# Mass diffusion: is $D_{AB} \neq D_{BA}$ at high pressures? If so, why?

From [Takahashi][2], I validated some models I have for estimating diffusion coefficients (methods of Fuller modified by Riazi for high-pressures, all pulled from [Poling][3]). Here is the figure mixing experimental data and the models I was looking at.

The experimental data was measuring diffusion coefficients between CO2 and C2H4 over a range of pressure. As expected, at low pressures, does not matter if we are looking at how a trace of CO2 diffuses into C2H4 or if a trace of C2H4 diffuses in CO2, the mass is being diffused at the same speed and thus the diffusion coefficients are the same. However, at high pressures, it is not the case. I've seen complex mathematical expressions modeling it however, and clearly, even my crude model picks up at least the trend, but I'm not sure I understand exactly why it happens. Is it the diffusion matrix that becomes non-symmetric? Or the diffusion process can no longer be modeled just by this diffusion coefficient and other terms appear? Either way, from a molecular point of view, what explains this change of behavior?

[2]: S. Takahashi and M. Hongo. Diffusion coefficients of gases at high pressures in the CO2-C2H4 system. Journal of Chemical Engineering Japan, 15:57–59, 1982.

[3]: B. E. Poling, J. M. Prausnitz, and J. P. O’Connell. The Properties of Gases and Liquids, Fifth Edition. McGraw-Hill, 2001.

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If I were to hazard a guess, I would say that it's due to the intermolecular forces. The London dispersion force should increase with density (and hence pressure) making the gas molecules more attracted to each other.

Now, C2H4 is lighter than CO2 and thus has less intermolecular force. So, when you have just a trace of CO2 in C2H4 at high pressure, it should diffuse faster (less intermolecular force in the "bulk" gas) than when you have a trace of C2H4 in CO2 (higher intermolecular force in the "bulk" gas). This is reflected by the higher CO2-C2H4 coefficients.

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 Nicely put ! That's what I think too, let's see what other answers we get. – FrenchKheldar Nov 24 '12 at 7:50