Kitchen physics - making cross-bedding

It will be obvious to those who have read items on this blog that I find the bizarre behaviours of granular materials fascinating. It was only as I was working on the book that I encountered just how weird and wonderful these behaviours are, how much extraordinary research in physics and engineering is being done, how important these things are, and how often we unwittingly encounter them, in our daily lives. One of the signature characteristics of any granular material, whether it's sand, nuts, or the contents of your pharmaceutical capsule, is its extreme dislike of being mixed. A mixture of different types of grains will take advantage of the slightest opportunity to un-mix itself, to self-segregate; when shaken, stirred, rattled, vibrated, rotated - and even just poured - that's what granular materials do, they self-segregate. And one result of self-segregation is the formation of patterns, patterns that we can easily recognize in nature.

One of the deceptively simple demonstrations of this behaviour was the focus of research by Hernán Makse, published in Nature back in 1997. The paper by Makse, then at Boston University, and his colleagues, was titled "Spontaneous stratification in granular mixtures," and one of the illustrations is shown (with permission) at the top of this post. They demonstrated that a mixture of sand and sugar would separate into its components if you simply poured it slowly and evenly into a pile. “A miracle occurs,” said Eugene Stanley, one of the collaborators. “It’s like throwing a deck of cards on the table and having all the blacks fall on one side and the reds on the other.” Makse, Stanley, and their colleagues conducted a series of experiments using different materials - sand, glass beads, sugar crystals - and the results were clear. Typically, larger grains will have a steeper angle of repose than smaller ones, and they will roll down the slope more energetically. The smaller grains tend to get stuck at the top of the pile, the larger ones at the base—they spontaneously segregate. But things become more complicated. As the different angles of repose of different grains are reached and exceeded, successive avalanches will be made up of different-sized grains. The cascades of smaller grains will stop first, to be then covered by a layer of the larger grains still on the move. The process repeats itself over and over, creating a layered pile. Different (and unpredictable) results can be achieved by varying the size, density, and shape of the grains and therefore their angle of stability or repose.

The result is a very distinctive pattern. Philip Ball, the superb science writer, is fascinated by patterns in nature, and his book on the subject, The Self-Made Tapestry is one of my favourites. He has just updated the book into a series of three, Nature's Patterns: A Tapestry in Three Parts, the parts being Flow, Branches, and Shapes, and last month gave a talk at the Royal Institution in London, an event that I couldn't miss. It was riveting stuff, but I was particularly fascinated by the fact that, in the middle of the talk, he repeated Makse's experiment, like magic trick, before my very eyes. The device used is a Hele-Shaw cell, first developed (not a surprise, this) by the engineer Henry Selby Hele-Shaw in the early part of the last century to experiment with various kinds of fluid flow (Hele-Shaw invented, amongst many other things, the variable-pitch propeller). For granular flow experiments, it's a simple narrow box with perspex (plexiglass) sides, and, after his talk, Ball kindly showed me just how easy it is to make, and how he used a simple mixture of sugar and sand for his trick.

I resolved to try this for myself - the drama of the demonstration being ideal for the occasional talk that I give; not being confident about sawing perspex in my apartment garage, I once again sought the help of Trevor (who had built my arenophile shelves). When he arrived with the device, I was like a kid with a new toy - but nervous as to whether it would work. I had prepared a mixture of "play sand" and granulated sugar, and set up (my wife again long-suffering) in the kitchen. With a slightly shaking hand and an envelope with the corner cut off as a makeshift funnel, I poured the mixture into the cell (and on to the kitchen counter, floor, etc.). To my amazement (and that of my audience), it worked!

 

All I had to do was control the rate at which I poured, and the avalanching grains did exactly what they were supposed to do - they self-segregated and spontaneously stratified. In the interests of cleaning up the kitchen, I moved the cell, causing further avalanching and truncation of the underlying original pattern. I then tried it with just the play sand and, lo and behold, the dark grains separated themselves from the light grains. To the geologically-inclined, this pattern will be all too familiar - I had made cross-bedding. The second image below shows my experiment on the left and natural cross-bedding on the right.

 

Cross-bedding is formed when any mixture of sand grains is swept along by a current - whether water or air - and deposited, building up a slope, down which the next surge of grains cascades. Cross-bedding (so-called because it forms at an angle to the main surface of deposition, e.g. the beach) is found in ripples, river sand banks, marine bars, and dunes - essentially anywhere that sand falls out of a current. It tells us a great deal about the nature of the fluid flow, its direction, strength and so on - and the only reason we can see it is because of self-segregation and spontaneous stratification, grains of different colours (and different physical characteristics) picking out the internal structure. And, thanks to Hernán Makse, Philip Ball, my long-suffering wife, and Trevor, I had demonstrated this in my own kitchen.

I was, I suspect fairly obviously, thrilled to bits about this success. I now await delivery of a veritable rainbow of different coloured sands and glass beads with which I can expand my play; this is, of course, possible thanks to the new tradition of exchanging sand at wedding ceremonies and the keepers of aquaria requiring coloured substrates against which the denizens are best displayed. But this is also a simple and terrific way of demonstrating granular physics, natural pattern formation, and geological processes in any classroom. I discovered that Makse has developed a classroom version available here and that there are instructions (in different languages) for making various forms of Hele-Shaw cells on this site. 

[For further exploration of granular material behaviour, Makse's home page is a good starting point; make sure to have a look at the page on the spontaneous stratification experiment and the one on cross-bedding. For a spectacular series of images and animations of cross-bedding and bedforms in general, go to the work of Dave Rubin and Carissa Carter at the USGS: http://walrus.wr.usgs.gov/seds/bedforms/pindex.html]

Comments

[Jules]

Beautiful work Michael. The way the light reflected of the glass one can imagine immense sand dunes and a rich blue sky filled with mixed and cirrus shaped clouds.

I wonder how many other scientists kitchens(with long suffering wives or mothers)have doubled as laboratories?!

[Sandglass]

Or laboratories doubled as kitchens?

[Kamau]

Very interesting