In this thesis we investigate free-surface instabilities which occur in various
industrial processes involving liquid metal. Specifically, we examine a number
of simple problems with a view to developing a plausible theoretical description
based on MHD. Of particular interest is the behaviour of the free surface of a
pool of liquid metal when it is submitted to an alternating magnetic field.
The first problem we examine considers the effect of a low-frequency mag-
netic field on a pool of liquid metal. An initially circular pool is deformed into
radially oscillating starfish modes at certain critical magnetic field strengths.
We study these azimuthal modes theoretically by investigating the behaviour
of an isolated mode. We also consider the influence of geometry in our studies
of a related problem invloving a rectangular strip of liquid metal. At certain
critical magnetic field strengths, an elongated pool is deformed into transverse
modes. Aside from complicated mode coupling, the behaviour of these trans-
verse modes is similar to the starfish . Both the starfish and transverse
modes are caused by a Mathieu-type subharmonic instability.
We next consider the effect of a medium-frequency magnetic field on an
initially circular pool of liquid metal. Experimentally we study the effect of
a vertical alternating medium-frequency magnetic field on an initially circular
pool. We observe two types of behaviour: slow radial oscillation of the pool
perimeter and rotation of the pool about its centre. The physics of this problem
are significantly more complicated than the starfish and strip problems.
Accordingly a description in terms of the previous theory is not possible.
The final problem we consider is the effect of a high-frequency magnetic
field the surface of a conductor. Using a phase-field approach we consider two
simple problems: the first is to calculate the rest shape of an infinite strip
of liquid resting on a substrate in a vertical gravitational field; the second is
to calculate the equilibrium shape of the cross-section of a column of a liquid
conductor submitted to a high-frequency magnetic field whose field lines are
parallel far from the conductor. Our numeric solutions compare well with
previously known analytic solutions.
