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Clustering grains and traffic jams: a billion dollar problem

Collaboration with the Physics of Fluids group, University of Twente, The Netherlands,
originally sponsored by a research grant from FOM ("Maxwell's Demon in a Granular Gas", 2000-2004) and still ongoing.

One of the key features of agitated granular matter is its tendency to form clusters. This counterintuitive behavior is illustrated below
in a setup of five connected compartments, vertically vibrated with a certain amplitude and frequency. It is as if one is watching a
movie being played backwards: starting with 200 steel beads distributed equally over the five boxes, after a minute they have clustered
into a single compartment!



The clustering effect is due to the fact that the collisions between the particles are not entirely elastic. In every collision they lose a small
portion of their kinetic energy. This means that they collectively make each other slower. The loss of mobility is strongest in those compartments
where there happen to be a few extra particles (more collisions) and hence the outflow from these compartments is reduced. Incoming particles
from neighbouring compartments cause even more collisions and this leads to a snowball effect.

Eventually almost all particles cluster together in one compartment (it does not necessarily have to be the middle one). The other compartments
are practically empty now and the few particles found here are by contrast very energetic. This can be seen in the above pictures: the particles in
the diluted compartments jump considerably higher than those in the densely populated ones.

Clustering is a prime example of spontaneous pattern formation in multi-particle systems out of equilibrium and, moreover, a major issue in
many industries that handle grainy materials (pharmaceutical industry, food production, mining, and numerous others). It has been estimated
that worldwide no less than 5% of our energy budget -- 500 billion dollars annually -- is wasted due to problems with this type of matter!

In a series of papers combining experiments, theory, and numerical simulations (see Publ. 35, 36, 37, and further) we have shown that
the cluster formation in compartmentalized systems is well described - qualitatively and quantitatively - by a dynamical flux model first
introduced by Jens Eggers.

See also our current Complex Matter Project and:
> Collapse of a cluster
> Clustering on the highway
> Competitive clustering

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