# How small does sand have to be to get wet?

I think of sand as a lot of very small rocks.

Suppose I have a pile of rocks, each about 1cm in size, and the pile is a meter tall. If I pour a bucket of water on the rocks, most of the water will fall through the rocks and form a puddle on the ground.

On the other hand, if I have a pile of sand one meter tall and I pour a bucket of water on it, the water will stick to the sand and I'll have a bunch of wet sand, and not much water on the ground.

Further, the wet sand acts distinctly differently from dry sand. For example, the angle of repose of wet sand is different from dry sand. An hourglass with wet sand it in might not work, or would run at a different speed from a dry hourglass. But I don't think the angle of repose of a pile of wet 1cm rocks is significantly different from that of dry rocks.

So, how small should rocks be before they show wetting properties the way sand does?

• Hmmm ... surface tension ... average distance between surfaces ... surface area to volume ratio ... gradual onset. I'll bet you know (and I) know all the pieces of the puzzle, but I am also very interested in how they all come together. – dmckee Mar 25 '15 at 16:38
• Sad, while I was writing my answer, 2 new ones showed up that contain all the same information I had. :/ – tpg2114 Mar 25 '15 at 16:49
• Interesting and we'll posed question – docscience Mar 25 '15 at 19:27
• How small does sand have to be to not get wet? – Mazura Mar 26 '15 at 9:21
• On phrasing of the question: I hear from sand professionals that sand can't get to be big or small but rather coarse grained or fine grained, respectively. – Pavel Mar 26 '15 at 15:33

For a packing of grains to stay wet up to a height $h$, the gravitational pressure $\rho g h$ needs to be balanced by the capillary pressure $\sigma cos(\theta)/r$. Here, $r$ represents the effective pore radius of the packing, $\theta$ the wetting angle (angle at which the air-water interface meets the sand grains), $\rho$ the water density, $g$ the gravitational acceleration, and $\sigma$ the surface tension associated with the air-water interface.

It follows that the hydrostatic head $h$ is given by: $$h=\frac{\sigma cos(\theta)}{\rho g r}$$ For an order-of-magnitude estimate you can equate the capillary radius $r$ to the grain radius $R_{grain}$, and $cos(\theta)$ to unity (fully water-wet grains). Together with $\sigma \approx 0.1 N/m$, $\rho \approx 10^3 kg/m^3$, and $g \approx 10 m/s^2$, it follows that $$h \approx \frac{A_{cap}}{R_{grain}}$$ with $A_{cap} \approx 10^{-5}m^2$.

As an aside, petroleum engineers use an approach like the above (replacing the air by oil) to determine the transition zone thickness in oil reservoirs. This is the zone over which the oil saturation 'builds up' above the water-bearing zone. As reservoir rock is usually fine-grained, and $\rho$ is replaced by the oil-water density difference, this transition zone can be tens of meters thick.

• @AdamDavis, as the question is written this is the best possible answer. The question is very generic. – Mr. Mascaro Mar 26 '15 at 22:30
• @Adam: The order-of-magnitude estimate is $h \approx 10^{-5}/r$ in meters. For reference, sand grains are about $10^{-4}$ to $10^{-3}$ meters in diameter. – Rahul Mar 27 '15 at 5:32
• @AdamDavis - have added the requested info (confirming Rahul's estimate). Thanks. – Johannes Mar 27 '15 at 16:59

Here is a heuristic. The actual details will depend on the details of what type of rock it is, and materials science and chemistry beyond my pay grade, but this gives what I think should be the general idea.

All rocks get wet when you put water on them, the surface gets slick, and the like. When this happens, what you get is the water adhering to the surface of the rock. Let's say that if the surface area of the rock is $A$, then the mass of water that adheres to the rock is $\sigma A$, where $\sigma$ is some number that depends on the material that the rock is made out of, how porous the surface is, etc, etc.

Now, we have a rock that has water mass $\rho_{w}\sigma A$ and rock mass $\rho_{r}V$. Thus, our wet rock has a water content fraction of $\frac{\rho_{w}\sigma 4\pi r^{2}}{\rho_{r}\frac{4}{3}\pi r^{3}} = 3\sigma\frac{\rho_{w}}{r\rho_{r}}$. So, for large rocks, the rock is mostly made out of rock, but for small rocks, the rock is mostly made out of water. Thus, as the particle size decreases, we expect the rock to behave in more water-like ways, because the rock is more and more made out of water.

In reality, this will be further magnified because the water will extend out from the rock some, and the particle-particle interactions will depend on things like surface tension and the like (not to mention that there will be some cutoff to all of this, because you don't expect the ratio to ever diverge). But the per-particle water/rock ratio alone shows you that you expect the thing to behave in a more water-like way as the particle size decreases.

Wetting here is most likely a capillary effect: Your question is about the size of the air gaps between grains (or rocks) of sand, not the size of the grains or rocks. In practice, except perhaps for very peculiarly shaped objects, these will be of similar magnitude to the smallest gap-filling grains.

What happens is that the energy required to create the air-liquid surface tension is not needed where the water does not have an air interface but contacts a material. With glass (or sand), there is a strong attraction between the polar water molecules and the polar silicon oxide material. Hence the water gets (slightly) sucked into especially small gaps. For this capillary action to cause pure water at room temperature to rise one meter in a glass capillary, the diameter would have to be at most $15\,\mathrm{\mu m}$. That is a (very rough) measure for the gap size you can have without water starting to partially drain. Note that this draining would be gradual: Only the (few?) gaps that are too large and too high would loose their water. Hence the observation that the sand is somewhat wet may still occur even if only some paths of the smallest gaps suffice for capillary wetting.

There is a good chance that your grains of sand (or rocks) may be porous and hence wet at least a bit better than you would expect from similarly sized pieces of unfractured glass. This will not matter much for the pile of rocks (so each rock gets slightly wetter/soaked), but might make all the difference for a pile of sand where internal capillaries might allow sand to soak up water even if all other paths of actual gaps were too large to allow it. Taken to the extreme, for example in silica gel, it allows sand-like grains to strongly adsorb water even just as humidity.