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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?

Camilo Rada
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    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. – Communisty Jan 22 '18 at 10:34
  • http://www.npl.co.uk/reference/faqs/what-is-the-difference-between-density-and-specific-gravity-(faq-mass-and-density) Specific gravity is different than density, right? And what is it about gases labeled "Poorly Mixing"? – stormy Jan 22 '18 at 23:19
  • http://www.energen.com/operations/safety-and-public-awareness/basic-natural-gas-safety-537.html This little article was good for comparing sp. gravities...esp. of CO2. 1.53 – stormy Jan 22 '18 at 23:33
  • This depends on phases of matter right? Been a long time. – stormy Jan 22 '18 at 23:41
  • Gases are in a ratio with gases, liquids with water? – stormy Jan 23 '18 at 00:26
  • Oxygen would be at the top of the cave if air was displaced by CO2 otherwise CH4, H2S and CO are replacing air in an enclosed system. – stormy Jan 23 '18 at 00:29
  • Why don't you think there is stratification ? I know stratification of H ( in air) is a problem in industries that use H , not outside. It goes up to the ceiling , mixes with a little oxygen and waits for an ignition source.Also CO2 drops when not outside. – blacksmith37 Jan 23 '18 at 01:16
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    @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? – Camilo Rada Jan 23 '18 at 16:36
  • Isotopes (different atomic weight) can be separated using centrifuges, eg. to enrich Uranium. This is really a Physics question. – Keith McClary Jan 29 '18 at 04:17
  • @KeithMcClary I agree this is about physics. I originally though climatologist were the most suited to answer it. But no answer so far have been fully satisfactory. I should perhaps pot it in the physics forum. – Camilo Rada Jan 29 '18 at 04:22
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    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. –  Feb 04 '20 at 10:30

2 Answers2

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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.

David Hammen
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  • 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? – AtmosphericPrisonEscape Jan 23 '18 at 14:27
  • 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. – Camilo Rada Jan 23 '18 at 16:13
  • 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. – Camilo Rada Jan 23 '18 at 16:29
  • @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. – David Hammen Jan 23 '18 at 20:02
  • For a gas less dense than air (e.g., CO), the initial response is to rise (if it can). Given time, it disperses, if it can. For gases trapped in a mine, that dispersion can take a long time. – David Hammen Jan 23 '18 at 20:03
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    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. – John Jan 24 '18 at 06:15
  • @DavidHammen So you mean that given enough time any mix of gasses will be an homogeneous mix independently of the differences in molecular weight of each gas? – Camilo Rada Jan 24 '18 at 21:21
  • @CamiloRada - Exactly. There's nothing special about nitrogen, oxygen, and argon. – David Hammen Jan 24 '18 at 23:29
  • @DavidHammen OK, sounds good, but I still don't understand why. Is it what John say (that they are unbound molecules). It is still hard to wrap my head around the idea that a heavy molecule wouldn't sink, or a light one rise, as a helium filled balloon does. Why that happen with a balloon and not at a molecular scale? – Camilo Rada Jan 25 '18 at 00:10
  • @CamiloRada - Suppose you have a non-leaky but expansive balloon. Fill it with helium. It expands to match the local pressure and temperature and hence rises due to buoyancy. It rises and rises because it expands to match local pressure and temperature. Suppose now you have a leaky balloon. It, too, initially rises due to buoyancy. But eventually, all the helium leaks out and the now empty balloon falls to the ground. The helium that was once in those balloons? It's now dispersing throughout the atmosphere. – David Hammen Jan 25 '18 at 14:28
  • There's nothing special about helium in a well-mixed atmosphere. It eventually spreads throughout. The same goes for any gas that is close to ideal. There is one gas in our atmosphere that is not anywhere close to ideal, and that's water vapor due to its boiling and melting points. But even with water, that temperature is well below boiling does not prevent liquid water from evaporating or ice from sublimating. All that matters is the partial pressure of water vapor in the atmosphere. – David Hammen Jan 25 '18 at 14:32
  • I found an interesting article that mention the formation of a "lake" of CO2. So as mentioned that will happen near the source, but then it will dissipate to never stratify again: https://www.sciencealert.com/ancient-roman-gate-to-hell-plutonium-sacrifice-killed-carbon-dioxide – Camilo Rada Feb 20 '18 at 00:02
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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.

AtmosphericPrisonEscape
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  • 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. – Camilo Rada Jan 23 '18 at 16:31
  • @CamiloRada: Well, it does stratify. That's part of what makes mining adventures dangerous. – AtmosphericPrisonEscape Jan 23 '18 at 19:47
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    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 https://caves.org/pub/journal/PDF/v71/cave-71-01-100.pdf – John Jan 24 '18 at 06:07
  • @John: Interesting, didn't know that. It's of course a subtle distinction, but the one that makes all the difference here. – AtmosphericPrisonEscape Jan 24 '18 at 13:13
  • @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. – David Hammen Jan 24 '18 at 18:32