As I'm sure I've said before, to watch the sands of an hourglass in action is to observe all kinds of natural phenomena at work - and all kinds of questions to which we have no answers. It's not just the cascades and avalanches, but the liquid stream of grains itself that holds mysteries, interactions and behaviours too minute and too rapid for the eye and the brain to grasp. Traditionally, we have to resort to statistics, to averages, to clumps and groupings - to model at the level of individual grains is just too complex and there are too many of them. But now we are beginning to be able to peer into the nano-world of an individual grain and to simulate its interactions with its colleagues, thanks to the continuing, revelatory, research into granular materials. Friends have recently drawn my attention to two specific examples that I'll mention here.
The University of Chicago has long been a fluidised bed of granular behaviour research, with Sidney R. Nagel and Heinrich M. Jaeger as the uber-gurus of the bizarre (remember the Brazil nut effect and then the reverse Brazil nut effect), and now Jaeger, together with his students and colleagues, has yet again achieved something extraordinary. Look again at the flowing stream of sand grains in the hourglass: until recently, studies of so-called "free falling granular streams" tracked shape changes in flows of dry materials, but were unable to observe the full evolution of the forming droplets or the clustering mechanisms involved. But, as recently reported in Science Daily, with the aid of a very expensive and very high-speed camera, Jaeger has been able to track the formation of "droplets" in the granular stream and show that surface tension effects 100,000 times smaller than those that operate in liquids are at work. The dry material behaves as if it were a liquid with very low surface tension - as suggested in the graphic at right, above, and a short but dramatic video is available at the NSF site here.
"At first we thought grain-grain interactions would be far too weak to influence the granular stream," said John Royer, a graduate student on the team. "The atomic force microscopy surprised us by demonstrating that small changes in these interactions could have a large impact on the break up of the stream, conclusively showing that these interactions were actually controlling the droplet formation." So streaming sand not only looks like a liquid, but actually behaves like one, once again raising the question of exactly what form of matter this is. And, as with all this kind of research, it's not just of academic interest - the efficient filling of pharmaceutical capsules is but one (important) industrial process that could benefit. And it's also a further wonderful example of the deeper we look, the more complex things become and the more the questions that are raised. As Jaeger says, these "experimental results open up new territory for which there currently is no theoretical framework."
So Jaeger is breaking new ground in the experimental observation of individual grain interactions, but are we doomed to be unable to computationally model these things, overwhelmed by the sheer numbers, the scale of the problem in a different sense? Well, no, not if Dan Negrut, Toby Heyn, and Justin Madsen at the University of Wisconsin have anything to do with it. Working at the Simulation-Based Engineering Laboratory in Madison, they have developed both the theoretical and mathematical basis, and the power of parallel computing, for modelling the movements of huge numbers of grains. There's a report on their work on Science News, but the best thing to do is to go to their website and enjoy some of their simulations (you'll need to download the VLC viewer for which instructions are given). Not surprisingly, my favourite is their virtual hourglass (illustrated at left at the top of this post); this uses the relatively modest number of 25,000 individual "objects", i.e., grains, but it's incredibly realistic. There are other simulations involving hundreds of thousands of grains and the capability is growing all the time - Negrut hopes his simulation will analyze millions of grains in a single day, if not a matter of hours. To model the interactions of individual grains requires a firm theoretical foundation and the team has made great progress in establishing this; a planned collaboration with Professor Alessandro Tasora from the University of Parma will further refine this. Negrut kindly supplied me with a preprint of the group's forthcoming paper, A Parallel Algorithm for Solving Complex Multibody Problems with Stream Processors. Unfortunately, I have to confess that it's entirely beyond me, even the abstract outstripping my modest mathematical and computational capacity. Here's an extract - I recognised two sand grains in Figure 1 and was then terminally lost:
But among the simulations viewable on their website is one of work they are doing on a Mars rover moving over granular materials. This, as I recently noted (Stuck in the Sand) is currently a major problem for the Mars Rover Spirit, and its engineers back on earth. Thanks to being again alerted by a reader, I now find that the Rover's dilemma (sounds like the name of a pub) is being used to good effect to study details of the diverse granular materials revealed by its spinning wheel. As reported in Science Daily, "One of the rover's wheels tore into the site, exposing colored sandy materials and a miniature cliff of cemented sands. Some disturbed material cascaded down, evidence of the looseness that will be a challenge for getting Spirit out. But at the edge of the disturbed patch, the soil is cohesive enough to hold its shape as a steep cross-section." Ray Arvidson of Washington University in St. Louis, deputy principal investigator for the science payloads on Spirit and its twin rover, Opportunity, said "We are able here to study each layer, each different color of the interesting soils exposed by the wheels," adding that "The layers have basaltic sand, sulfate-rich sand and areas with the addition of silica-rich materials, possibly sorted by wind and cemented by the action of thin films of water. We're still at a stage of multiple working hypotheses." Below is an image of the revealed materials (NASA/JPL-Caltech/Cornell University).
There is, literally, no end to the extraordinary journeys that granular materials can take us on, so next time you watch an hourglass in action, think of low surface tension liquids, parallel computing and Spirit.
[I have to thank Richard Cathcart and Dominion Rognstad for drawing my attention to these topics - my theme for this blog is so wide-ranging that I can't possibly keep track of all the items of interest and I very much appreciate any suggestions and links that readers might send me.]