Paper to the Polymer Processing Society 14th Annual Meeting, Yokohama, Japan, 8th-12th June 1998, paper 2-6.

S F Bush with F G Torres

Introduction

A model proposed by Bush1 has been extended and numerically implemented to produce molecular chain conformations in polymer flows. The effect of shear and extensional flows is studied. The chain shape is defined as a primary transport variable and viscosity is predicted thereof.

Two main approaches have been used in the modelling of polymer flows: the continuum mechanics approach and the molecular approach. The present work is based on the second one. Chain shape is a term used to express the actual conformations of a single entangled polymer chain at a specific time and place in the flow domain. The chain shape and the number of entanglements determine the resistance to flow of a polymer melt. So, viscosity is obtained as a function of the actual chain shape. To allow for the simulation of chain conformations, equivalent chain segments have been defined as primary transport variables, which are convected from one point to another in the flow field. Due to its formulation, the present model allows for polymer viscoelasticity to be represented in a natural way, with the shear and normal stresses being calculated as a function of the chain shape and of the velocity gradients. The treatment followed in this work can be extended in a straightforward manner for the modelling of polymer crystallisation and the prediction of shrinkage in plastic parts.

References

[1] BUSH S F, “Representation of Polymer Chain Shape in Injection Moulding simulation” Poly Proc Soc (PPS European Regional Mtg) Sept 1988, Brunel Univ, UK.

[2] TORRES F G, MPhil Thesis, UMIST, Manchester, UK, 1997.

[3] BUSH S F and DYER P, “The Experimental and Computational Determination of Complex Chemical Kinetics Mechanisms”, Proc Royal Soc, London, A 351, pp 33-53, 1976

See also the section on Mathematics & Computation.