Prediction of rheometrical and complex flows of entangled linear polymers using the double-convection reptation model with chain stretch
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We study the rheometrical and complex flow response of the double-convection-reptation (DCR) model with chain stretch proposed recently by Ianniruberto and Marrucci (2002) for entangled linear polymers. The single- and two-mode differential versions of the model are used, with the parameter values identified by Ianniruberto and Marrucci (2002) for a nearly monodisperse polybutadiene solution. These authors found that the DCR model with stretch predicts the rheometrical shear behavior of the fluid well in the modest experimental range of deformation rates. Our calculations for the higher shear rates reached in simulations of complex flow reveal anomalous or questionable behavior, namely, shear thickening over an intermediate range of shear rates and large chain stretch in fast shear flows. This behavior is shown to be shared by the original integro-differential DCR theory, of which the differential DCR model is actually a mathematical approximation. We also show that the original DCR theory with stretch predicts excessive shear thinning at high shear rates, while its differential approximation remains stable for all shear rates. Using the backward-tracking Lagrangian particle method [Wapperom et al. (2000)], we investigate the response of the differential DCR model in start-up flow through an axisymmetric contraction/expansion geometry. We compare the single- and two-mode model predictions (in terms of the steady-state vortex structure, chain stretch, and overall pressure drop), and correlate these with the steady and start-up rheometrical responses in shear and extension. Significant chain stretch is predicted in the vicinity of the axis of symmetry and in thin boundary layers located at the constriction wall. As a result, the DCR predictions significantly depart from the stress-optical rule in these flow regions. Chain stretch also affects the flow kinematics, with the appearance of a large upstream steady-state vortex. Surprisingly, however, the predicted pressure drop is not affected much by these kinematical changes, and is, qualitatively described by a simple inelastic, shear-thinning model. (C) 2003 The Society of Rheology.