Microforces and the Theory of Solute Transport

Details Microforces and the Theory of Solute Transport Microforces and the Theory of Solute Transport

1999-04-22

arxiv.org/abs/cond-mat/9904312v1

Physics

Condensed Matter

Soft Condensed Matter

17 pages

Scientific paper

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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