ON CONSISTENCY CRITERIA FOR STRESS TENSORS IN KINETIC-THEORY MODELS

Two different consistency criteria are considered for the stress tense r expressions of two different kinetic theory models for dilute polyme r solutions. The criteria are material objectivity and thermodynamic c onsistency. Two separate approaches for checking thermodynamic consist ency are considered, the first proposed by Grmela [Phys. Lett. 111A, 4 1 (1985)] and the second by Jongschaap [Lecture Notes in Physics (Spri nger, Berlin, 1991)]. The two models considered are a Hookean dumbbell model with internal,viscosity (no linearization or rotation matrix ap proximations), and an inertial, elastic bead-spring chain. Both sets o f criteria may be applied to these models without finding either a clo sed-form expression for the stress tenser, or solving any of the equat ions. We find that the Giesekus form for the stress tenser expression for a Hookean dumbbell with internal viscosity is both thermodynamical ly consistent and objective, whereas the Kramers form is not thermodyn amically consistent. The Kramers form for the stress tenser is found t o be thermodynamically consistent for an inertial, elastic bead-spring chain, but is not materially objective. We also find that the approac hes of Grmela and Jongschaap are the same, although each requires a di fferent ansatz for the relationship between thermodynamic quantities a nd polymer conformations.