Mastering a liquid magnet

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The ability to manipulate and control liquid surfaces and interfaces is of crucial importance in a host of different engineering and industrial applications. Typically, control is best achieved in a non-invasive manner via some external agency (e.g. an electric field or a magnetic field). Liquid surfaces are highly susceptible to instabilities and a target surface shape for a particular application can be challenging to achieve. The integrity of the surface can be easily compromised by wavelike disturbances and other surface irregularities. In this project we will investigate how to control surface shape for a ferrofluid. Motivation comes from the atomisation industry: during atomisation small toroidal-shaped liquid drops may form as part of the droplet cluster. Such drops rapidly disintegrate as a result of surface tension. The manner in which this disintegration occurs is not fully understood and experiments are complicated by the difficulty of achieving a toroidal drop as an initial condition. We will aim to show that this can be achieved by use of a ferrofluid. Such fluids contain large numbers of tiny magnetizable particles in a stable suspension and which experience a body force when exposed to a magnetic field. In essence they behave like a liquid magnet. The magnetic body force can act to stabilise a ferrofluid in surprising ways. For example, it is known that a liquid cylinder composed of a ferrofluid can be entirely stabilised when acted upon by an azimuthal magnetic field that is generated by a current-carrying wire along the axis of the liquid cylinder. Under normal circumstances such a liquid cylinder will be rapidly driven out of equilibrium and ultimately break up into droplets. The same stability may be possible for a toroidal drop; if so it would provide a means to create a controllable initial state that can be set to disintegrate at a specified time by switching off the stabilising field as required. Aims and method: The principal aims of the project will be to investigate ferrofluid surface equilibria, one example being the liquid torus, and to determine their stability. A secondary goal will be to study the propagation of disturbances (e.g. solitary waves) along these equilibrium structures. The equilibrium problem will be formulated as a coupled boundary-integral problem to determine the surface shape and static magnetic field simultaneously. This will be done numerically by some asymptotic analysis will be possible in certain limits. Once equilibria have been computed their stability will be studied via a variational formulation.