| In the last decade significant progress has taken place within non-equilibrium thermodynamics resulting in several formulations for coupled transport phenomena that allowed for an extension and a more systematic application of continuum mechanics to continua endowed with an internal microstructure. A particular fruitful area for applications has been the rheology of complex systems where nonequilibrium thermodynamics has been used to connect the modeling for the mechanical behavior to a description of the internal microstructure. Nonequilibrium thermodynamics can place constraints on model admissibility through the requirement of non-negative entropy production and establish links between various parts of the governing equations linking terms in the expression for the stress tensor to others appearing in the evolution of the internal structure or in mass transfer. Moreover, thermodynamic phase transitions and surface-induced effects can now be consistently described under nonequilibrium conditions. Finally, the connection between various levels of description (for example, microscopic versus macroscopic) can more consistently be made. A particular example in polymer rheology is the nonequilibrium casting of kinetic theory models that has allowed for a more systematic handling of heat and mass transfer effects. In this presentation we will first outline the general modern approach that involves the merging of the more traditional approach of modeling dissipative phenomena through Linear Irreversible Thermodynamics (and its nonlinear generalizations) with the most general Poisson-bracket description of conservative dynamics. Then, we will overview illustrative examples to rheology with particular emphasis to the study of polymer systems under flow. New phenomena are observed due to the coupling between various transport and relaxation processes with important consequences as far as the understanding of the nonlinear dynamics and the rheology of complex systems. |
