Equal Low-Order Finite Element Simulation of the Planar Contraction Flow for Branched Polymer Melts

Abstract

The rheological characteristics of branched polymer melts is described by the modified XPP model, which is discretized by inconsistent streamline-upwind method. A finite increment calculus procedure is introduced to reformulate the mass equation and to overcome oscillations of the pressure field. Moreover, the governing equations are discretized and solved by the iterative fractional step algorithm. Thus the equal low-order finite elements for velocity-pressure-stress variables are adopted to calculate the planar contraction viscoelastic flows. The influences of the Weissenberg number and the amount of branched-arms on the rheological behavior of the Pom-Pom molecule are discussed. Results demonstrate good agreement with those given in the literatures.

Keywords:

• Equal low-order finite element
• Fractional step algorithm
• Planar contraction
• Rheological behavior
• Viscoelastic flow
• XPP model

ACKNOWLEDGMENTS

The authors are pleased to acknowledge the support of this work by the National Natural Science Foundation of China through Contract/Grant numbers 10590354, 10672033 and 10272027. The first author would also like to acknowledge Prof. Q.Y. Wu for many stimulating discussions.