Fick's law: A derivation based on continuum mechanics

Abstract

In this study we derive Fick's law on the basis of the principles of chemical species mass and momentum conservation. The goal is to provide a simple derivation of this equation using a continuum mechanics approach. In addition, the associated assumptions and constraints that may limit its application are clearly identified. Our result is an analysis that derives Fick's law in liquid systems, and it is presented so that only a basic knowledge of continuum mechanics is needed to follow the derivation.

Keywords: Fick's law, dilute solution, diffusion velocity, continuum mechanics, multicomponent mixtures.

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