Want to build a super sand castle? Please accept this ultimate raiders

Figure 1 Super Sandcastle | Source: guinnessworldrecords.com

Building sandcastles is one of the little pleasures of a beach holiday, but do you really know the science behind these buildings? Pick up buckets and shovels, and let's explore the wonderful world of sand science.

By Ian Randall

Translated by Zhao Jinyu

Proofreading and Translation of Qian Ming

Edit | Feng Hao

Under the blue sky, an unparalleled bunker towering into the sky. The center of the building is pyramid-shaped, and dozens of minarets and towers with different shapes and designs are spent between the battlements and buttresses around it. There is a reinforced wall around the foundation. Behind the wall, a vigilant dragon floats on the water, and a lighthouse stands beside it.

No, no, take it easy. We are not talking about the design of the new headquarters of the physical world, but a huge sculpture that recently broke the Guinness World Record-the tallest sand castle ever. This castle (see figure 1) is 32 meters wide and 2 16 meters high. It was built by Dutch artist Wilfred Stijer and his team of more than 30 sculptors with 4860 tons of sand. With the help of an exquisite wooden scaffold, this castle was built in July, 20021in the Danish seaside village of Blokhus in northern jutland. After the completion, the builder painted a layer of glue on its surface, expecting this super sand castle to be exhibited to tourists until the next heavy frost comes in February or March next year.

But dealing with sand is not as easy as it looks. Before Stail and his team succeeded, the highest sand castle in the world was built by another Dutch sand sculptor, Thomas van den Dungen, in the German seaside resort of bins, with a height of 17.65 meters. Deng Gen once participated in the creation of the world's longest sand sculpture (27.3km) and built the most sand castles (2,230) in one hour. He is really a sand player.

However, Deng Gen's previous two attempts to break the record of the highest sandcastle failed. One of the buildings collapsed a few days before completion, and the construction of the other building was interrupted by a group of shore swallows nesting in the construction site. When vacationing on the beach, no one may be willing to go to so much trouble to challenge the world record. However, can science tell us how to build the perfect sandcastle?

Let's start with Matthew Bennett, an environmental scientist at Bournemouth University in England. In 2004, Bennett was entrusted by Teletext Holidays to decide the most suitable beach for building sand castles in Britain. Different beaches have different types of sand, so his job is to find out which sand is the best.

Bennett equipped his students with buckets and shovels, sent them to the most popular beaches in Britain, and taught them how to collect sand samples from each beach. When the students brought the sand back to the lab, his team dried it, poured it into beakers, added water, and then turned each container full of sand upside down. Bennett explained: "Then we loaded the weight on the top of each' experimental castle' and recorded the total tolerable weight before it collapsed."

The research team found that the key to building a solid sand castle is to mix one bucket of water for every eight buckets of sand. The plot ratio of 8: 1 is the same in all 10 test sites. In fact, when the high tide reaches the sea area closest to the coast, the sand-water volume ratio of the real beach is roughly the same.

According to Bennett, this perfect ratio ensures that water will only bind sand, not act as a lubricant. If there is too much water, buildings will flow and collapse, which will happen when sandcastles meet their natural enemies-tides; On the contrary, if there is too little water, the sand (building) will break.

In fact, the strength of sand piles depends on two factors. The first is the structure of a single particle. Particles with larger and more irregular edges will be more closely bound than those that have been smoothed by long-distance transportation-these particles will be ground under the action of wind and waves. Bennett explained that this is why sand containing many tiny and angular shell fragments is more conducive to building strong sand castles. Another more important factor is water content. The smaller the particles, the higher the water they can hold.

After research, Bennett called Torquay, located in the southwest of England, the best sand castle construction site in Britain, which was attributed to what he called "charming red sand". This was followed by Bridlington, Bournemouth, Daya Mouth and Tenby in East Yorkshire, which tied for third place. "It was a simple but effective experiment," Bennett recalled, explaining that he still thought the study was an interesting attempt to make people understand the concept of geology.

However, he also admitted that, in principle, any sand can be used to build sand castles-and Torquay's red sand was chosen as the "winner" of his research in 2004, largely because of its attractive aesthetic characteristics. Not only that, these "champion" sands originated more than 200 million years ago, when Britain was still in a desert larger than Sahara, located in the inland of Pangea. Therefore, there are many fine particles in the foundation sand, which enhance its cohesiveness.

For physicists, a sandcastle is just a structure composed of compacted particles (sand) and liquid (water or seawater). But how does this water help sand grains stick together? The answer lies in the surface tension of water film formed between particles. Just as the liquid level in a test tube bends at the edge due to the adhesion between glass and liquid, water forms a tiny "capillary bridge" between sand grains. These bridges pull sand grains toward each other, reducing the surface area between water and air, while increasing the surface area between water and attracted sand.

