Microforces and the Theory of Solute Transport

TL;DR

This paper introduces a generalized continuum framework for solute transport in fluids, incorporating a distinct force balance for solutes that extends traditional diffusion models and enables complex nonlinear and coupled behaviors.

Contribution

It develops a systematic approach to extend convection-diffusion models by including external forces, nonlinearities, and coupling effects in solute transport theory.

Findings

Derives a generalized Smoluchowski equation for solute mass fraction.

Provides a systematic method to incorporate external forces and nonlinearities.

Connects the new framework with classical diffusion theories like Nernst's.

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.