Peter Wapperom and Roland Keunings
Simulation of linear polymer melts in transient complex flow
Journal of Non-Newtonian Fluid Mechanics 95 (2000) 67-83
Recently, much progress has been made in improving the modeling 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 (Rheol. Acta 2000), 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
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 also in complex flow, 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.
Lagrangian particle methods; deformation field method; integral models;