Avalanches and mixed solids.
As a step toward elucidating the basic physical principles underlying the mixing of solids, researchers have now proposed a simple model that captures some of the key features of slow granular mixing -- a process frequently used in industry. Chemical engineers Guy Metcalfe, Troy Shinbrot, J.J. McCarthy, and Julio M. Ottino of Northwestern University in Evanston, Ill., describe their approach in the March 2 Nature.
The researchers focused on the mixing behavior of particles in a hollow vertical disk partially filled with dyed crystals of table salt. The transparent cylindrical container is thin enough that as it rotates about a horizontal axis, the particle motion inside is effectively two-dimensional.
As the disk slowly rotates, the enclosed material's upper surface becomes increasingly steep, eventually triggering an avalanche. Such an avalanche transfers a thin wedge of material from the upper to the lower part of the inclined surface (see diagrams). This material remains there until the disk's rotation brings it back to the top. By considering the geometrical behavior of these wedges without going into the details of particle motion, Ottino and his coworkers found they could make useful predictions about granular mixing.
When the disk is exactly half full, wedges of material suffer repeated avalanches, but no mixing between the wedges occurs. If the disk is less than half full, material from a given avalanche doesn't stay in the same wedge in successive avalanches. The material gets mixed up. When the disk is more than half full, wedges of material mix, but because these wedges don't penetrate to the disk's center, the process leaves an unmixed core.
Computer simulations and calculations based on the geometry of avalanche mixing show that the most efficient mixing occurs when the disk is a quarter full. Experiments produce practically the same result.
The researchers have demonstrated "that a simple but original model can describe a good deal about the particularly important process of mixing," comments Robert P. Behringer of Duke University in Durham, N.C., in the same issue of Nature.
Now, Ottino and his coworkers want to extend their model to more complicated situations in which mixing occurs in three dimensions and in noncylindrical containers. They would also like to see what happens when particles have a range of sizes.
Avalanche mixing in quarter-filled (a), half-filled (b), and three-quarter-filled disks (c). As the disk slowly rotates, material from an uphill wedge (dark gray) shifts to a downhill wedge (white).
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|Title Annotation:||researchers develop model that demonstrates process of slow granular mixing of solids|
|Date:||Mar 11, 1995|
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