Simulation of linear polymer melts in transient complex flow

Abstract

Recently, much progress has been made in improving the modelling of linear polymer melts with the aid of reptation theory. In simple shear flows, this has resulted in a much better prediction of the shear viscosity and normal stress ratio. Here, we evaluate in complex flow the transient and steady-state behaviour of a recently proposed reptation model, the Marrucci–Greco–Ianniruberto model [G. Marrucci, F. Greco, G. Ianniruberto, Rheol. Acta, 2000, submitted for publication], that includes convective constraint release and a force balance on the entanglement nodes. To incorporate integral type models into the numerical framework of Lagrangian particle methods, developed previously to simulate dilute polymer solutions, we have included the so-called deformation field method. For the contraction/expansion flow that we consider, we find that a correction of the convective constraint release contribution to the relaxation time is necessary to avoid the unphysical situation of negative relaxation times. With this correction, we could obtain mesh and time convergence for high Weissenberg numbers without adding any solvent viscosity. We find that in complex flow also, both the steady-state and transient response of the integral model can be very well approximated by a constitutive equation of differential type. Due to the dominance of the strong thinning in both shear and elongational flows for the model, however, the inelastic Carreau–Yasuda model reproduces the steady-state kinematics and pressure drop as well.