How Are Sandcastles Formed? 150-Year-Old Math Equation Helps Solve Mystery Behind Beach Sculptures

Building sandcastles seems like an innocent, fun activity for children. But how do sand particles hold together and maintain the shape?

Sandcastles could be children's earliest introduction to physics if a recent study from a group of physicists, led by Nobel Laureate Andre Geim, is anything to go by. Sand sticks together to form the beach sculptures because of a process called capillary condensation.

The group of scientists from the University of Manchester explained that the process is a "textbook phenomenon." It involves "few molecular layers of water condensing in the minuscule space between adjoining surfaces," the team explained in a study published in the journal Nature.

Capillary condensation affects other natural phenomena such as friction, adhesion, stiction, lubrication and corrosion. The process is also vital in many processes used by microelectronics, pharmaceuticals and food industries.

The study showed that capillary condensation can be best explained using a 150-year-old equation, proposed by Victorian physicist Lord Kelvin in 1871.

The study is significant not just because it explains how sandcastles are formed, but more importantly, the result gave the Kelvin equation its long-overdue recognition. For decades, the Kelvin equation has been referred to as a "poor man's approach" within the scientific community.

The Kelvin equation was originally based on observations of water menisci in millimeter-sized tubes. The new study found that the Kelvin equation can also be used in observing water in tubes that are as small as 10 nanometers or the size of a human hair. Interestingly, even Kelvin didn't believe that his equation was applicable even at the one-atom measurement, the researchers noted.

"Good theory often works beyond its applicability limits. Lord Kelvin was a remarkable scientist, making many discoveries but even he would surely be surprised to find that his theory – originally observed in millimeter-sized tubes – holds even at the one-atom scale," Geim, who is also a professor at the University of Manchester, said in a press release.