Prediction of Stress Jump and Elongational Viscosity via Network Theory

Abstract

Abstract The network model, originally developed for rubber like materials and later extended to model liquids, is subject to modifications. In this work, we look at the adaptation for improved elongational viscosity predictions and to allow for stress jump predictions. A new formulation involving non-affine motion is proposed and its applications are presented. The major improvement is that a finite elongational viscosity is predicted for finite elongational rate, contrary to infinite elongational viscosities existing at some elongational rates predicted by most previous network models. Comparisons with experimental data on shear viscosity, primary normal stress coefficient and elongational viscosity are given, in terms of the same set of model parameters. The model is successfully tested with data on a polyisobutylene solution (S1). A further extension of the network model is related to the prediction of the stress jump phenomenon which is defined as the instantaneous gain or loss of stress on startup or cessation of flow. It is not predicted by most existing models. In this work, the internal viscosity idea used in the dumbbell model is incorporated into the transient network model. Via appropriate approximations, a closed form constitutive equation, which predicts a stress jump, is obtained. Successful comparisons with the available stress jump measurements are given. In addition, the model yields good quantitative predictions of the standard steady and dynamic material functions, for xanthan solutions and for Polyacrylamide solutions.