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Making sandcastles on the beach is a time-honored tradition around the world, thanks to hundreds of annual competitions. While basic underlying physics is well known, physicists have continued to gain new insights into this fascinating granular material over the last decade or so. Recent advances have come from the laboratory of Nobel laureate Andre Game at Manchester University in England, where Game and his colleagues have solved a math puzzle – the “Kelvin Equation”, a new paper published recently in Nature after 150 years.
All you need to make a sandcastle is sand and water; Water acts as a kind of glue that holds the sand grains together by capillary forces. Studies have shown that the ideal ratio for building structurally noisy sandcastles is one pile of water for every eight piles, although it is still possible to build a suitable structure with different water content. But if you want to build the kind of competition-winning, expansive, wide sandcastle, it would be wise for you to stick to that ideal ratio.
Back in 2008, physicists decided to take a closer look at why sand becomes moist when it gets wet. Using X-ray microtography, they took 3D images of a wet glass structure of the same shape and size as a grain of sand. When they added liquid to the dry nest, they observed the liquid forming a “capillary bridge” between the individual nests. Adding more fluid caused the bridges to get bigger, and as it happened the surface of the bead became more exposed to water and the binding effect increased. However, as the bridge structures grew larger most of the bounding effect was eliminated by a corresponding decrease in the forces of the capillaries. The team concluded that even if the humidity changes, the binding forces to the bead do not change.
It is similar to how soap bubbles tend to be spherical, as it is the shape that reduces the total surface area, at least there using a razor, a physicist from the University of Amsterdam who has done many sand experiments over the years. . Bone has become something of a complete expert involved in creating the perfect sandcastle. “Similarly, a small amount between two grains of sand creates a small liquid bridge that reduces the surface area between water and air,” he told Wise in 2015. “If one moves one grain after another in relation to another, it automatically creates a surface area. This energy consumes energy, and therefore will be resistant to distortion.”
Mathematically, this type of capillary contraction – i.e., how the vapor from aerated air will decrease spontaneously between porous materials or touching surfaces – is typically described by Sir William Thompson (later Lord Calvin) and first reference Given in the 1871 paper. . It is a macroscopic equation that has proven to be remarkably accurate on a 10-nanometer scale, but the lack of a full description of what is responsible for even small-sized scales has long been frustrated by physicists.
The typical humidity for this type of condensation is between 30 and 50 percent, but 1 nanometer or less (one water molecule is about 0.3nm in diameter), one or two atomic layers of water can fit within 1nm. -Solar capillaries. On that scale, the Kelvin equation makes no sense. It may not make a difference to make sandcastles, but capillary condensation is also relevant to many microelectronic, pharmaceutical and food processing industries. Gim and his colleagues found a way to overcome the long-standing experimental challenges of studying capillaries on the nuclear scale.
Gamine won the 2010 Nobel Prize in Physics for his groundbreaking experiments on graphene, a thin flake of ordinary carbon that was only one atom thick, which gave the material unusual properties. Physicists struggled to separate graphene from graphene (as found in pencils), but Game and his Manchester colleague Konstantin Novoselov developed a novel method using scotch tape used to collect atomic-thick flakes from graphite. He also won the IG Nobel Prize for his discovery of the diamagnetic levitation of water – a feature famously included in the lab using magnets to draw frogs. And he once made a gecko-inspired sticky tape that could suspend Spider-Man action figures from the ceiling indefinitely.
For this latest work, Gim’s team built atom-scale blood centers by placing atom-thin crystals of mica and graphite on top of each other, with narrow strips of graphene between each layer to serve as interstices. With this method, the team created capillaries of varying heights, including capillaries that were only one atom high – a structure as small as possible, fitting only one layer of water molecules.
Jim Et al. Found that the Kelvin equation is still an excellent qualitative description of capillary condensation on a molecular scale – contradicting expectations, as the properties of water are expected to become more complex and layered on a 1nm scale. Apparently in that regime, there are microscopic adjustments in the capillaries, to suppress any additional effects that might break the equation as expected.
“This was a big surprise. I was expecting a complete breakdown of traditional physics,” said co-author Qian Yang. “The old equation went well. A little disappointing but finally exciting to solve the century-old mystery. So we can rest, all these numerous condensation effects and related properties are now backed by hard evidence rather than rigid that ‘it seems that So it’s okay to use that equation. “
“Good theory often works beyond the limits of its application,” Game said. “Lord Calvin was a remarkable scientist, he made a lot of discoveries, but he would surely be surprised to know that his theory – originally considering millimeter-sized tubes, is also on an atomic scale. .So our work has at the same time proved it both true and false. “
DOI: Nature, 2020. 10.1038 / s41586-020-2978-1 (About DOI).
