Labyrinthine Instability and Pattern Formation in Ferrofluids

TL;DR

This study investigates pattern formation and instability in ferrofluids under magnetic fields, comparing experimental results with theoretical predictions and revealing complex behaviors like area variation and labyrinthine angles.

Contribution

It provides experimental validation of theoretical models for ferrofluid instability patterns and uncovers new phenomena such as area changes at high magnetic fields.

Findings

Elliptical instability points match predictions at moderate sizes.

Labyrinthine pattern angles are wider than 120 degrees, indicating arm repulsion.

Ferrofluid area initially decreases then increases with magnetic field strength.

Abstract

This paper has been withdrawn by the author. Ferrofluids suspended in liquids and constrained in quasi-two dimensional domains were exposed to transverse magnetic fields. The points of elliptical instability of nearly circular drops were measured and compared to the theoretical prediction using a fitting parameter. The data matched the predicted trend well for 3 different liquids used as suspensions; however, at extreme values of drop radius, there was a significant deviation from prediction. The angles at each node of the labyrinthine pattern, formed using high magnetic fields, were measured and compared with the prediction of 120 degrees. For the dense labyrinth the most common angles were between 135 degrees -144 degrees, suggesting interaction between arms were having a repelling effect causing angles to widen. For the less dense labyrinth the most frequent angle category decreased, supporting this hypothesis. In the experiments the area, which theoretically should be constant, was noticed to change and this encouraged an investigation into how the area varied with an increasing field. A decrease in area is seen initially, as expected, due to the ferrofluid experiencing a force upwards due to the field. This was deduced to be an effect of modelling the 3 dimensional system as quasi-two dimensional. An unpredicted effect, causing the area to increase after elliptical instability had been reached, was noted in several results and was hypothesised to be due to a bulging around the sides of the ferrofluid when the field was large.