The shape of a magnetic liquid drop

We study the equilibrium shape of a ferrofluid drop with a boundary which is partially or totally free.
When no magnetic field exists, a limited volume of magnetic capillary fluid placed in a vertical gravitational field on a solid surface takes on a stable equilibrium form. When a vertical uniform external magnetic field is applied and as its intensity increases, the magnetic liquid drop volume tends to extend along the direction of the magnetic field.
When the magnetic field intensity is in excess of a certain critical value dependent on the magnetic liquid drop properties and its volume, the single-bonded form becomes topologically unstable: a vertical groove is formed on one side of the volume, beginning from the point of contact with the solid surface; along the groove, expanding with time, the droplet breaks down into two droplets approximately equal in volume which are stationary at some distance from each other.

The motion of a magnetic liquid drop

When a time depending and not uniform external magnetic field is applied, a magnetic liquid drop is forced to move.
We investigate the velocity and the change of shape of a magnetic liquid drop.