Decades-old mathematics could finally help explain some peculiar characteristics of ‘oddballs’ in the world of matter: granular materials that can act like a solid but can also flow like a liquid.
Think of sand in an hourglass compared to sand on a beach. Pour sand—or rice or coffee—slowly through a narrow opening, and it flows easily. But if you funnel it quickly or stamp down hard, those same particles can jam, shifting from a flowing state to a solid-like one.
To better understand how and when this sudden shift happens, two US-based physicists believe they’ve found a way to describe the behavior of granular materials approaching that ‘jamming point’.
“The tendency of flowing granular matter to get ‘jammed’ and stop flowing at low densities is a practical problem that limits the flow rate in the industrial use of granular materials,” said Onuttom Narayan of the University of California and Harsh Mathur at Case Western Reserve University in Ohio in their published paper.
The implications of understanding this transition are extensive, given that granular materials are used in industries ranging from agriculture and pharmaceuticals to construction. We’re talking about compacting granules into pills, processing cereals, and predicting the behavior of sediments where buildings are anchored.
Narayan and Mathur used numerical data from laboratory studies of frictionless polystyrene beads for their simulations, comparing their results with predictions from a branch of mathematics developed in the 1950s called random matrix theory.
Their focus was on the vibrations within bead packs. These vibrations create a ‘spectrum’ of frequencies that can propagate through granular materials, referred to by physicists as the system’s density of states.
Researchers have long studied the distribution of these vibrational states in granular materials nearing the jamming point, where particles are jostling before they get stuck. This problem lends itself to random matrix theory, which describes systems with many random variables. However, previous studies couldn’t conclusively determine which form of random matrix theory applied to granular materials.
Narayan and Mathur succeeded where others struggled: Their comparison of numerical simulations and theoretical predictions showed a specific distribution of statistical probabilities known as a Wishart–Laguerre ensemble that “correctly reproduces the universal statistical properties of jammed granular matter.”
They observed that as beads bump into each other, they act like springs, compressing and recoiling, such that even slight contacts can produce significant forces.
Moreover, the pair developed a model that could describe the properties of granular materials near and far from the jamming point. This achievement suggests a broader application of their model to understand granular physics.
“That the same model is able to reproduce both the static and vibrational properties of granular matter suggests it may be more broadly applicable to provide a unified understanding of the physics of granular matter,” Narayan and Mathur conclude.
The study has been published in the European Physical Journal E.
