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 Smoluchuwski 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.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
TAM R 904
1999-6006
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112612
Sponsor(s)/Grant Number(s)
Energy Department; EPSRC UK
Copyright and License Information
Copyright 1999 Board of Trustees of the University of Illinois
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.
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