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Mathematics developed over decades may finally explain some of the features of matter's "freaks": granular materials that sometimes behave like a solid and sometimes flow like a liquid.
As strange as it may sound, imagine the sand in an hourglass compared to the sand on the beach. Poured slowly through the constriction, the sand – or rice or coffee – will flow freely. If you pour the same material fast enough or push it hard enough, its particles tend to get stuck, going from a flow state to a solid state.
To avoid sudden blockages where a smooth flow is needed, we need to understand how and when this sudden shift occurs. Two American physicists believe they have found a way to describe the behavior of granular materials approaching this "sticking point."
"The propensity of loose granular materials to 'jam' and stop flowing at low densities is a practical problem that limits flow rates in industrial applications of granular materials," explain Onutthom Narayan of the University of California and Harsh Mathur of Case Western Reserve University in Ohio in their published articles.
This problem becomes even more complex when you consider that it affects different materials in industries as diverse as agriculture, pharmaceuticals and construction. We're talking about pressing pellets into pellets to make tablets, processing grains, and in civil engineering, predicting the behavior of the various sedimentary rocks on which our buildings may be anchored.
For their simulations, Narayan and Mathur used numerical data obtained by other researchers studying frictionless bundles of polystyrene beads in the laboratory. They compared their simulations of balls approaching a sticking point with predictions from a branch of mathematics developed in the 1950s called random matrix theory.
In particular, Narayan and Mathur studied the vibrations inside bundles of beads. Although different batches of beads oscillate at different frequencies, it creates a "spectrum" of oscillation frequencies that varies from batch to batch.
In other words, the granular material allows only certain frequencies of oscillations to propagate through it - a property that physicists call the density of states of the system.
Other researchers have tried to study how the distribution of these vibrational states evolves in granular materials approaching the jamming point, where particles collide with each other before becoming stuck.
This problem lends itself to random matrix theory, which can be used to describe physical systems with many random variables. But without comparing the calculations with the numerical data of the beads themselves, previous studies could not distinguish the different "flavors" of random matrix theory that could explain the vibrations in granular materials.
Where those researchers failed, Narayan and Mathur succeeded: Their comparison of numerical simulations and theoretical predictions showed that a specific statistical probability distribution known as the Wishart-Laguerre ensemble "correctly reproduces the universal statistical properties of trapped granular matter."
The crucial observation, they said, was the recognition that when the beads bump into each other, they compress and rebound like a spring, so that the slight contact of two beads results in quite large forces.
Moreover, the pair also developed a model that was able to describe the properties of the beads close to the jamming point and far from it, when the granular materials are not moving.
"The fact that the same model is able to reproduce both static and vibrational properties of granular matter suggests that it may be more widely applicable to provide a unified understanding of granular matter physics," Narayan and Mathur conclude.
