Physicists Explain Sudden Stop in Sand Hourglass Flow

Older mathematical theories may finally clarify the behavior of granular materials, which can act as solids or flow like liquids unpredictably.

Consider the sand in an hourglass versus the sand on a beach. When poured slowly through a narrow opening, materials like sand, rice, or coffee flow easily. However, pouring or compressing these materials quickly can cause them to jam, transitioning from a flowing to a solid state.

Understanding this sudden transition is crucial to prevent unexpected blockages in desired flow conditions. Two US physicists believe they’ve made progress in describing this behavior in granular materials approaching the jamming point.

Flowing Granular Materials

“The tendency for flowing granular materials to jam and stop flowing at low densities is a practical challenge that restricts flow rates in industries using these materials,” explain Onuttom Narayan from the University of California and Harsh Mathur from Case Western Reserve University in Ohio.

This issue becomes even more complex when applied across diverse industries like agriculture, pharmaceuticals, and construction. Examples include compacting granules into pills, processing cereals, and predicting sediment behaviors in civil engineering.

In their research, Narayan and Mathur used data from previous studies on frictionless polystyrene bead packs. They compared their simulations of beads nearing the jamming point with predictions from a 1950s mathematical theory known as random matrix theory.

Vibrational Dynamics of Bead Packs

Narayan and Mathur focused on studying vibrations within bead packs. These beads vibrate at specific frequencies, resulting in a range or ‘spectrum’ of vibrational frequencies.

In simpler terms, granular materials selectively allow certain vibrational frequencies to travel through them, a characteristic known to physicists as the system’s density of states.

Previous studies have attempted to analyze how the distribution of these vibrational states changes as granular materials approach the jamming point, where particles are closely packed and on the verge of becoming stuck.

Random matrix theory, capable of describing physical systems with numerous random variables, is applicable to this problem. However, earlier research lacked the comparison of calculations with actual bead data, making it challenging to identify the appropriate random matrix theory ‘flavor’ to explain these vibrations.

Bridging Theory and Simulation

Narayan and Mathur addressed this gap successfully. Their comparison of numerical simulations with theoretical predictions revealed that a specific statistical probability distribution, known as a Wishart–Laguerre ensemble, accurately captures the universal statistical properties of jammed granular materials.

The key insight, according to them, was understanding that when beads collide, they compress and bounce back similar to a spring, leading to significant forces even with minor contact.

Additionally, the duo created a model that effectively describes the characteristics of beads near the jamming point as well as those far from it, where granular materials remain stationary.

Narayan and Mathur conclude that the model’s ability to accurately represent both the static and vibrational properties of granular matter suggests its potential for offering a comprehensive understanding of granular material physics.

Read the original article on: Science Alert

Also Read: Renowned Physicist Peter Higgs, Predictor of the Higgs boson, Dies at 94