A constitutive equation for entangled linear polymers inspired by reptation theory and consistent with non-equilibrium thermodynamics

Adrien Leygue (1) , Anthony Beris (1) , Roland Keunings (1)

1 CESAME - Centre for systems engineering and applied mechanics [Louvain]

Using the single generator bracket formalism of non-equilibrium thermodynamics, we build a thermodynamically consistent constitutive equation of the differential type for linear entangled polymers. The starting point of our developments is the MGI rheological model proposed recently by Marrucci et al. [Rheol. Acta 40 (2) (2001) 98], which can be viewed as a modification of the classical Doi–Edwards reptation theory that includes convective constraint release and a modified strain measure. The proposed constitutive equation has an additional parameter which governs the dissipative part of the model. The MGI model is recovered as a particular case, but with a stress-conformation relationship which contains an additional term suggested by non-equilibrium thermodynamics. Predictions of the proposed model in steady and transient shear flows are shown to be in qualitative agreement with experimental observations.

Mots clés: Non-equilibrium thermodynamics; Reptation theory; Linear polymers; Constitutive equation

Domaines: Mécanique [physics.med-ph]; Matériaux

Adrien Leygue, Anthony Beris, Roland Keunings. A constitutive equation for entangled linear polymers inspired by reptation theory and consistent with non-equilibrium thermodynamics. Journal of Non-Newtonian Fluid Mechanics, 2001, 101 (1-3), pp.95-111. ⟨10.1016/S0377-0257(01)00143-4⟩. ⟨hal-01004691⟩