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I risk repeating a question that has been asked too many times, but ... is there a rigorous (but not too complicated) way to derive Fick's first law?

In this post the answer starts from what is supposed to be the end.

As the related Wikipedia page pointed out, there is a rigorous derivation for gas mixtures in the book Combustion theory by F. A. Williams, specifically in Appendix E.2. However, in order to understand it, the reader has to be familiar with objects like pressure tensors, Sonine polynomials expansion and so on. Is this all really necessary? After all, the final result is relatively simple.

Qmechanic
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  • This one is okay for you ? – Agnius Vasiliauskas Dec 27 '22 at 19:52
  • The best way to understand it is that ficks law arrises from an expansion to lowest order in gradients of a density/ concentration. One can include gradients of arbitrarily high order but normally they are irrelevant to slow dynamics. To me it's a similar question to deriving a Landau free energy from first principles, which generally isn't possible. – Luke Dec 27 '22 at 20:06

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