Diffusion in binary mixtures: an analysis of the dependence on the thermodynamic factor

We study the diffusion process in binary mixtures using transition probabilities that depend on a mean-field potential. This approach reproduces the Darken equation, a relationship between the intrinsic and the tracer diffusion coefficients, \(D_A\) and \(D_A^*\), through the thermodynamic factor \(...

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Bibliographic Details
Published in:arXiv.org 2019-05
Main Authors: Marisel Di Pietro Martínez, Hoyuelos, Miguel
Format: Article
Language:English
Subjects:
Activity coefficients
Binary mixtures
Dependence
Diffusion
Tracer diffusion
Transition probabilities
Online Access:Get full text
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Summary:We study the diffusion process in binary mixtures using transition probabilities that depend on a mean-field potential. This approach reproduces the Darken equation, a relationship between the intrinsic and the tracer diffusion coefficients, \(D_A\) and \(D_A^*\), through the thermodynamic factor \(\Phi\) (a function of the derivative of the activity coefficient against molar fraction). The mean-field approach allows us to go beyond the Darken equation and separately specify the dependence of \(D_A\) and \(D_A^*\) on the thermodynamic factor. We obtain that \(\Phi\) appears in the expression for \(D_A^*\), but the intrinsic diffusivity \(D_A\) turns out to be independent of \(\Phi\). Experimental results taken from the literature on diffusion in metal alloys are consistent with this theoretical prediction.
ISSN:2331-8422
DOI:10.48550/arxiv.1905.07249