How Can Gravity and Diffusion Be Modeled in a Two-Gas System?

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SUMMARY

The discussion focuses on modeling the concentration distribution of two gases with different densities in a closed vertical cylinder, specifically addressing the effects of gravity and diffusion. The lighter gas remains at the top, while the heavier gas settles below, leading to a gradient rather than a sharp boundary. Participants suggest utilizing the binary diffusion coefficient and potentially the Boltzmann distribution to calculate the steady-state concentration distribution. The conversation emphasizes the need for a formal approach, possibly involving kinetic theory of gases.

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bemortu
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Hi.
I've thought for some time about a problem that I'm not able to solve (to my own surprise).

We have closed container, say a relatively high cylinder, placed vertically. In it are two gases of different density enclosed. Obviously the lighter one will 'fleet' and stay on top of the heavier gas. I suppose, though, that the boundary between the two gases will not be sharp. Rather I would expect them to mix due to diffusion. Suppose that we know the densities and the binary diffusion coefficient, how can the resulting concentration distribution be calculated (in steady state)?

Is it necessary to go back to some sort of kinetic theory of gases here or can it be done on a 'higher' level? I just don't find the right formalism to approach it...

Anybody has any idea?
 
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