Facebook
Twitter
Pocket
Reddit
Email
A mysterious form of matter is hiding in plain sight—in cereal boxes and sand dunes, and concrete mixers and volcanic slopes. It can flow like a liquid, fracture like a solid, and organize itself spontaneously in ways that defy physical theory and mathematical description.
This enigmatic stuff is granular matter—collections of particles, like sand. No one knows how to predict how the stuff behaves, in aggregate, based on what the individual grains are like, their shape and makeup. But being able to foresee how this sort of matter will act would be groundbreaking: A general theory of granular materials would be immediately valuable in areas as diverse as drug manufacturing, which requires well-mixed powders, and predicting when a rain-soaked hillside, scorched by wildfire, will cause a landslide, which involves particles of many sizes acting as a menacing collective.
A new paper published in the Proceedings of the National Academy of Sciences gets researchers closer to grasping how granular matter moves.
Scientists have had their work cut out for them, because even the simplest forms of granular matter—consisting of spherical particles of uniform size—are challenging to model. Subtle frictional interactions between not only neighboring particles but also more distant ones affect the material’s bulk behavior. Understanding granular mixtures—with particles of different sizes and shapes—is a more dizzying endeavor still.
Why would there be such a difference when the larger particles were cubes versus spheres?
Consider the “Brazil nut effect”—the tendency of large particles in a granular mixture to rise to the top when shaken or otherwise agitated. You can observe this in a can of mixed nuts: The biggest ones tend to be at the top. While earlier studies have explored such “granular segregation” for spheres of different sizes, few have looked into the role of grain shape. This is because the way non-spherical particles orient themselves affects the frictional interactions among them, and grain orientations change constantly in an agitated medium. Modeling this has, until recently, been too complex for numerical simulations. For non-spherical particles, the interactions between grains have to be updated for every time step, which is very computationally intensive.
But the new study from a trio of researchers—geophysicists and mechanical engineers at the University of Rochester led by Rachel Glade—explores the Brazil nut effect in mixtures with grains of both different sizes and shapes.
The scientists carried out a series of computer simulations, modeling how mixtures of spheres and cubes of different sizes behaved in a rotating drum (as in many industrial mixers) as well as in flowing water (as on a river bed). It’ll take some more research before results from experiments like these are applicable to truly unruly phenomena like landslides and mudflows, which involve a wider range of particle shapes and sizes. Yet despite how seemingly simple these systems are, experimenting with them yields some surprising results. In that way, how granular materials behave is an excellent analog for human interactions: familiar, ubiquitous, complex, and often counterintuitive.
To tease apart the effects of size and shape, the researchers first ran their model for two dry mixtures, one with big and small spheres, and one with big and small cubes. (Real-life examples of cubic or near-cubic grains include crystals of salt and sugar in food mixtures, and angular chunks of rock in a mud flow.) They tumbled these mixtures in a virtual drum, for 40 revolutions, well past the point at which the material reached a steady state, where the degree of segregation by particle size ceased to change. As the drum rotated, a broadly concentric pattern emerged, with larger grains forming a ring around the smaller ones. This happens because large grains tend to accumulate at the top of the avalanching pile and on along the lower wall of the drum, while smaller ones form an inner area of more slowly rolling particles.
The researchers quantified how much the grains segregated using a measure called “S” with values from zero, for randomly mixed grains, to one, for completely sorted grains. For a wide range of size ratios between the large and small particles, the experiments showed that spherical mixtures sorted themselves more efficiently by size than cubic mixtures did. In other words, at the end of the simulations, the large and small spheres were more strongly segregated than the large and small cubes were. The researchers suggest that this is because smoothly rolling spheres allow the largest particles to migrate to the outside of the pile while the sharp edges and corners of cubes limit the degree of “upward mobility” of large cubes in the drum.
If we dare to anthropomorphize this result, we might say that the cubes, in aggregate, enforce a kind of egalitarianism among large and small grains.
How do things shake up in wet conditions, like when a flowing current roils sediments along a river?
Intriguingly, for both cubes and spheres, the segregation level S first increases as the size difference among the particles in the mixture increases, but then the degree of sorting reaches a peak at a size ratio of around 10, beyond which self-sorting begins to decrease. The researchers still don’t fully understand why this transition occurs. In a socioeconomic analogy, it would mean that as wealth differences increase, people would separate themselves more and more by class (all too common)—until at a certain extreme disparity in affluence, they would begin to live in the same neighborhoods again (rarely observed).
In the next set of simulations, the researchers tumbled dry 50-50 mixtures of cubes and spheres of two distinct sizes—so, either large cubes with small spheres or small cubes with large spheres. The experiments again showed the sharp-corner effect of cubes: Any mixtures containing cubes and spheres sorted themselves less than mixtures containing only big and small spheres. Yet what the researchers found fascinating was that mixtures of large cubes and small spheres segregated themselves nearly as well as the sphere-only mixtures—and more than twice as well as mixtures of small cubes and large spheres. They didn’t expect to see that at all. They had predicted that cube-sphere mixtures would sort themselves equally well regardless of which shape in the mixture had bigger particles. Why, they wondered, would there be such a difference between mixtures in which the larger particles were cubes versus spheres?
Glade and her colleagues speculate that the shape of small grains is the primary factor that governs how mixed-shaped granular materials behave overall. They suspect that the amount of contact between the pointy parts of small cubes causes enough friction to stop large spheres from migrating toward the outside of the pile. In contrast, small spheres, with no sharp corners, do not act collectively to impede the passage of large cubes.
It is tempting to think of these phenomena as an economic or political allegory. In “small-cube” societies, it seems, strong and varied social connections may act to prevent stratification, while in “small-sphere” societies, weak and uniform bonds can facilitate the ascendancy of a class of oligarchs.
How do things shake up in wet conditions, like when a flowing current roils sediments along a river? With cubes in the mix, the granular mixtures become even more segregated than the mixtures containing only spheres. What’s more, not only large but also small cubes tend to migrate toward the top of the sediment. The researchers speculate that cubes experience a higher drag force from the fluid, which imparts, statistically, a small upward vertical component to their velocities as they tumble downstream. Spheres, meanwhile, have net downward trajectories and tend to accumulate at the bottom.
Once again, sociological analogies are tantalizing. In the face of strong political or cultural “currents,” it seems, rounded, compliant (or conformist) citizens roll comfortably along, while angular, idiosyncratic (or disagreeable) ones are prone to being buffeted about by these external forces—but may ultimately rise to the top. 
Lead image: pundapanda / Shutterstock
Get the Nautilus newsletter
Cutting-edge science, unraveled by the very brightest living thinkers.
