A model with coupled Maxwell modes using Giesekus' postulate

Relaxation modes must be considered coupled on several occasions, such as in polymer blends. Edwards et al. [J. Rheol, 40, 917–942 (1996)], using the generalized bracket formalism of non-equilibrium thermodynamics, provided the first thermodynamically derived constitutive model with coupled Maxwell modes by introducing relaxation coupling between the modes. In this work, we derive a similar model wherein coupling is introduced by using Giesekus' postulate to the mobility tensor and its introduction in the relaxation matrices, without considering cross-relaxation matrices. Our approach bears the following advantages over the work of Edwards et al.: (a) it derives the coupling term, instead of simply invoking it, by using the Giesekus postulate, (b) it is more in line with rheological experimental data for polymer blends, and (c) the proof of thermodynamic admissibility is easier to perform.