The atmosphere is composed primarily of oxygen and nitrogen. These gases have different molar weights; molecular diffusion and bulk convection endeavor to keep them homogenously mixed, but gravity, working on their different molar weights, endeavors to stratify them, with the heavier molecules at the bottom of the pile.
So how strong is the tendency toward stratification? If I eliminate bulk convection by enclosing a quiescent volume of air in a room-sized chamber with all surfaces at one constant temperature, how much do the concentrations of nitrogen and oxygen differ at the top and bottom of the chamber?
What if the chamber is several miles tall?
What if instead of oxygen/nitrogen (molar weights = 32 and 28, respectively), I use a blend of hydrogen (molar weight =2) and uranium hexafluoride (molar weight = 352)?
Gases don’t really stratify, because they pass right through each other. What you’ll have is a partial pressure of each gas, and that partial pressure will decrease with height, and the partial pressures of different gases will decrease at different rates.
That is to say, at the bottom, you’ll have all of the gases mixed together. As you go higher, all of the gases will get thinner, but the heavy gases will get thinner more quickly. So at a higher altitude, you’ll still have all of the gases mixed together, but the proportions will favor the lighter gases more than they did at ground level. With an extreme difference in molecular weights, like hydrogen and UF[sub]6[/sub], you’ll have a height where you’ve got almost pure hydrogen with almost none of the UF[sub]6[/sub], but there won’t be any clear boundary where that happens: You’ll get some height where the heavy gas is only 10% of the total, and another height where it’s 1%, and another height where it’s 0.1%, and so on.
Now, in the short term, if you start off with heavy gases at the bottom and lighter gases on top, it’ll stay that way for a while (allowing you to pull tricks like floating an aluminum-foil boat in a fishtank of sulfur hexafluoride). But in the long run, even without temperature variations or air currents, you’ll eventually reach the mixed equilibrium I described above.
This implies no impediment to the motion of the constituent molecules, i.e. the only thing any given molecule of gas ever collides with is the chamber wall. In reality, the mean free path for air molecules under STP is tiny, on the order of a few dozen nanometers. Shouldn’t the existence of a finite mean free path induce some degree of stratification beyond what a simple partial-pressure/density/altitude model would predict?
As long as the collisions are elastic (ideal gas), then it doesn’t matter (on average) if a Molecule-A bounces off another Molecule-A or a Molecule-B or the walls. The only thing that influences the height profile of Molecules-A are their gravitational potential energy and the average kinetic energy of the Molecules-A. The collisions maintain the equilibrium, but a given collision doesn’t care about up versus down.
I have in my mind an analogy involving a blend of pea gravel and plastic beads in a vibrating bin: over time the gravel will force its way to the bottom of the bin, and the beads will be buoyed up to the top.
Assuming you’re right, can you help me figure out where that analogy deviates from the behavior of a real gas blend?
In particle segregation, particles are densely packed with many-body interations, have non-trivial shapes, have complex interaction dynamics (e.g., cubes of crystals spinning off each other or supporting each other), undergo inelastic collisions (friction), and have physical sizes that are large compared to typical particle spacing. In the end, it’s a very rich set of physical interactions. You don’t even need gravity. That is, macroscopic particles layering the bottom of a flat container will exhibit complex segregation phenomena in the horizontal plane when agitated.
The easiest segregation mechanism to visualize is whereby a mixture of small spheres and large spheres stratifies under gravity. The small spheres can physically fit through the holes between the large spheres, and so the small spheres sift their way inevitably down.
None of this stuff applies to an ideal gas. The molecules are well separated, with long distances between them relative to their molecular size, and they experience trivial elastic collisions.
