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

Building sandcastles on the beach is a centuries-old tradition around the world, elevated to art in recent years through hundreds of annual competitions. Although the basic underlying physics is well known, physicists have continued to gain new knowledge about this fascinating granular material over the past decade. The latest breakthrough comes from the laboratory of Nobel laureate Andre Geim at the University of Manchester in England, where Geim and his colleagues solved a mathematical puzzle – “the Kelvin equation” – dating back 150 years, according to one. new article 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 healthy sand castle is one bucket of water to eight buckets of sand, although it is still possible to build a decent structure with varying water content. But if you want to build the kind of intricate, towering sandcastles that win competitions, you’d better stick to this ideal ratio.

In 2008, physicists decided to dig a little deeper into why sand gets sticky when wet. Using X-ray microtomography, they took 3D images of wet glass beads similar in shape and size to grains of sand. When they added liquid to the dry beads, they observed liquid “capillary bridges” forming between the individual beads. Adding more liquid made the bridges bigger, and when that happened, the surfaces of the beads came into contact with more water, further increasing the binding effect. However, the increased binding effect was canceled out by a corresponding decrease in capillary forces as the bridge structures became larger. The team concluded that even if the moisture content changes, the forces binding the beads together do not change.

This is similar to how soap bubbles will tend to be spherical, as it is the shape that minimizes the total area, thus 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 it takes to build the perfect sandcastle. “Likewise, a small amount of water between two grains of sand forms a small liquid bridge that minimizes the area between the water and the air,” he told Vice in 2015. “If one then moves one grain relative to the other, one automatically creates a surface. It costs energy and therefore there will be resistance to deformation. “

Mathematically, this type of capillary condensation – that is, how water vapor from ambient air condenses spontaneously within porous materials or between contacting surfaces – is usually described by a designed equation. by Sir William Thompson (later Lord Kelvin) and first referenced in an article from 1871.. It’s a macroscopic equation that has nonetheless been shown to be remarkably accurate down to the 10-nanometer scale, but the lack of a complete description that can explain even smaller scales has long frustrated physicists.

The typical humidity for this type of condensation is between 30 and 50 percent, but at molecular scales of 1 nanometer or less (a water molecule is about 0.3nm in diameter), only one or two molecular layers of water could fit within 1 nm. – thick capillaries. At this scale, Kelvin’s equation didn’t seem logical. It may not matter for sandcastle building, but capillary condensation is also relevant for many microelectronics, pharmaceutical and food industries. Geim and his colleagues have found a way to overcome the long-standing experimental challenges of studying capillaries at the molecular level.

Geim won the 2010 Nobel Prize in Physics for his groundbreaking experiments with graphene, a thin ordinary carbon flake only one atom thick, giving the material unusual properties. Physicists have struggled to isolate graphene from graphite (just like that found in pencils), but Geim and his Manchester colleague Konstantin Novoselov developed a new method using scotch tape used to collect flakes of thickness of the atoms of graphite. He also won an Ig Nobel Prize for his discovery of direct diamagnetic levitation of water – work that involved the use of magnets to levitate a frog in the lab. And he once created a gecko-inspired duct tape strong enough to hang a Spider-Man figure indefinitely from the ceiling.

For this latest work, Geim’s team painstakingly constructed molecular-scale capillaries by layering thin crystals of mica and graphite, with narrow bands of graphene between each layer to act as spacers. With this method, the team built capillaries of varying heights, including capillaries that were only one atom tall – just enough to fit a layer of water molecules, the smallest structure. possible.

Geim et al. found that the Kelvin equation is still an excellent qualitative description of capillary condensation at the molecular scale – contradicting expectations, since the properties of water are expected to become more discrete and stratified at the 1nm scale. Apparently, in this diet, there are microscopic adjustments to the capillaries, which remove any additional effects that might otherwise cause the equation to break as expected.

“It was a big surprise. I expected a complete break from conventional physics,” said co-author Qian Yang. “The old equation turned out to work well. A little disappointing but also exciting to finally solve the century-old mystery. So that we can relax, all of those many condensation effects and related properties are now underpinned by hard evidence rather than a hunch that seems to work, so it should be acceptable to use the equation. ‘”

“A good theory often works beyond its limits of applicability,” Geim said. “Lord Kelvin was a remarkable scientist, making many discoveries, but even he would surely be surprised to find that his theory – originally considering millimeter-sized tubes – even holds the scale of an atom. In his seminal article, Kelvin commented on exactly that impossibility, so our work proved him both right and wrong. “

DOI: Nature, 2020. 10.1038 / s41586-020-2978-1 (About DOIs).