On the hysteretic behaviour of dilute polymer solutions in relaxation following extensional flow

Abstract

The hysteretic behaviour of dilute polymer solutions in relaxation following extensional flow is studied in the framework of three distinct theoretical models. For ideal kinematics of uniaxial elongation, we show that the kinetic theory of FENE dumbbells and its FENE-L approximation present a hysteresis when plotting polymer stress versus average molecular extension. Similar behaviour is obtained for ideal extensional kinematics using a FENE-P constitutive equation with a spectrum of finite extensibility parameters. Finally, a numerical simulation of the filament-stretching device shows that spatial inhomogeneities of the stress and average conformation fields also lead to hysteretic behaviour with a single-mode FENE-CR constitutive equation. In all three cases, hysteretic behaviour results from the combined effect of dispersity and non-linearity. We also address the validity of the stress-optic law for FENE dumbbells in relaxation following start-up of uniaxial extension. The simulation results show that the stress-optic coefficient remains constant at low strains only. Plots of stress-optic coefficient versus birefringence show hysteresis as well. This rules out a modified stress-optic law for FENE dumbbells wherein the stress-optic coefficient would be a function of the second moment of the configuration distribution function alone. Finally, it is shown in the Appendix that a proper selection of the spectrum of finite extensibilities can be made so that the multi-mode FENE-P model gives essentially the same stress response as the kinetic theory of FENE dumbbells in transient uniaxial extension.