How do sand balls retain their integrity for so long? A friend showed me how to make sand balls at the beach, like shown here on this YouTube video.
We were both wondering how they managed to keep their shape way longer than any other sandcastle bits. I’m thinking this has to do with water tension being in a sphere having some kind of balance that makes it particularly strong.
Any idea?
 A: A great question about granular physics.
We have to start with sandcastle physics, such as discussed in this Nature article on "What keeps sandcastles standing?" or this Physical Review Letter on "How Sandcastles Fall". Sand balls are a bit different, but I think the essential physics is the same.
Sand castles (or balls) are held together by capillary adhesive bonds formed by interstitial water between the sand grains. For surface tension to work, there actually have to be some water surfaces, which is why both completely dry and completely saturated sand have no structural strength. As water is added to dry sand, it is energetically favourable for it to gather at the points of contact between the grains, which why so little water is needed establish bonds. X-ray microtomography indicates that as water is added to spherical grains, bonds quickly form creating grain dimers, trimers, …, until at about 1% water each grain has on average 6 bonds with other grains. As more water is added, the bonds coalesce into fewer but broader bonds.
According to "How to construct the perfect sandcastle", for clean fine beach sand with $\sim 0.1$ mm grains, a 1% volume ratio of deionized water"  gives optimum strength for sand castles. The shear_modulus of the sand falls off above or below 1% water content.
That's some of the science, but now we can speculate.  In the video, sand is rubbed on the outside of the ball to dry it out and this should maximize the strength of the outer shell of sand on the ball. This is because any sand on the surface that is too wet or too dry it will be weaker and fall off, leaving sand with the optimum amount of water.  The spherical shape minimizes surface area to volume ratio, which may allow the interior water to keep the surface sand at optimum strength for longer.
Of course, since the video shows real beach sand and water, it is also very likely that salt and organic matter in the water and sand may form a glue that binds the outer layer of sand together as it drys. It would be an interesting student research project get some sand and compare the strength of raw beach sand balls/castles and the same sand after very careful washing. If this glue turns out to be critical, we can hand the problem over to Chemistry Stack Exchange.