Now, although the most suitable ratio of sand to water for carving may be 8: 1, it turns out that wet sand is stable in a wide range of water content-like a solid. Obviously, the force that binds sand together is a bit strange, which inspired the physicist Stephen Herminghaus of Max Planck Institute for Dynamics and Self-organization in G? ttingen, Germany, who made an in-depth study of this phenomenon.

Instead of studying the sand itself, he and his team used a wet glass bead model similar in size and shape to the sand. Using X-ray chromatography microscope (which can generate digital cross-sectional images without damaging objects), researchers can generate 3D images of beads and test what happens when more water is added to the beads. (With the increase of water) At first, the micro-capillary bridge connecting the two separated particles began to grow and fuse, and gradually formed an increasingly complex structure, which looked like a string of pop-can tabs stuck together (Figure 2).

Figure 2 Sandcastles in the laboratory | Source: Reprinted with permission from springer: Natural Materials 7 189 2008.

In order to simulate the role of water in binding sand grains, a team led by physicist Stephan Herminghaus of Max Planck Institute of Dynamics and Self-organization in G? ttingen, Germany, created 3D images of wet glass beads using X-ray chromatography microscope. (a) The computer model of these beads (yellow) shows 3D "capillary bridges" (blue) that attract the beads together, and these bridges produce the same attraction in real sand. (b) With the increase of water quantity between particles (from left to right), more capillary bridges (white areas) are formed.

As the capillary bridges become larger, their contact area with sand particles also becomes larger. Because sand is attractive to water, the binding effect of water is enhanced. But at the same time, the concave arch of capillary bridge becomes less obvious, which leads to the decrease of negative pressure of water. It is the negative pressure of water that makes the particles gather together, so reducing the negative pressure of water will make the particles difficult to gather.

These two effects are balanced, which means that when more water is added, the "sand" in these experiments keeps the same viscosity. However, once water occupies 15% of the sand pile, or 35% of the total effective pores between sand grains, this law is broken. Beyond this limit, the firmness of the sand pile begins to weaken.

In the paper [1] in 2008, the researchers pointed out: "The liquid content has little effect on the mechanical properties of the sand pile, because the special organization of the liquid in the sand pile forms an open structure." In other words, now we know why we don't need much water to build tall sand castles: it's all thanks to tiny capillary bridges, which are like glue between grains of sand.

But is there a theoretical limit to how high a sandcastle can be built? In 20 12, Daniel Bonn, a physicist at the University of Amsterdam in the Netherlands, began to study this problem with his colleagues. They poured different amounts of wet sand into plastic cylinders with different diameters, and then cut off the mold to see how high the cylinder could be before it collapsed.

The research team found that when a pillar elastically bends under its own weight, it will collapse. In view of this, the researchers determined that the maximum possible height of the sand column increases with the 2/3 power of the radius of the bottom of the sand column. You will find that to build a sand pillar twice the height of your friend, you need to make its radius the radius of your friend.

Time magazine. At the same time, according to the measurement of the elastic modulus of wet sand, they concluded that the sand pile can reach the best strength when the liquid volume fraction is about 65438 0%.

Figure 3 Maximum Height (Source: Mehdi Habibi)

Researchers at the University of Amsterdam in the Netherlands, led by Daniel Bonn, poured wet sand into a plastic cylinder and found that the maximum possible height of the sand column was proportional to the 2/3 power of its bottom radius.

But this figure is different from the proportion found by Bennett with buckets and shovels, which may not be surprising, because the real sandcastles in Bonn research are often not cylindrical, but conical. After all, a simulation study published by Zhang Wenqiang of Zhengzhou University last year showed that conical sand castles have the highest stability.

When asked if there were any practical skills to share with budding sand castle sculptors, Bonn said that compaction is the key to maintaining stability. This is why professional sand castle builders usually use "thumping" machines for mechanical compaction, and then trample the sand repeatedly. Compacting sand helps to shorten the capillary bridge and make the sand castle stronger.

It is also useful to contain polydisperse sands with different particle sizes. Although we think that sand seems to be composed only of time, to geologists, this term refers to any broken rock particle with a size between 62.5 microns and 2 mm. Professional sand castle builders usually prefer to carve with "river sand", which contains finer clay particles with the size of 0.98 microns to 3.9 millimeters. Bonn said that small particles in river sand can effectively use space and accumulate in the gaps between large particles, thus producing more capillary bridges and stronger structures.

In other words, clay is like a binder between particles, even if there is little or no water. But if there is no river sand, a similar effect can be obtained with seawater. When your sandcastle dries, the salt crystals deposited on the sand will act as glue. This is an added benefit of building sand castles by the sea.

However, even if there is no ocean nearby to keep water, capillary bridges will be formed between sand grains due to spontaneous condensation of water vapor inside the porous material and between adjacent surfaces. This phenomenon is called "capillary condensation", which not only affects adhesion, but also affects various properties such as corrosion and friction. In fact, ancient Egyptians may have inadvertently benefited from capillary bridges. They pour water on the sand, which makes it easier to transport heavy stone products (Figure 4).

Fig.4 Water the Egyptians (Source: Sir john gardner Wilkinson, 1854).

