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The different gases that make up the air have different densities. So, naively, one would expect the heavier gasses to pool in the lower atmosphere and the light ones at the top.

I asked myself this question a long time ago and I found the answer to be that the mixing produced by atmospheric circulation was more than enough to keep the whole mix homogeneous, and I was happy with that answer until I considered the case of caves, or chambers within the Earth that have been discovered in underground mines, and that have been isolated for millions of years. But despite of that, there is no reports of miners dying because on the top of the cavity the air was only nitrogen or oxygen at the bottom.

Is the mixing produced by molecular movement due its temperature enough to avoid stratification? Or is there another reason? Would air at very low temperature suffer from density stratification?

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    $\begingroup$ Mixing by turbulent movement is much more efficient than by Brownian movement. My guess is that the existence of wind (and thus turbulence) enables this high degree of mixing of different density gases. Without winds the atmosphere would definitely more stratified, but by how much I don't know. $\endgroup$
    – Communisty
    Commented Jan 22, 2018 at 10:34
  • $\begingroup$ npl.co.uk/reference/faqs/… Specific gravity is different than density, right? And what is it about gases labeled "Poorly Mixing"? $\endgroup$
    – stormy
    Commented Jan 22, 2018 at 23:19
  • $\begingroup$ energen.com/operations/safety-and-public-awareness/… This little article was good for comparing sp. gravities...esp. of CO2. 1.53 $\endgroup$
    – stormy
    Commented Jan 22, 2018 at 23:33
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    $\begingroup$ @blacksmith37 I know H, CO and CH4 and other gases DO stratify and form layers, my question is why the main constituents of the air (O2, N2 and Argon) DO NOT stratify. One can argue that if there were a light component of air (like Hydrogen), it would go to the top and would be preferentially lost to space, so the air that will "survive" won't have such light elements. However that's not true for the heavy ones. So: Why there is not a layer of pure Argon at the bottom of caves? $\endgroup$
    – Camilo Rada
    Commented Jan 23, 2018 at 16:36
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    $\begingroup$ Coincidentally I was talking to an ex-miner two days ago, while in a (closed) coal mine. And he told me that people indeed do die in mines because the mixture of gases varies within spaces: you can be fine at the top of a space, and dead at the bottom. Coal mines (at least the modern one I was in) have complicated arrangements of fans and airtight doors to ensure there is rapid air circulation through the mine to keep everything well-mixed and to remove the various 'damps' which accumulate otherwise. $\endgroup$
    – user18801
    Commented Feb 4, 2020 at 10:30

2 Answers 2

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So, naively, one would expect the heavier gasses to pool in the lower atmosphere and the light ones at the top.

That's overly naive. That same naive expectation would lead one to think that uranium should be concentrated in the Earth's core, or that a mix of water and ethanol should be differentiated with water on the bottom and ethanol on top. Uranium is instead concentrated in the Earth's crust, and water and ethanol readily mix. Entropy and chemistry can lead to counterintuitive results.

That most certainly is the case with gases. The entropically-favored distribution is a thorough mix. Attaining this thorough mix can take a long time if only molecular diffusion is in play. Turbulent mixing makes the mixing proceed much more rapidly.

There are places where this entropically-favored distribution does not occur. Gases can be concentrated in mines and in basements. For example, mines have problems with concentrations of methane and carbon monoxide (both less dense than air), but also with concentrations of carbon dioxide and sulfur sulfide (both more dense than air). Basements in areas with lots of granite have problems with radon (significantly more dense than air). Gases can concentrate in mines and basements due to a diminished turbulent mixing. This enables processes that produce gases to overwhelm the slow molecular dispersion process, resulting in an entropically-disfavors distribution.

The Earth's upper atmosphere is also differentiated. Here, the extreme rarity of the upper atmosphere means that turbulent mixing is highly attenuated. Extreme solar radiation (high UV and x-rays) produces gases by splitting molecular oxygen, water vapor, and to a lesser extent, nitrogen, into constituent parts. The very long mean free path in the upper atmosphere means that the lighter components move higher than do the heavier components.

