Brain games with sand grains

Sand grains are not uniform in size. The minimum diameter of a sand grain is only 62.5 micrometers or 0.0625 millimeters while the upper limit of a sand grains diameter is 2 millimeters.

It is common knowledge but why such numbers? One may say that you simply have to draw the border somewhere in order to be able to differentiate sand from silt or gravel. So are these numbers completely arbitrary? Yes and no. Exact numbers are definitely arbitrary. They are determined by the logarithmic scale which also determines the borders between fine, medium, and coarse sand.

However, this classification scheme is chosen to make as much sense in geology as possible. It reflects the movement of sand grains in water. In the river water, the sand grains are not carried in the suspension. They tend to move in jumps — running water occasionally lifts sand grains up but is not able to carry them far. Sand grains settle again and wait for the next jump. Such mode of movement is called saltation and it is especially characteristic to sand grains. Gravel just rolls on the river bed while silt is usually carried in the suspension.

Sure, it depends on the speed the river water is running. Sometimes (in the fast moving mountain streams) granules saltate as well. And sometimes the river water is not capable of lifting sand grains up even temporarily. Nature doesn’t classify. It has no need for it. But we humans desperately need the classification schemes in order to categorize things and try to make some sense of the world surrounding us. Therefore, no classification scheme is perfect and the one used now is by no means the only one possible.

How the smallest sand grain compares to the largest

The gray circle resembles the upper limit of a sand grains (very coarse) size while the smallest red circle resembles the smallest. Black, blue, green, and yellow are the upper borders of coarse, medium, fine, and very fine sand grains respectively. The graph is to scale.

It is perhaps rather difficult to imagine how different can two grains be if one of them has a diameter of only 62.5 micrometers while the other is 2000 micrometers or 2 millimeters thick. The first one is barely visible while the other is as big as the head of a match. How much is one bigger than the other? It should be simple, we just divide 2000 with 62.5 and get the result of 32. However, such a result may be mathematically correct but it makes no sense. The true measure of a grain size is its volume. After all, whether the river water is capable of carrying the grain depends on the mass and volume of the grains, not on the diameter.

If we assume that our grains are perfect spheres, then the bigger one has 32,768 times larger volume. That’s a huge difference and obviously has to significantly influence the behavor of the grains.

How much one sand grain weighs? Let’s assume that we are dealing with quartz grains. Quartz has a density of 2.65 grams per cubic centimeter. A grain with a diameter of 2 millimeters makes up only little more than four thousands of a cubic centimeter, and it weighs approximately 0.011 grams. I am not giving the mass of a smaller grain, the number would be ridiculously small but you can easily calculate it by dividing 0.011 with 32,768.

Now we know that even the largest sand grains are lightweight. How about the number of grains that we can fit into a container with a definite volume, let’s say 1 cubic centimeter? In order to calculate that, we need to know how many grains we can press into this container. Theoretical calculations show that if the grains are placed irregularly, you can not achieve better packing than about 63%. It means that about 37% of your container will be filled with air, water or something else. It makes up the pore space volume which is a very important metric if we try to calculate, for example, how much crude oil a sandstone layer can contain. Simple calculation yields a result that 1 cubic centimeter can contain 151 sand grains with a diameter of 2 mm and 4,959,645 sand grains with a diameter of 62.5 micrometers.

Most sand collectors prefer to have at least 30 ml of sand per sample. I am an exception because I am satisfied with much less than that. Here are some calculations why this is the case. Let’s assume that average sand grain has a diameter of 250 micrometers (this is a borderline between fine- and medium-grained sand). If you have 30 ml of such sand, then you have 2,324,833 sand grains. Do you really need that many if your goal is to get a general overview of the sand samples composition? Definitely not. Even one hundredth of that is good enough. That is the basis of my claim that if you have a very interesting sand sample but can only send one gram, I would still be happy. It is more than I need.

Can we try to estimate how many sand grains are there in the whole world? Well, no one ever counted them but I think we can make some very rough estimations. There are approximately 200 million cubic kilometers of continental sediments. Assuming that about fourth of it is sand, the total volume of sand is perhaps 50 million cubic kilometers. If we assume that the average sand grain has a diameter of 250 micrometers, then we have approximately 4 x 1027 sand grains in the crust.

This is a really huge number. I remember Carl Sagan once said in his television series Cosmos that there are perhaps more stars in the Universe than there are sand grains on all of the beaches. That may be true but beaches are not the only places where sand can be found. If we calculate the number of all sand grains covering the Crust, I think the sand grains still have the last laugh.

Grain size (µm)Aggregate nameVolume differenceNo. of grains in 1 cm3
62.5Very fine sand14,959,645
125Fine sand8619,956
250Medium sand6477,494
500Coarse sand5129687
1000Very coarse sand40961211

4 comments to Brain games with sand grains

  • Interesting post. I really like the assertion that we should think carefully about the most relevant metrics to compare and consider. For example, it’s very common to see geologists wielding X-ray diffraction data to help interpret sedimentological and diagenetic observations. This is fine, as long as the geologist appreciates that the data are in weight percent, not volume percent. Sometimes you want weight percent, but sometimes you don’t (e.g. when comparing with porosity).

    Another metric that’s interesting for some purposes, diagenetic interpretation for instance, is surface area. Another column for your table would look like this (grain surface area in cm²): 609, 304, 152, 76, 38, 19. It’s fun to get smaller too: one cubic centimetre of 1 µm spherical particles contains 1.2 trillion ‘grains’, with a surface area of 38 000 cm², or nearly four square metres! In fact, real clay particles are so strange that they have even larger surface areas than this; according to Passey et al (2010) in SPE 131350, just 1 g of smectite crystals have an external surface area of 50 m², plus another 750 m² (that’s not a typo) of internal, inter-layer area. All of this area is covered with one or two water molecules.

    Cheers! Matt

  • Yes, clay minerals and other sheet silicates too have very interesting properties. I find it fun to think that since one biotite flake has a width of 10.18 ångströms, you could theoretically split 1 cm thick mica book into 9.82 million separate flakes. These flakes would have a surface area of 1965 m². 1 gram of biotite flakes (SG~3) has a surface area of 650 m².

  • Glen

    I was wondering if anyone has ever done a study on where the finest sand in the world is located..which beach has the finest or coarsest sand etc.
    I did an internet search but come up with only ads from local beaches claiming to have the finest sand but they all cant be right

  • Glen, sand grains have certain size limits. Anything less than 1/16 mm in diameter is not a sand grain anymore, it is called silt. And larger than 2 mm is gravel. Many beaches may have average grain size close to these limits but I am not aware of any specific study.