Physicists Can Finally Explain How Sand in an Hourglass Can Suddenly Stop Flowing

Granular materials such as sand present a fascinating dichotomy: they flow freely as a liquid or aggregate into a solid state.

Granular materials, such as sand or rice, present a fascinating dichotomy: they flow freely as a liquid or aggregate into a solid state, a phenomenon that has puzzled scientists and engineers for decades. Recently, researchers turned to a mathematical framework dating back more than half a century, hinting at a possible solution to the mysteries surrounding these enigmatic substances.

In a landmark study, physicists Onuttom Narayan of the University of California and Harsh Mathur of Case Western Reserve University in Ohio have pioneered a new approach to unraveling the behavior of granular materials as they approach a critical threshold known as the “sticking point.

where the flow transitions into jammed states – where, for example, sand stops flowing into an hourglass. Their findings, documented in published work, address a fundamental challenge encountered in various industries: the abrupt transition from flow states to jam states at low densities, which can hinder efficient handling of granular materials. Narayan and Mathur’s research explores the vibrational dynamics of granular materials using advanced numerical simulations and insights drawn from random matrix theory, a remarkable branch of mathematics that began in the 1950s.

By examining vibrations in frictionless arrays of polystyrene beads under controlled laboratory conditions, the duo revealed a specific distribution of vibrational frequencies, known as the density of states, which encapsulates the behavior of granular materials approaching the point of entanglement.

Their research revealed a striking parallel between the statistical properties of vibrating granular materials and theoretical predictions derived from random matrix theory. By contrasting numerical simulations with theoretical predictions, Narayan and Mathur demonstrated that a particular statistical probability distribution, called the Wishart-Laguerre set, accurately reflects the universal characteristics of granular matter entanglement.

Furthermore, the researchers formulated a comprehensive model capable of elucidating both the static and vibrational properties of granular materials, offering a coherent framework for understanding their physics in different situations. The implications of this research extend well beyond granular materials, suggesting broader applications of the proposed model in various fields.

By shedding light on the complex behavior of granular materials, Narayan and Mathur’s study heralds the prospect of more effective and evidence-based strategies for managing these ubiquitous substances in various industrial contexts.