  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.
