Physicists solve 150-year-old mystery of equation governing sandcastle physics
Enlarge / The secret to a stable sandcastle primarily lies in the right proportion of water to sand. Mathematically, the forces at play are described by the "Kelvin equation," first referenced in 1871. (credit: ac productions/Getty Images)
Building sandcastles at the beach is a time-honored tradition around the world, elevated into an art form in recent years thanks to hundreds of annual competitions. While the basic underlying physics is well-known, physicists have continued to gain new insights into this fascinating granular material over the last decade or so. The latest breakthrough comes from Nobel Laureate Andre Geim's laboratory at the University of Manchester in England, where Geim and his colleagues have solved a mathematical puzzle-the "Kelvin equation"-dating back 150 years, according to a new paper just published in Nature.
All you really need to make a sandcastle is sand and water; the water acts as a kind of glue holding the grains of sand together via capillary forces. Studies have shown that the ideal ratio for building a structurally sound sandcastle is one pail of water for every eight pails of sand, although it's still possible to build a decent structure with varying water content. But if you want to build the kind of elaborate, towering sandcastles that win competitions, you'd be wise to stick with that ideal ratio.
Back in 2008, physicists decided to delve a little deeper into why sand becomes sticky when it gets wet. Using X-ray microtomography, they took 3D images of wet glass beads of similar shape and size as grains of sand. When they added liquid to dry beads, they observed liquid "capillary bridges" forming between individual beads. Adding more liquid caused the bridges to grow larger, and as that happened, the bead surfaces came into contact with more water, further increasing the binding effect. However, the increased binding effect was canceled out by a corresponding decrease of the capillary forces as the bridge structures grew bigger. The team concluded that even if the moisture content changes, the forces binding the beads together do not change.
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