# The sandcastle equation was solved 150 years ago

[एपोच टाइम्स २६ दिसंबर २०१०](Epoch Times reporter Zhang Ni compiled a report) A new study found that the laws summarized by a mathematical physicist 150 years ago were actually in the microscopic world at the nano scale. Still applies.

The construction of a palace on the beach is a traditional entertainment with a long history. Relying only on water and sand, through the right proportions, can make a strong and delicate beach palace. Later, people organized competitions for this entertainment to encourage the craftsmen to build more sophisticated palaces.

Studies have shown that the best ratio is one bucket of water to eight buckets of sand. Of course, random ratios can create castles of different genres, but if you want to build the strongest castle that can win the game, you have to follow this ratio.

In 1871, British mathematical physicist William Thomson (formerly Baron Calvin) summarized an equation that described the phenomenon that the evaporation of water from the environment would make the porous material more tightly bound. This was called the “Kelvin equation”. “Because it may well explain the robustness of the sand castle, it is also called the” sand castle equation “.

This equation describes the laws of the macro world, but physicists wonder if this equation is valid on a small scale?

Capillary compaction effect

Scientists have discovered that it is caused by a type of “capillary condensation effect” produced by the liquid in small pipes.

Physicists use X-ray microtomography to observe interactions between glass beads, which are about the same size and shape as sand particles, and water in the microscopic world. They observed that after adding water to the dried glass beads, the water formed a small bridge-like capillary connection structure between the glass beads.

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Physicist Daniel Bonn of the University of Amsterdam in the Netherlands discovered the secret. This, he said, is similar to the reason that soap bubbles are always spherical, because the surface area of ​​the sphere is the smallest in the case of different shapes of the same volume, and can be maintained with the smallest energy. “Similarly, a small amount of water between two grains of sand forms a small tube, which reduces the contact area between water and air. If sand is transported at one end, it causes water and air The middle surface area will increase, which will require energy consumption. Therefore, resistance has to be done to prevent this deformation from happening. “

The sum of the forces of a large number of thin tubes creates a clear overall effect, which acts like glue to the water, holding the sand together.

However, studies have shown that after reaching a certain level of this effect, when water is added and the amount of thin tube structure exceeds a certain limit, the adhesion between the glass beads increases in the thin tube. The weakening of the force of K will be offset.

Mathematical calculations show that this condensation effect is strongest when the humidity is 30% to 50%, but less than 1 nanometer at the molecular scale, because the water molecule has a diameter of about 0.3 nanometers, which means It is that a layer of capillary moisture only one nanometer thick with one or two water molecules thick. Scientists speculate that under this scale, this equation may not apply.

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But this problem has not been solved for more than 100 years. This law is not only meaningful for sand castles, but the capillary condensation effect is of great importance for many fields such as modern microelectronics, pharmaceuticals, and food processing industries.

“Graphene’s father” got the answer

150 years later, physicist Andre Geim of the University of Manchester finally solved this mathematical problem. Heim and his colleagues invented a very simple tape method to separate the graphene material from graphene with only one layer of carbon atoms and won the 2010 Nobel Prize in Physics. Graphene is a widely used material in modern times, and people call heme “the father of graphene”.

Heme is very experienced in the study of single-layer atomic materials and has found a way to find out the law of capillary action at the molecular scale.

Heme has mica and graphite, which is only one layer of atomic thickness, to form a capillary that is only molecular scale, with narrow graphene strips as gaps in between. In this way, researchers have constructed capillaries of various lengths, some of which are only one atom long and only large that hold a layer of water molecules. This is the smallest structure possible.

Heim’s research states: “In this case, the water is more diffuse and becomes a layered structure with a thickness of only 1 nanometer. This results in a subtle adjustment of the capillary and suppresses the factors that make up the equation. Can make it ineffective. ” In other words, Heim believes that the capillary condensation equation is still valid at the microscopic level — as opposed to the approximate condition.

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Heim said: “A good principle can break through boundaries and still apply.” Baron Calvin “is an amazing scientist. I believe he himself did not expect that this theory was still valid on the scale of just one atom. In fact, he commented on the paper at the time. It is impossible to say. So our research proves that he is right and he is wrong. “

Editor in charge: Zhu Hanru

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