A mesoscopic thermodynamical description of rheological models

Abstract

We propose a simple and systematic description of the most used viscoelastic models by using a non-equilibrium thermodynamic approach, generally referred to as the internal variables theory. The main idea is to elevate the conformation tensor $\textsf{C}$ describing the geometrical configuration of the macromolecules to the status of independent variable. It is shown that the sole knowledge of the Helmholtz free energy— whose explicit expression is provided by the kinetic theory—allows to derive the expressions of the polymeric stress tensor and the time evolution equation of the internal variable $\textsf{C}$, which represents the main ingredients of the rheological models. As illustrations, the Hookean, FENE-P Giesekus, and Bird’s encapsulated dumbbell models are discussed. For completeness, the results are compared with these provided by extended irreversible thermodynamics.