# Levitated granular gases - work done in collaboration with the University of Konstanz

## Granular matter as a model for non-equilibrium physics

Granular materials are inherent non-equilibrium materials and hence are model systems for the study of systems far from thermodynamic equilibrium. This gives rise to counterintuitive phenomena such as size-separation of binary mixtures or clustering transitions leading to compartmentalization of an initially well mixed collection of grains. We investigate the influence of gravitation on these phenomena by levitating the samples in a strong magnetic field gradient.

## Setup for diamagnetic levitation

Using a 20T cryomagnet, we can produce a field gradient capable of
levitating most diamagnetic materials [Berry and Geim, Eur. J. Phys. **18**, 307 (2000)].
This means that we can
carry out experiments testing the influence of gravity on the
dynamics of granular gases. In addition, the fact that the
effective gravity can be experimentally controlled in such a
setup, it is possible to excite granular gases in a unique way. By
applying an ac component to the main field, the levitation point
of the particles is shifted, thus leading to a homogeneously
shaken granular gas. This has implications on the nature of the
velocity distribution of the gas and deviations from the
Maxwell-Boltzmann distribution usually observed in granular
materials.

## Cooling of a granular gas

To describe the behaviour of granular materials kinetic gas theory
as been often used with varying success. We have studied
the simplest case, namely that of a freely cooling granular gas
(i.e. a granular gas in the absence of any external potentials).
This is possible due to the fact that in our levitation setup we
can compensate for the potential induced by gravity, while the
confining potential is rather shallow on the scale of the
excitation. This means that we have a good approximation of a free
granular gas, whose cooling we can study using video-imaging
and particle tracking. We find good agreement with the classical
theory of Haff [Haff, J. Fluid. Mech. **134**, 401 (1983)], where the theory needs to be adjusted for the presence of clustering at long times. With these adjustments, the data are described over the whole range without adjustable parameters. See also our 2008 PRL on the subject under publications.

## Separation in a Maxwell's demon experiment

When a container with two connected compartments is shaken
vigourously, the number of grains in each compartment is equalized
as one would expect from the behaviour of a molecular gas [Eggers, Phys. Rev. Lett. **83**, 5322 (1999)]. In a
granular gas however, this is no longer true when the container is
shaken slowly. This is due to the inelasticity of the collisions
between grains leading to an instability breaking the symmetry.
The theoretical description of this phenomenon explicitly takes
into account the effect of gravity via a barometric distribution
of the particle density with height. Using our setup, we can check
this prediction of the scaling of the critical frequency with g
experimentally, where we find that the predicted scaling is violated at low effective g. Building on our work on the free cooling of granular gases, we have been able to describe these deviations quantitatively. See also our 2009 EPJE on the subject under publications.