Physicists Have Unraveled the Surprisingly Hot Mystery of Sand in an Hourglass
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To model how sand jams in an hourglass, physicists combine two gridlike math models.
Flowing sand is vulnerable to jamming, including a jamming transition that could be disrupted.
Granules and the subset of powders have their own entire area of physics.
In new peer-reviewed research, physicists try to navigate a thorny problem known as granular packing. When sand or any other granular material flows through a funnel, it can seize up and stop flowing in a way that seems spontaneous and inexplicable. This “jamming transition” marks when things like sand stop acting like liquids and start acting like solids, and the likelihood of this transition occurring seems to grow as sand flows faster, or if something strikes it from above. Interrupting the jamming transition could save a lot of energy and money for people who work with granules.
These qualities might remind you of oobleck, the Seuss-ian non-Newtonian fluid made of corn starch and water. It becomes solid when struck, but remains liquid otherwise. But oobleck only seems chaotic from the outside—its mechanisms, like unusual shear strength that makes the molecules cling together under stress, are pretty well understood. That’s not been the case for the hourglass problem, leaving an open question as to whose solution could really help companies that work with granular materials like sand.
In European Physics Journal E, Onuttom Narayan and Harsh Mathur have now claimed to have settled part of the question of granular packing. Over time, physicists have reduced the possibilities down to just random matrix theory—an influential math model where physics is represented by a grid of numbers, some of which can be random. This fits with our understanding of granular flow, which the researchers say sometimes behaves like springs, as explained by Clare Watson of Science Alert. But there are a number of random matrix types with different parameters and styles of distribution. Which one is right?
Previously, physicists believed hourglass sand was an orthogonal (or perpendicular-acting) random matrix, but could not decide between two types: Gaussian and Laguerre (mathematicians Gauss and Laguerre wrote influential styles of polynomials that have differently shaped graphs and slightly different applications, including in quantum mechanics). And while the study of hourglass physics has focused on Gaussian random matrices, this paper is a but of a persuasive essay to look elsewhere—not just at Laguerre random matrices, but also a random lattice theory.
Lattices are used in widely varying contexts in both pure and applied math, but Narayan and Mathur have “grafted” them here as a way to continue to model how granules flow (based on Narayan’s own previous work studying granules in a pile rather than a constricted flow). The lattice model fills in some gaps, and still arrives at similar values to the Laguerre random matrix model. It could be that this thorny problem is best described by considering both models at once, like the two lenses of 3D glasses.
The math and physics of this problem are interesting, but the jamming transition is also of real financial interest to anyone using granular materials like sand, or even large circular candies. If materials stop flowing, that creates problems and expenses in the supply chain. Powders are considered a subset of granules, and they’re even more vulnerable to expensive hiccups like clumping—they can be fine enough that they’re affected more directly by the forces that pull atoms and molecules together.
Indeed, the same way we prevent clumping using grains of rice or desiccant packets, sand chutes might need their version of the grain of rice that will stop the jamming transition and restore normal flow. That could also mean no more jammed candy machines at the grocery store. Finally, some good news.
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