Decades-old mathematics may finally explain some of the “weird” features of matter: granular materials that sometimes behave like solids and other times flow like liquids.
As strange as it sounds, just compare the sand in an hourglass to the sand on the beach. Pour slowly into tight spots and the sand, rice or coffee will flow freely. Funnel the same material quickly enough or press hard on it, and its particles will often clog, suddenly going from a flowing state to a solid state.
To avoid sudden blockages in situations where gentle flow is required, we need to understand how and when this sudden transition occurs. Two US physicists now think they have found a way to describe the behavior of granular materials close to the “disturbance point”.
“Flowing granular materials tend to ‘clog’ and stop flowing at low densities, which is a practical problem that limits flow rates in industrial uses of granular materials,” said Onuttom Narayan of the University of California and Harsh Mathur of Case Western University, Ohio Reserve University. This is explained in his published paper.
The issue becomes increasingly complex when you consider that it involves a variety of materials in industries as diverse as agriculture, pharmaceuticals and construction. We’re talking about compacting granules into granules to make pills, processing grains, and in civil engineering predicting the behavior of different sediments that our buildings may be anchored to.
In their simulations, Narayan and Mathur used numerical data collected by other researchers studying frictionless polystyrene beads in the laboratory.The pair compared their simulations of beads near interference points with predictions from a branch of mathematics Developed in the 1950s is called random matrix theory.
Specifically, Narayan and Mathur are studying vibrations inside bead packets. Although each batch is different, the beads vibrate at a specific frequency, creating a “spectrum” of vibrational frequencies.
In other words, a granular material allows only certain vibrational frequencies to propagate through it, which physicists call the system’s density of states.
Other researchers have tried to study how the distribution of these vibrational states evolves in granular materials close to the drying point, where the particles collide with each other before becoming stuck.
This question applies to stochastic matrix theory, which can be used to describe physical systems with many random variables. But without comparing the calculations to numerical data from the beads themselves, earlier studies were unable to distinguish between different “flavors” of random matrix theory that might explain the vibrations of granular materials.
Where these researchers failed, Narayan and Mathur succeeded: Their comparison of numerical simulations and theoretical predictions revealed that a specific statistical probability distribution, called the Wishatra-Gal ensemble, “correctly “It perfectly reproduces the universal statistical properties of clogging particulate matter.”
The key observation, they say, was the realization that when beads collide with each other, they compress and recoil like springs, so that the slightest contact between two beads can produce considerable force.
What’s more, the pair also developed a model that describes the properties of beads near and far from the interference point when the granular material is not moving.
“The ability of the same model to reproduce both static and vibrational properties of granular matter suggests that it may be more broadly applicable to providing a unified understanding of granular matter physics,” Narayan and Mathur concluded.
The study was published in European Physical Journal E.
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