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


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.


Backward-tracking Lagrangian particle method; deformation field method; branched polymer melts; pompom model; contraction/expansion