Shape and fission instabilities of ferrofluids in non-uniform magnetic fields

TL;DR

This paper investigates how non-uniform magnetic fields influence the shape, stability, and droplet formation of ferrofluids, revealing complex phase transitions and providing theoretical models validated by experiments.

Contribution

It introduces a comprehensive theoretical framework for ferrofluid behavior under non-uniform magnetic fields, including shape instabilities and droplet splitting, supported by experimental validation.

Findings

Modified normal-field instability in gradient fields

Rich phase transition phenomena observed

Quantitative agreement between theory and experiments

Abstract

We study static distributions of ferrofluid submitted to non-uniform magnetic fields. We show how the normal-field instability is modified in the presence of a weak magnetic field gradient. Then we consider a ferrofluid droplet and show how the gradient affects its shape. A rich phase transitions phenomenology is found. We also investigate the creation of droplets by successive splits when a magnet is vertically approached from below and derive theoretical expressions which are solved numerically to obtain the number of droplets and their aspect ratio as function of the field configuration. A quantitative comparison is performed with previous experimental results, as well as with our own experiments, and yields good agreement with the theoretical modeling.