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Corrected Diffusivity in Draken's equation

Physics Asked on November 30, 2021

In the article I have been reading, we introduce the term "corrected diffusivity".
Diffusion alone and the rest of the article is pretty much clear, but I can’t quite grasp the physical meaning behind corrected diffusivity.
The term is found in the Draken’s equations which connects transport diffusion with corrected diffusion:

$$ D_t(c) = D_0(c) left[ frac{(partial{ln{f}})}{partial{ln{c}}} right]_T $$

Calculation for corrected diffusion:

$$ D_0 = frac{1}{6N}lim_{ttoinfty} frac{1}{t}left< |sum_{i=1}^{N} (r_i(t)-r_i(t_0))|^2 right> $$

The article is based around molecular simulation of the diffusion of hydrocarbons.

Problem seems to be quite specific for the area so I am sorry I’m not able to give better explanation. I was hoping some of you are doing research in the similar field and will be able to give me some insight into meaning of the term corrected diffusivity used here.

One Answer

Assuming that an answer is still needed: According to an article by Jörg Kärger and Douglas M. Ruthven (DOI:10.1039/C5NJ02836A) the transport diffusivity is the product of an "intrinsic" mobility multiplied by the thermodynamic factor. One can interprete it in such a way that the corrrected diffusivity is the pure diffusivity/mobility of molecules without the influence on sorption behavior on it.

A similar equation to the first one in the question uses the thermodynamic factor to link concentration gradients to chemical potential gradients, for example Krishna et al. (DOI:10.1021/jp906879d) and Dubbeldam and Snurr (DOI:10.1080/08927020601156418), effectively connecting chemical potential based diffusion coefficients (the corrected one) and concentration based diffusion coefficients (the transport one, Fickean).

Answered by GoodLuck on November 30, 2021

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