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

AI Thread Summary
In a closed vertical cylinder containing two gases of different densities, the lighter gas will rise above the heavier one, but the boundary between them is expected to be mixed due to diffusion. The discussion centers on calculating the resulting concentration distribution in a steady state, given the densities and binary diffusion coefficient. Participants explore whether a kinetic theory of gases approach is necessary or if a higher-level method can be applied. The Boltzmann distribution is mentioned as a potential consideration in the analysis. The conversation seeks a formalism to effectively model the interaction of gravity and diffusion in this two-gas system.
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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