### Peter Wapperom, Roland Keunings and Giovanni Ianiruberto

### Prediction of
rheometrical and complex flows of entangled linear polymers using the
double-convection-reptation model with chain stretch

#### Journal of Rheology **47**, 2003, p. 247-265

#### Abstract

We study the rheometrical and complex flow response of the
double-convection-reptation (DCR) model with chain stretch
proposed recently by (J. Non-Newtonian Fluid
Mech. 102 (2002) 383--395) for entangled linear
polymers. The single- and two-mode
differential versions of the model are used, with parameter values
identified by (J. Non-Newtonian Fluid
Mech. 102 (2002) 383--395) for
a nearly monodisperse polybutadiene solution. These authors found that
the DCR model with stretch predicts well the
rheometrical shear behavior of the fluid in the modest experimental
range of
deformation rates. Our calculations for the higher shear rates reached
in the simulations of complex flow reveal
anomalous or questionable behavior, namely shear-thickening over an
intermediaterange of shear rates and large chain stretch reached 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
(J. Non-Newtonian Fluid Mech. 91 (2000) 273--295), 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 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
much affected by these kinematical changes, and is qualitatively
described by a simple inelastic,
shear-thinning model.
#### Keywords

Numerical simulation; contraction/expansion; DCR model