavior.

Findings

Formation of triangular ordered rotating structures observed experimentally.

Model accurately predicts periodic dynamics of four-droplet ensembles.

Derived magnetic interaction expression considering magnetic charges at droplet tips.

Abstract

Ensembles of elongated magnetic droplets in a rotating field are studied experimentally. In a given range of field strength and frequency the droplets form rotating structures with a triangular order - rotating crystals. A model is developed to describe ensembles of several droplets, taking into account the hydrodynamic interactions between the rotating droplets in the presence of a solid wall below the rotating ensemble. A good agreement with the experimentally observed periodic dynamics for an ensemble of four droplets is obtained. During the rotation, the tips of the elongated magnetic droplets approach close to one another. An expression is derived that gives the magnetic interaction between such droplets by taking into account the coulombian forces between magnetic charges on the droplet tips.