where mA is the mass of a molecule of species A. Thus, the particle density decays exponentially with scale height Ha. Note that this is identical in form to the particle density given by hydrostatic balance, except that the equation we have just derived applies to the particle density of each species separately, and not just to the particle density of all species together. In fact, in equilibrium each species acts as if it were in hydrostatic equilibrium separately, and has the same hydrostatic scale height as if the other gases weren't there at all. Since we are assuming thermodynamic equilibrium, all species are characterized by the same temperature, and of course all species are subject to the same gravitational acceleration. Thus, the scale height varies inversely with the molecular weight of the species. Since the density of light species decays less sharply with altitude than the density of heavier species, the atmosphere will tend to sort itself out in the vertical according to molecular weight. Light constituents will congregate near the top of the atmosphere like escaped helium balloons at the top of a circus tent.
This can only happen, however, if the mixing is dominated by molecular diffusion. In the lower atmosphere, mixing is overwhelmingly due to turbulent fluid motions, which treat all species equally and keep the mixing ratios uniform, in the absence of strong sinks or sources by chemistry or phase change. Since the molecular diffusivity is inversely proportional to total particle density, it will increase roughly exponentially with altitude, and will therefore come to dominate turbulent mixing at sufficiently high altitudes. The altitude where diffusive segregation begins to set in is called the homopause (sometimes turbopause) and the lower part of the atmosphere where mixing ratios of nonreactive substances are uniform is called the homosphere. It is very difficult to get an a priori estimate of turbulent mixing rates - indeed at one time it was expected that the Earth's stratosphere would be diffusively segregated. More often than not, observations of atmospheric composition provide the most reliable estimate of the degree of turbulent mixing. For the present Earth, the homopause is near 100km, at which point the observed particle density is nh(Earth) = 1.2 • 1019/m3.
Above the homopause, then, atmospheric constituents segregate in the vertical according to molecular weight. The region above the homopause is also typically (though not necessarily) where atmospheric molecules begin to be exposed to ultraviolet photons sufficiently energetic to break up even the more stable components into lighter constituents, which also will stratify according to molecular weight. For Earth the scale height for N2 is 9.1 km, for CO2 is 5.8km, for O2 is 8.0km, for atomic oxygen is 15.9km, for H2 is 127.3km and for atomic hydrogen is 254.5km, all based on a temperature of 300K. Numbers for Venus are similar. The first implication of these numbers is that the scale height for hydrogen is so large that even a small concentration of hydrogen at the homopause can cause the atmosphere to become hydrogen dominated a small distance above the homopause. For example, if an N2/H2 atmosphere contains 1% molar concentration of H2 at the homopause, then 50km up the concentration has risen to 63% and 70km up it is 93%. If the
H2 is converted to atomic hydrogen above the homopause, the segregation is even more effective. Similarly, if we take an Earthlike atmosphere that is 80% N2 and 20% O2 at the homopause, and then convert the O2 into atomic oxygen, we wind up with 33% atomic oxygen near the homopause. By 20km up, the concentration reaches 56%, and at 40km it is 76% and thoroughly dominates the atmospheric composition. Finally, if we take an Early Earth CO2/N2 atmosphere consisting of 10% CO2 at the homopause, then the CO2 concentration falls to 0.5% 50km up, whereby we expect the outer atmosphere to be N2 dominated. It is possible that the dissociation of CO2 into CO and O could lead to an atomic oxygen dominated exobase, but the fact that this does not happen on Venus today suggests strongly that the dissociation is too weak for this to happen, or the recombination of the two species is too efficient 3.
Given an estimate of the turbulent diffusivity Dturb, the homopause density can be estimated directly from the scaling of the diffusion coefficient. Specifically, since D « ^(kT/m)1 then setting D = Dturb and using the expression for the mean free path I implies
Was this article helpful?