If building sand castles can't satisfy your desire to build, don't worry, sand and water can also be used to build more complex buildings. The research team led by Daniel Bonn, a particle physicist at the University of Amsterdam, pointed out in a paper published on 20 14 that the ancient Egyptians used water to harden sand in the desert. This hard material made it easier for Egyptians to move sledges carrying heavy stones when building pyramids and other giant monuments.

The idea was inspired by a mural about 3,900 years ago, which was decorated on the wall of Djehutihotep's tomb. From 2050 BC to 1780 BC, Yehuti Hotep was one of the most influential consuls (or governors) in the Middle Kingdom of Egypt. This mural depicts a colossus of Jahuti Hotep with a height of four people, which was pulled across the desert by 172 workers in a sleigh.

Interestingly, in the mural, the man standing in front of the sled is watering the sand where the colossus is about to pass, while the other two slaves are replenishing him with water. Egyptian scientists have always regarded this strange behavior as a ritual, but Bonn and his colleagues have proved through experiments that adding a certain amount of water to sand can form a microscopic "capillary bridge", thus hardening the sand.

Capillary bridge reduces the friction coefficient of sand, and also prevents sand from piling up in front of the sled or getting stuck in the sand. Specifically, the research team found that when the water content of sand reaches about 5%, the dynamic friction coefficient is halved. But when the water content is high, the friction will increase, and when the water content is 10%, it will even exceed the dynamic friction coefficient of dry sand.

Capillary condensation is usually described by the equation put forward by British physicist and mathematician William Thomson in 187 1 (later Lord Kelvin). This equation relates some macroscopic properties such as pressure, curvature and surface tension. However, this equation is also true on the micro scale. In fact, even on the scale of 10 nanometer, it has been proved to be surprisingly accurate.

In order to explore the reasons for this phenomenon, a research team led by Andre Geim, a Nobel Prize winner and a physicist at the University of Manchester, recently made the smallest possible capillary. Some are only as high as a single atom, and consist of mica and graphite layers with atomic thickness, separated by graphene strips. Heim and his team found that these tiny capillaries can only hold one layer of water molecules [4].

By studying the condensation in these capillaries, the team realized that even on the molecular scale, Kelvin equation can still make a good qualitative description-the structure of water becomes more discrete and layered, and its properties will change. Yang Qian, the first author of the paper, said: "This surprised me. I thought that the traditional physics society was completely ineffective at this scale, but I didn't expect the old formula to still be effective. "

However, according to the research team, the consistency between qualitative equation and reality is also accidental. Capillary condensation at ambient humidity will produce a pressure of about 1000 bar, which is greater than the pressure on the deepest seabed on earth. This pressure may coagulate the particles in the sand castle, but in the experiments of researchers, it will also cause tiny deformation of tiny capillaries, thus offsetting the changes in the properties of water on the molecular scale.

"Good theories are often proved to be effective outside their scope of application," Heim said. "Lord Kelvin is an outstanding scientist and has made many discoveries, but even he will be surprised to find that the theory originally drawn in millimeter-scale test tubes-even on the monoatomic scale. In fact, in his groundbreaking paper, Kelvin clearly pointed out that this is impossible. Therefore, our work also proves that he is both right and wrong. "

Studying the physical characteristics of sand and the capillary force that binds sand together is not only for building the best sand castle. For example, the imaging technology developed by Herminghaus and his team to study glass beads can be more widely applied to the particle-liquid-air interface. Therefore, these studies are not only useful for building sand castles on the seashore, but also have many practical applications-for example, from preventing powder from caking to improving our ability to prevent landslides.

Determining the mechanical properties of wet sand is also beneficial to construction work. After all, most roads, railways, houses and buildings are built on sand, but if these structures are to be durable, they must remain stable. Water can reinforce sand piles, but it may contribute to stability and reduce the degree of compaction.

Any civil engineer knows that building a house on loose sand will face the risk of "quicksand", which is an architect's nightmare. Quicksand is composed of loose sandy soil saturated with water. It looks solid at first, but it will liquefy when disturbed (such as ground vibration) and become a non-Newtonian fluid. It will form suspended matter, lose its viscosity, and cause the contacted objects to sink into the sand.

This is particularly problematic in the Netherlands, where Bonn is located. There is a lot of quicksand on the land reclaimed by the dam. Because it is impossible to build on this piece of land called "polder field" immediately, builders have to wait for several years before starting construction until the sand is compacted. Bonn said, "If the sand is not compacted, you may sink and get stuck in it."

So don't rush to the beach, let's review the main points first. Building a truly amazing sandcastle:

It is best to choose a place with more fine sand.

Wet sand is taken from around the high tide point, so that an ideal sand-water mixture of 8: 1 can be obtained.

Compacting wet sand to improve stability.

If you want to build a tall tower, you'd better have a wide base and make it into a cone.

Last step, release your creativity!

Well, enjoy your masterpiece ... until it is inevitably washed away by the tide.

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