Peter Wapperom and Roland Keunings
Numerical simulation of branched polymer melts in transient complex
flow using pom-pom models
Journal of Non-Newtonian Fluid Mechanics 97 (2001) 267-281
Abstract
In recent years, a number of constitutive equations have been derived
from reptation theory to describe the rheology of both linear and
branched polymer melts. While their predictions in rheometrical flows
have been discussed in detail, not much is known of their behaviour in
complex flows. In the present paper, we study by way of numerical
simulation the transient, start-up flow of branched polymers through a
planar contraction/expansion geometry. The constitutive equation is
the so-called pom-pom model introduced by McLeish and Larson
(J. Rheol. 42), and later modified by Blackwell et al.
(J. Rheol. 44). By combining the Backward-tracking Lagrangian
Particle (J. Non-Newtonian Fluid Mech. 91) and Deformation Field
(J. Non-Newtonian Fluid Mech. 89)
methods, we obtain results for the original,
integral pom-pom model which makes use of the Doi-Edwards orientation
tensor. Two simplified versions of the pom-pom model are also
considered, namely one based on the Currie approximation for the
orientation tensor, and a differential constitutive equation proposed
by McLeish and Larson (J. Rheol. 42). Finally, the simulation results
are compared to
those obtained with the so-called MGI model proposed recently by
Marrucci et al. (Rheol. Acta, 2000) for describing linear
polymer melts.
Keywords
Backward-tracking Lagrangian particle method; deformation field method;
branched polymer melts; pompom model; contraction/expansion