For visualization purposes, you could sort of convert your gravel/bead example into more of an ideal gas example by considering a large glass box (say, 10 m[sup]3[/sup]) filled with a hundred or so super bouncy balls of two different sizes. If you shook the thing really hard, you’d could get the balls bouncing all over at high speed. If they didn’t lose any energy in collisions – or if you kept adding energy into the system – then they’d keep on pinging around in there forever and would establish independent height profiles. (Some of the energy would end up in rotations, but that’s okay.) In reality, they lose a lot of energy in each collision and a few hundred particles isn’t enough to usefully think in terms of statistical mechanics (thermal equilibrium, etc.), but on the whole the dynamics will be governed simply by the kinetic energy available to lift the balls, the potential energy cost of lifting the balls, and the balance thereof.
If you introduce a heavy gas out of equilibrium (as with radon in a basement), it may take a long time to reach equilibrium and you can have localized high concentrations. If you have gases in equilibrium, though, they will not spontaneously stratify further (i.e., beyond the equilibrium height profiles Chronos described above).
Partial Pressures are same as mole percent or percent molecules (at least for atmospheric gases at normal pressures)
Need a cite. From here : Up to around 100 km the composition is fairly “normal”, in that it’s what we surface-dwellers would expect: mostly molecular nitrogen (N2 rather than N) and molecular oxygen (O2) with a small amount (0.93%) of argon and traces of some other gases (carbon dioxide, neon, etc.).
Note that Argon has a Molecular weight of 40 compared to Nitrogen (32) and still remains at the same concentration (partial pressure) for 100km.
Again, need a cite, please. This is same as partial pressure.
Please take note that the OP is describing a ISOTHERMAL system (i.e. no change in temperature with height) while the earth’s atmosphere is more closer to an ADIABATIC one i.e. gases cool down as they go up due to adiabatic expansion.
Also note that the compositions at higher altitudes (>100km) is decided more by radiation effects (UV) creating species like Ozone and Monoatomic Nitrogen. I am not sure if the Helium or Hydrogen is there because of its low molecular weight (density / lightness) or its high diffusivity.
The atmosphere has lots of other dynamics at play.
In an idealized chamber as suggested in the OP, the behavior is as described upthread. In contrast, the atmosphere is a roiling turbulent mess, and this keeps the air well mixed below 100 km. Above that, additional processes become important (such as the radiation effects you note).
Perhaps I should not have specified isothermal. My intent was to describe a chamber in which there is no bulk convection of the gas mixture, such that diffusion was the only mechanism for transporting molecules of gas. An isothermal chamber would achieve this, as would one in which the walls were held at a temperature that matched an adiabatic temperature-versus-height profile in the gas mixture.
Not to derail, but because you are describing this better than half a dozen physics courses I would be interested in how this does work in the atmosphere. I know that Helium and Argon on the earth are almost exclusively the result of radioactive decay, thus helium-4 being the most common form on earth despite being one of the least common in the universe as a whole.
My misunderstanding was due to the lightness of these elements that they have a tenancy to rise high enough to be carried away by the solar winds.
I realize that the ionosphere gets complicated and is not related to the ideal gas model but I would appreciate any clarification you can provide on that subject.
If you mean atmospheric mixing as a whole, then there are bulk motions driven by convection from large variations in solar heating (dependent on all three of altitude, latitude, and longitude) and by inertial forces due to the air moving on a rotating earth. Add in turbulence, gravity waves, and convection on lengths scales smaller than the bulk motion, and you end up with thorough mixing.
This applies to species that don’t have significant sources or sinks. The above dynamical processes have timescales measured in hours to months to years, so the basic atmospheric components stay mixed since they are being introduced or removed on way longer time scales – even geological time scales in some cases (key word: “residence time”).
This holds up to an altitude where molecule diffusion becomes dominant. As the atmosphere gets thinner, diffusion velocities become higher. This transition happens at the turbopause, below which turbulent and other mixing effects dominate.
Above the turbopause, the species take on their mass-dependent profiles as discussed upthread, with lighter isotopes stretching higher up. There is a big temperature gradient and the introduction of additional species at these altitudes as well due to molecular dissociation from UV light.
The light isotopes (hydrogen and helium) escape primarily by having a velocity higher than earth’s escape velocity. The earth’s magnetic field keeps the solar wind at bay.