Ferrofluids are incredibly interesting substances. Their behavior within the magnetic field is fascinating. But still more fascinating is the behavior of plastic microspheres dispersed within a ferrofluid. The idea to put the plastic microspheres into the ferrofluid was formulated by Arne Skjeltorp. (

A plastic, thus diamagnetic, sphere submerged within the ferrofluid can be seen as a spherically shaped, stable hole within it. When the ferrofluid is magnetized by an external magnetic field, the hole remains free of magnetization. One can imagine that the magnetization is reduced to zero inside the hole by a virtual magnetic dipole moment located in its center and oriented in the direction opposite to the bulk magnetization. Two such holes interact as two dipole moments.

Imagine that the system of magnetic holes is limited by a pair of parallel glass plates to thin layer. Let the thickness of the layer be slightly larger than the diameter of the holes. In such an experimental set-up the motion of the magnetic holes is limited to a plane - the system becomes practically two-dimensional.

Put the sample prepared in such a manner into a rotating magnetic field and using a microscope observe the motion of the magnetic holes. Figure below presents the experimental set-up. It was created in the Arne Skjeltorp's laboratory within the Institute for Energy Technology in Kjeller, Norway. Geir Helgesen was working on it.

The dynamics of the holes motion is incredibly rich. To describe it, we applied the formalism of the braid theory.

For details see:

G. Helgesen, P. Pieranski and A. Skjeltorp,
Nonlinear phenomena in systems of magnetic holes,
Phys. Rev.  Letters, 64, 1425 (1990).

G. Helgesen, P. Pieranski and A. Skjeltorp
Dynamic behavior of simple magnetic holes systems,
Phys. Rev.  A 41, 7271 (1990).

P. Pieranski, G. Helgesen, S. Clausen and A. Skjeltorp,
Braids plaited by magnetic holes,
Phys. Rev. Letters, 77, 1620 (1996).

A pop-science article on the braid description of the magnetic holes dances has been published within La science des noeuds, a dossier of the French Pour La Science magazine.

The magnetic holes experimental set-up is not difficult to build. But it takes time. If you want to see its virtual version have a look at Magnetic Holes Workbench, a  simulation program I wrote a few years ago. It is a DOS program and it uses a low resolution graphic mode. Certainly, not up-to-date.

The American Institute of Physics report

Phillip F. Schewe and Ben Stein, BRAIDS PLAITED BY MAGNETIC HOLES Physics News Update, September 9, 1996.