Before you head off to the beach, you might want to jot down the equation in the image above. Because this is good news for sandcastle builders. Had you been depressed by the fact that science can easily demonstrate that the maximum height of a sandcastle is 20 cms (assuming you believe that what’s going on is driven by capillary forces), then you should celebrate the news that new science now allows for sandcastles several meters high. But then again, your own kids have probable demonstrated that elevations of significantly more than 20 cms are no problem at all, never mind the stark evidence of the towering sand sculptures routinely constructed in events around the world. Those capillary guys really need to get out of the lab, look around occasionally at reality, and get a life.
A just-published report from Nature, playfully titled “How to construct the perfect sandcastle,” is a work of serious science, and one of those delightful international collaborations between researchers, in this case from Iran, the Netherlands, and France.
The challenges that dry granular materials pose to science are seemingly endless, and have been reported on this blog too often to link here (just put “granular” into the search box for a sampling). But wet granular materials represent depths still unchartered by physics, and the act of building a sandcastle is the quintessential illustration of this – just add water to dry sand, and it becomes an entirely new and different material. Add more water and everything changes yet again (no wonder that researchers are trying to develop phase diagrams – like those for ice, water, and steam – for granular stuff). This recent work has taken a simple, ground-upwards (so to speak) approach to the mechanisms of sandcastle stability:
To account for the (in)stability of sandcastles, we show here that it is sufficient to consider that the limit of instability is reached when a column of sand undergoes a buckling transition under its own weight. An elastic rod becomes elastically unstable and buckles under its own weight when exceeding a critical height.
This, of course, again reflects real experience – adding that last bucket of sand to the top of the castle causes the whole thing to collapse, tragically and infuriatingly. There’s a standard equation for the maximum height of a cylinder before it buckles under its own weight that incorporates its radius and density, gravity (inevitably), a rather esoteric term that, quite frankly I don’t understand, and, critically, the elastic modulus of the material. This latter characteristic is critical – also known as Young’s Modulus, it describes how strong a material is, how well it responds to strain. In this case the strain is its own weight, and the strength of wet sand comes entirely from the surface tension effects of just a little water between the grains.
I sometimes use a dramatic demonstration of the potency of surface tension – simply wet a number of ping-pong balls, cluster them together, and see how many you can drag across the surface of a table by just pulling one of them. It’s surface tension that allows us to build a sandcastle, that gives the wet sand its strength. For physicists, the reality of exactly what’s going on between the grains is somewhat more complex, but the authors of this paper have taken the model for the strength of wet granular matter and worked it to develop an equation for the optimum strength, or elastic modulus. Plug that back into the equation for the maximum height of a cylinder, and you end up with the wonderful expression for “h,” the maximum height of a sandcastle, in the image above. The researchers then tested this by making their own cylinders of sand with varying diameters, and found that reality correlated well with prediction:
"To verify this experimentally, beach sand with an average radius of 100 mm was mixed with a small amount of deionized water. Cylindrical ‘sandcastles’ were constructed using non-wetting PVC pipes of different diameters cut in half over the length of the tube. The two halves were assembled, and the wet sand was put in the tube standing on vertically on a surface. The wet sand was poured into the pipe in small portions and compacted by dropping a thumper into the pipe at least 70 times. This process was repeated until the pipe was filled with sand up to a certain height. The two halves of
the cylindrical tube were then carefully removed and if the sand column was stable, a new experiment was launched filling the tube to a larger height, until the column collapsed. Several experiments were done at each filling height to ensure the reproducibility of the results. Figure 1 shows two columns of sand with height 27 cm and 60 cm with diameters 2 cm and 7 cm. This procedure was followed for 8 pipes of diameter ranging between 0.5 and 7.5 centimeters."
As they note, the compaction is critical. Look at the equation in the image at the head of this post – in order to maximise the height, h, of your sandcastle, you don’t have a lot of options. You can increase the radius of the base (“R”), but can’t do much about gravity (“g”), the size of the grains (“a”), or the density of your mixture (“ρ”), but that mysterious little “α” is, as the authors remark, a “potent power.” And α is a measure of how strong the bonds are between the grains – compact the sand and this increases, and therefore, very importantly, so does the potential height of your castle. The sand sculptors of the world are very well aware of how critical compaction is to their art.
Larry Nelson is a sand sculptor based in Venice Beach, California, and his work is extraordinary. Larry was of enormous help to me when I was writing the Sand book, and he achieves forms with sand that seem impossible: fragile soaring arches, interlocking curves.To achieve these exquisite results, he has developed an intimate relationship with his material, and his description of the character of wet sand eloquently summarizes its magic – and its physics:
It doesn’t take long to learn that water mixed with sand changes both completely. Two fluids become a formable solid. It may be counterintuitive, but anyone who has spent time in the playground knows this in the fingers.
Water tends to pull in on itself. This makes raindrops, rainbows, and flying sparks from every sprinkler. Anything in contact with the water feels this pull, imparting a tiny tensile characteristic to damp sand. It sticks together.
This adhesion is the essence of sand sculpture. It’s also the bane, because damp sand stickily resists being compacted beyond a certain point, no matter how hard it’s hit. Granular materials naturally form arch structures, tiny but powerfully resistant to compaction. Smack it on top, and your pile simply spreads sideways.
Here is just a sample of Larry’s wonderful creations – and note the compacted layers:
So, take the equation to the beach, be inspired by Larry Nelson, look after your radius, and make sure you maximise your alpha. Oh, and I almost forgot – the researchers found that “the optimum strength is achieved at a very low liquid volume fraction of about 1%” – you need 99% sand and just a very little water.
[The paper from Nature: Pakpour, M., Habibi, M., Møller, P. & Bonn, D. How to construct the perfect sandcastle. Sci. Rep. 2, 549; DOI:10.1038/srep00549 (2012). Thank you, Jan Kirchner, for pointing me to it and to Andrew Dwyer, my fearless Outback leader, for bringing the article about it in the Australian Geographic to my attention. Sand sculpture image at the head of the post from the Sand Castle Days 2006 event on South Padre Island, photographed by Sam on the Poof’n’whiffs blog.]