The Ascent of Sand

/ by Maggie Wittlin /

Physicists devise a model for sturdier sandcastles

“Einstein’s down on the beach staring into the sand,” sing the Counting Crows on their album Films About Ghosts. Alas, Albert has departed this earth, but if our mustachioed friend were still around, he would be staring at a web of grains held together by elastic water bridges, according to recent research by a group of MIT and Clark University granular physicists. By the researchers’ estimation, the mush between Einstein’s toes could best be turned into a sandcastle if the grains are small, the walls of the castle are short, and the liquid between the grains has a high surface tension.

In a paper published in Nature Physics, Sarah Nowak, Dr. Azadeh Samadani, and Professor Arshad Kudrolli revamp old theories of how wet sand holds together. The team examined how sand behaves in the presence of a liquid by mixing idealized sand with either water or silicon. They put each mixture in a tumbler and observed how far they could tilt the tumbler before the sand avalanched.

Physicists tend to approximate everything from electrons to their mothers as solid spherical masses, and sand is no exception; the researchers used tiny glass balls in place of sand grains.

Lucinda Wierenga, a sandcastle instructor, champion sandcastle builder, and author of Sand Castles Made Simple, said that flat-grain and angular-grain sand is best for building. The model the researchers used only reflects round-grain sand, which is the worst kind for sandcastles.

Even under imperfect, round-grained conditions, the researchers were able to determine a few factors that make for stable structure. According to Kudrolli, the team found that the maximum angle of tilt without avalanche was improved by smaller grains, smaller tumblers, and higher surface tension of the liquid.

Nowak explained that the surface tension of the liquid influenced the maximum angle of tilt because the liquid holds the grains of sand together by forming bridges between them, and that high surface tension makes for strong bridges.

“The surface tension of the liquid gets you liquid bridge surfaces, kind of related to the meniscus you see when you have a glass of water,” she said. “There’s an energy associated with having a surface of liquid. If you have a bridge between two particles and you try to pull them apart, you’re increasing the surface, and increasing that surface increases the energy.”

This increase in potential energy creates a force that pulls the grains of sand together.

Knowing about water bridges can do more than boost your scientific street cred; it can help you decide how much water to add to sand in order to make the stablest, most architecturally sound sandcastle on the beach.

Kudrolli said that either too little or too much water could be problematic. If you have too little water, bridges don’t form uniformly, and if you have too much water, the grains of sand are “drowned” in the liquid—no bridges form.

“It’s a forgiving ratio once you put in a certain amount [of water],” according to Kudrolli.

Nowak said a mere bucket of water for every 500 buckets of sand you use in your castle would probably suffice.

Wierenga, the castle-builder, said that, because of the idealized conditions of the study, it is only applicable to a small portion of the sand actually found at beaches.

“Some sand works better for sand castle building than other sand. If sand has more natural clay in it, it requires a lot less water,” said Wierenga, who sometimes goes by the pseudonym Sandy Feet. “The clay holds the moisture in, so if the sand doesn’t have a lot of clay in it, the water just runs right through.”

The scientists said that, in their model, faults in the sand structure occur at points of maximal pressure, not necessarily at the surface of the sand, as old models purported. Therefore, steep angles can only be achieved with very small walls.

“If failure occurs at the surface, the liquid bridges have to support the weight of only one layer of particles. This is unaffected by the size of the pile,” Nowak said. “If failure occurs within the pile, for the same surface angle, there is more material for the liquid bridges to support if the pile is larger. This means that larger piles are less stable.”

Wierenga said that she can make a large, steep wall with sand with natural clay.

“We can probably do five or six feet,” she said. “That would be sheer, but it probably wouldn’t stand that long.”

The scientists are not fazed. While their model may only apply to idealized sand, Kudrolli said it fits the data far better than any of its predecessors.

Originally published September 30, 2005

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