June 2009

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-gurusof 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.] SIGNATURE

Originally published at: https://throughthesandglass.typepad.com/through_the_sandglass/2009/06/index.html