Microforces and the Theory of Solute Transport
Abstract
A generalized continuum framework for the theory of solute transport in fluids is proposed and systematically developed. This framework rests on the introduction of a generic force balance for the solute, a balance distinct from the macroscopic momentum balance associated with the mixture. Special forms of such a force balance have been proposed and used going back at least as far as Nernst's 1888 theory of diffusion. Under certain circumstances, this force balance yields a Fickian constitutive relation for the diffusive solute flux, and, in conjunction with the solute mass balance, provides a generalized Smoluchowski equation for the mass fraction. Our format furnishes a systematic procedure for generalizing convection-diffusion models of solute transport, allowing for constitutive nonlinearities, external forces acting on the diffusing constituents, and coupling between convection and diffusion.
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Cite
@article{arxiv.cond-mat/9904312,
title = {Microforces and the Theory of Solute Transport},
author = {Eliot Fried and Shaun Sellers},
journal= {arXiv preprint arXiv:cond-mat/9904312},
year = {2018}
}
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17 pages