Segregation of a Granular Medium in a Drum Mixer

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Take a mixture of sand of two different sizes, with each size a different colour. Use the mixture to partially fill a horizontal tube. Then rotate the tube on its axis fast enough that the sand is continuously avalanching down the front face of the heap. You will find, if you have done things right, that the two sizes segregate along the axis of the tube, making a series of bands of colour, like this:

Drum mixer, schematic

This seems completely counterintuitive: it seems like the sand ought to mix, but it unmixes. It is usually cliamed that the explanation has to do with the fact that the two sizes have different angles at which they like to stream down the avalanching front of the heap. Mixtures of the two sizes like to stream at intermediate angles. The streaming angle at some axial location is coupled to the concentration of the mixture at that point. If there is a small fluctuation in the streaming angle, or the concentration, as a function of axial position in the tube, the streaming sand in the vicinity takes the path of descent which is appropriate to its concentration. This tends to reinforce the concentration fluctuation and there is an instability that leads to segregation. Indeed, one can clearly see the variation in streaming angle in the tube after the segregation gets established. However, other explanations have been offered in which the angle difference is not important. The general problem remains unsolved.

For other experiments on this, see the Sand Land Page of James Kakalios' group at Minnesota.

We had some fun getting things to work, trying various items from the health food store. Here is a snap of how not to do the experiment using dried rice and peas:(click to get full size)

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We are currently working on a version of this experiment, using white table salt and black hobby sand. Here is a pretty picture of nearly complete segregation a short tube:(click to get full size)

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More recently, we have done experiments using the same white table salt and black hobby sand in a very long tube. Here is a picture of that tube in action:(click to get full size)

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In this tube, we have observed traveling waves and other interesting dynamics. Here is an abstract of a paper on this, and here is another one. This wave phenomenon has recently been captured theoretically in a new model of the process: see here for a preprint. For more on this, see our sand papers page.

The people who have worked on this experiment are Kiam Choo, Michael Baker and Tim Molteno.

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The Experimental Nonlinear Physics Group, Dept. of Physics, University of Toronto, 60 St. George St. Toronto, Ontario, Canada, M5S 1A7. Phone (416) 978 - 6810, Fax (416) 978 - 1545 webmaster@mobydick.physics.utoronto.ca