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  • $\begingroup$ Interesting, is there some kind of theorem stating two gases mixed have less entropy than if they were layered on top of each other? Would it be enough to compare the potential temperatures of both cases? $\endgroup$
    – AtmosphericPrisonEscape
    Commented Jan 23, 2018 at 14:27
  • $\begingroup$ OK, but what is exactly the difference between CO and Argon, that allows the first to form layers but not the second? And the analogy with liquids is not fair, as molecular interactions are much stronger, and in that case and the rules for mixing and saturation/precipitation of mixes are controlled by a different physics. $\endgroup$
    – Camilo Rada
    Commented Jan 23, 2018 at 16:13
  • $\begingroup$ In addition, the inner hearth have a very heavy density stratification, with much of the heavier elements on the core, and the crust is mostly composed of the lighter elements. So it is not and overly naive expectation. I think it is the other way around, and the Uranium case is an exception to the general rule. $\endgroup$
    – Camilo Rada
    Commented Jan 23, 2018 at 16:29
  • $\begingroup$ @CamiloRada - Re "what is exactly the difference between CO and Argon?" The answer is time. Suppose you open a pressure vessel that contains argon (which is much denser than air). The argon will initially flow downward out of the vessel and spread out in a layer along the ground. The argon does not mix initially; that mixing takes time. Over time, the argon will diffuse into the atmosphere, with some of it eventually reaching up to the Karman line. The same applies to any gas denser than air. $\endgroup$
    – David Hammen
    Commented Jan 23, 2018 at 20:02
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    $\begingroup$ It is is really difficult to stratify gases more than temporarily, the nature of gases as unbound molecules mean they will tend to form distribution gradients not discreet barriers, and thus it only takes minute stirring forces(like adding heat) to disrupt these gradients into more thorough mixing. $\endgroup$
    – John
    Commented Jan 24, 2018 at 6:15
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But despite of that, there is no reports of miners dying because on the top of the cavity the air was only nitrogen or oxygen at the bottom.

Yes and no, miners die from other causes, like lack of oxygen, sulphur poisoning, etc.
But for example you can already get a case of sulphur poisoning near Fumaroles in volcanic regions, simply because the air that has the sulphur dissolved in it is heavier than the surrounding air.
So that's the effect you have been asking for, but you still need a severe lack of wind and the right topography to make the stratification happen.

So now let's zoom out a bit. Earth has a surface. This provides friction and slows down surface winds considerably, creating the Planetary boundary layer (PBL). You can think of the PBL as 'what the free-streaming atmosphere would want to do, but then it encounters a surface'.
Only because of the friction of the surface, we have only moderately strong winds on the surface that allow for special phenomena like little valleys filled with sulphur.

Higher up in the atmosphere velocities are much faster. Thus, Reynolds numbers are higher, destabilization of flows comes easier and turbulence sets in, mixing everything.
Only at the Karman-line around 100km height, things calm down sufficiently (in terms of frictional momentum density transfer from layer to layer) that molecules start separating by weight.

So I would say your initial intuition was right, it's just less intuitive how the planetary surface plays into this.
In the oceans btw. this phenomenon plays a huge role in determining global circulation. The different salinity of water layers leads to different densities and layered flows. And because the density of water is a factor of $10^6$ higher than that of air, one would need a much stronger source of momentum to mix those layers. But such a source doesn't exist, so we get layered flows of different densities.

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  • $\begingroup$ Your answer have very interesting content, but doesn't really answer the question of what prevents the air to stratify in environments with no turbulent mixing, like caves and underground chambers. $\endgroup$
    – Camilo Rada
    Commented Jan 23, 2018 at 16:31
  • $\begingroup$ @CamiloRada: Well, it does stratify. That's part of what makes mining adventures dangerous. $\endgroup$
    – AtmosphericPrisonEscape
    Commented Jan 23, 2018 at 19:47
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    $\begingroup$ it it not so much stratification as lack of mixing, the gases do not separate out, they just fail to mix when introduced separately. most gas layers in mines come from leak sources that then build up caves.org/pub/journal/PDF/v71/cave-71-01-100.pdf $\endgroup$
    – John
    Commented Jan 24, 2018 at 6:07
  • $\begingroup$ @John: Interesting, didn't know that. It's of course a subtle distinction, but the one that makes all the difference here. $\endgroup$
    – AtmosphericPrisonEscape
    Commented Jan 24, 2018 at 13:13
  • $\begingroup$ @AtmosphericPrisonEscape - It's not just a subtle distinction. It's a huge one. Get rid of the sources that result in those concentrations of gas and those concentrations will eventually disperse into the atmosphere as a whole if if those gases have an escape route to the atmosphere. "Eventually" might mean a long time if turbulent mixing is not in play as diffusion is a slow process. $\endgroup$
    – David Hammen
    Commented Jan 24, 2018 at 18:32

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