On the equilibrium of a toroidal droplet of ferrofluid #

Kraig Wymer-Webb, Mark Blyth, Robert Whittaker

12:50 Monday in 4Q04.

Part of the Droplets and impact session.

Abstract #

It is well-known that under ordinary conditions a cylindrical column of fluid will rapidly break down into droplets due to surface tension. However, this can be prevented if the fluid comprising the column is a magnetisable ferrofluid. Ferrofluids become magnetised in the presence of a magnetic field, such as those produced by current-carrying wires, and the force associated with the magnetisation opposes surface tension and can stabilise the fluid column.

In this talk, we will consider the system of a static toroidal droplet of ferrofluid surrounding a circular loop of current-carrying wire. Our aim is to investigate the possibility that the magnetisation force experienced by the ferrofluid may inhibit the surface tension driven instability of the toroidal droplet. In order to analyse the stability of this set-up, we need to first find an equilibrium state of the system. Complicating this is the fact that the shape of the toroidal free surface is not known in advance.

Ultimately, we arrive at a boundary-integral equation for the magnetic field and a dynamic boundary condition to be satisfied at the ferrofluid free surface. An equilibrium state of the system is then sought as a numerical solution to these equations. Some preliminary results will be presented.