Continuum thermodynamics and transport theory for polymer—fluid mixtures

The foundations of a self-consistent, continuum theory for the transport of small molecular- weight fluids in polymeric media are established, which can describe Fickian, Case II and other non-Fickian diffusion phenomena. The framework is founded on the basic principles of continuum thermodynamics, which include the entropy inequality and balances of mass, linear momentum, angular momentum, and energy. This framework has been implemented for a specific class of mixtures whose nonequilibrium thermodynamic properties depend on the instantaneous values of species' concentrations, velocities and density gradients, temperature gradient, and the histories of strain and temperature, The plasticization effect of fluids on the polymer viscoelastic properties is treated using the concept of a material time, where the effect of temperature and composition on the relaxation behavior is included via a time—temperature—concentration shift function. Component mass fluxes have been derived and include the effects of chemical-potential gradients, elastic and viscoelastic stresses, and thermal diffusion. Thus the general theory accounts for the stress-induced transport mechanism in nonequilibrium, viscoelastic materials without the near-equilibrium assumption of linear irreversible thermodynamics. All material properties required for this transport theory can be obtained by independent experiments. In this communication we establish the theory upon which numerical comparisons with experimental data are based in future communications.