Mixing liquids is easy, or at least scientifically understood: a drop of food coloring will eventually mix into a cup of water through diffusion, while a dollop of cream can be mixed into coffee with a spoon through what is called turbulent mixing.
But what about materials that have properties of both liquids and solids, such as concrete, paint and sand? Called yield stress materials, these mixtures can both flow like liquids and remain still like solids. Understanding how these materials mix has implications for industries such as pharmaceuticals and concrete manufacturing, but little is currently known about how best to mix them.
In a new paper in Nature Communications, researchers at Northwestern Engineering report that mixing yield stress materials creates both mixed and non-mixed regions, providing a fundamental first step in understanding how to design mixing protocols. Julio Ottino, Paul Umbanhowar and Richard Lueptow served as the paper's co-authors.
"The theoretical foundations of flow of granular matter are still very incomplete," said Ottino, professor of chemical and biological engineering. "We found remarkable persistence of order amid chaos."
The researchers wanted to know how well granular material could be mixed in a basic system: a spherical tumbler. Would the material mix like a solid, through a ‘cutting-and-shuffling’ method, similar to a deck of cards? Or would it mix like a viscous liquid such as honey, through a ‘stretching-and-folding’ process?
"This gives us a whole new tool to understand what mixes and what doesn't mix. These results can ultimately be used as a design tool."Paul Umbanhowar, Northwestern Engineering
To find out, the researchers half-filled a spherical tumbler with 2mm-sized glass beads. When the tumbler was rotated, they found that the top layer of beads flowed like a fluid down to the bottom of the sphere, while the other beads remained in place, like a solid.
Next, the researchers tried mixing the beads by rotating the tumbler along different axes. To track how well the beads mixed, they placed a 4mm tracer particle within the beads and ran the rotations over and over, sometimes up to 500 times, while taking X-ray images of the sphere to see where the tracer particle ended up.
Despite trying several different rotational protocols, the researchers found there were inevitably regions that mixed and regions that did not mix. This was caused by the interplay between the two mixing methods: cutting-and-shuffling and stretching-and-folding.
"Even though the material often moves in wedges in this cutting-and-shuffling manner, all those wedges do is move around together," said Umbanhowar, research professor of mechanical engineering. "There are regions that never get mixed."
Understanding this concept may lead to insights in interesting and unexpected places, such as the Spanish Christmas Lottery, where 100,000 small wooden balls with unique ticket numbers are tumbled in one sphere, while 1807 balls labeled with prizes are tumbled in another. During the drawing, one prize ball and one corresponding ticket number are plucked from each sphere until the prize ball sphere is empty. But if the tumbler includes regions that are mixed and regions that aren't, the ball's initial placement in the tumbler becomes an outsized factor in whether it will be chosen.
"There is an expectation of randomness, but our results show that this is not the case," Ottino said.
The researchers hope to conduct future studies to show how this information can be applied across different materials. "This gives us a whole new tool to understand what mixes and what doesn't mix," Umbanhowar said. "These results can ultimately be used as a design tool."
This story is adapted from material from Northwestern Engineering, with editorial changes made by Materials Today. The views expressed in this article do not necessarily represent those of Elsevier. Link to original source.