Equilibrium Configurations of Ferrofluid Droplets and Toroids

Wymer-Webb, Kraig (2026) Equilibrium Configurations of Ferrofluid Droplets and Toroids. Doctoral thesis, University of East Anglia.

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Abstract

The presented work provides a novel study into the equilibrium shapes of toroidal droplets of ferrofluid. We present a mathematical model describing the equilibrium shapes of ferrofluid toroids surrounding a circular loop of current-carrying wire. The obtained governing equations are then discretised and solved numerically using a boundary-integral technique. Validation of the numerical results is achieved via an asymptotic analysis of the special case of a toroidal droplet of small fluid volume.

The results obtained from the numerical solution of the mathematical model provides evidence to confirm the existence of toroidal droplets of ferrofluid that are in equilibrium. The droplets in question are parameterised by their fluid volume and a magnetic Bond number, which is the ration of magnetic effects to surface tension effects. An analysis of the equilibrium shape obtained as these parameters are varied is presented, determining regions in parameter space in which no equilibrium shapes can be found, as well as regions in parameter space where two equilibrium shapes can be found.

Finally, we consider how the model that was developed for toroidal droplets could be extended to include simply-connected ferrofluid droplets. Some preliminary results for the equilibrium shape of such droplets is presented and some possible links to toroidal droplets are identified.

Item Type:	Thesis (Doctoral)
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
Depositing User:	Chris White
Date Deposited:	12 May 2026 09:24
Last Modified:	12 May 2026 09:24
URI:	https://ueaeprints.uea.ac.uk/id/eprint/102951
DOI:

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