Physicists solve 150-year-old mystery of equation governing sandcastle physics

>"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."

[...]

"...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..."

[...]

"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."

[...]

"Mathematically, this kind of capillary condensation—i.e., how water vapor from ambient air will condense spontaneously inside porous materials or between touching surfaces—is typically described by an equation devised by Sir William Thompson (later Lord Kelvin) and first referenced in an 1871 paper. It's a macroscopic equation that nonetheless has proven to be remarkably accurate down to the 10-nanometer scale, but the lack of a complete description that can account for even tinier scales has long frustrated physicists."

[...]

"It's similar to how soap bubbles will tend to be spherical because that's the shape that

minimizes the total surface area,

thereby using the least energy,

according to Daniel Bonn, a physicist at the University of Amsterdam who has conducted several experiments with sand over the years. Bonn has become something of an expert on what's involved with building the perfect sandcastle. "Likewise, a small amount of water between two sand grains forms a small liquid bridge that minimizes the surface area between the water and the air..."

A physics professor once taught "a small amount of water is like glue, a lot of water is like a lubricant"