A stroll on the beach can mean sinking your toes into smooth sand or walking firm-footed on a surface that appears almost solid. While both properties are commonplace, exactly what it is that makes granular materials change from a flowing state to a "jammed," or solid, state? Whether it's sand on a beach or rice grains in a hopper, being able to predict the behavior of granular matter can help engineers and manufacturers of a wide range of products.
In a study out this week in the journal Nature, researchers at Brandeis in collaboration with Duke University explain how granular materials are transformed from a loose state to a solid state when force is applied at a particular angle, in a process known as shearing. "Traditionally people thought of shearing as a mechanism for breaking up materials," says Dapeng Bi, a graduate student in the Martin Fisher School of Physics. "In this case, we find shear actually drives solidification."
Bulbul Chakraborty, the Enid and Nate Ancell Professor of Physics, and Bi, analyzed an experiment performed at Duke which used photo-elastic discs of two different sizes to represent granular materials such as rice or sand. The discs were placed into a plastic box whose shape could be precisely manipulated and measured. The box was illuminated from the bottom, forcing light through the discs. A polarized lens placed on top of the box revealed the photo-elastic discs creating colorful patterns -- called force chains -- caused by the pressure they received when the sides of the box were moved to create a rectangle. Using a computer program the Duke researchers were able to determine the amount of force that was exerted by the discs on each other.
"The polarized light changes the index of refraction of the materials and makes the patterns non-uniform," says Bi. "We then use those numbers to calculate the forces and the geometry of the contact network that the discs formed."
The researchers found that when the shape of the box changed due to shear, the discs exhibited a solid state even without the density changing. This, Chakraborty says, is remarkable because usually it is an increase in density that transforms loose material to a solid. "For theorists like us, these experiments are wonderful because we can see exactly what this system is doing," says Chakraborty. "How these patterns change as the discs are pushed and altered gives us information such as how many contacts each grain makes, and the force at every contact."
Chakraborty says that using this data she and Bi constructed a theory that explains how the solid is being formed. "It's possible that if there was no friction between the discs that they would have been able to slide past each other and not get jammed," says Chakraborty. "We now are performing computer simulations to see if shear jamming will occur without friction."
In an abstract written in 2008 in Jamming of Granular Matter, Chakraborty and Robert P. Behringer of Duke University explained that jamming is the extension of the concept of freezing to the transition from a fluid state to a jammed state. Understanding jamming in granular systems, they say, is important from a technological, environmental, and basic science perspective. A jamming of grains in silos can cause catastrophic failures. Avalanches are examples of unjamming, which need to be understood in order to prevent and control, such as the avalanche that killed pro skier Jamie Pierre on November 13, 2011.
Shearing is a major force in nature, explains Chakraborty. When wind blows over the earth, shearing occurs in the sand. Understanding what shear does, she says, is very important.
"We have a very good theoretical framework as to how water behaves, or ice or air," says Chakraborty. "We don't have any fundamental theoretical framework to predict how sand behaves when the wind is blowing fast or slow."
This information could potentially be used to further understand things like avalanches and earthquakes and erosion. "Those are effects of shearing of granular materials," says Chakraborty. "What we're trying to do is get at a basic understanding of how sand responds to shear. Most natural forces are shearing forces."
The behavior seen here is similar to "shear thickening," which has been used when manufacturing bulletproof vests that present as a soft material when worn, but hardens upon impact of a bullet.
"The research shows that friction can fundamentally change the nature of granular materials in intriguing ways," says Daryl Hess, program director for condensed matter and materials theory at the National Science Foundation. "Friction and shear reveal the richness of possible states of granular matter, pointing us down a road paved with new discoveries. These may expose deeper connections between jamming and seemingly unrelated phenomena spanning from earthquakes to transformations occurring in other kinds of matter, like water to ice."
In industries where hoppers are used, like loading rice grains onto a truck for example, jamming can be a problem. One possible solution, says Chakraborty, is to change the traditional shape in order to both prevent and break up jams.
"We need these sort of laboratory-based experiments to construct and test theories," says Chakraborty. "Once you get into an industrial situation things are not controlled enough to understand."
- Dapeng Bi, Jie Zhang, Bulbul Chakraborty, R. P. Behringer. Jamming by shear. Nature, 2011; 480 (7377): 355 DOI: 10.1038/nature10667
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