Polymer orientation contributions in large-amplitude oscillatory shear flow

Abstract

Previously, we used a dilute suspension of rigid dumbbells as a model for the dynamics for polymeric liquids in large-amplitude oscillatory shear (LAOS) flow. We then use dumbbell orientation to explain fluid elasticity. We derived the expression for the polymer orientation distribution, and then we decomposed this function into its first five harmonics (the zeroth, first, second, third and fourth harmonics). We further separated the harmonics into their components, in-phase and out-of-phase with cos nωt. In this work, we deepen our understanding of the relationship between the orientation distribution function and the shear stress and normal stress differences. We also investigate the components of orientation that make no contribution at all to measured rheological responses. Further, the larger the γ˙0 of the oscillatory shear flow, the greater the fraction of polymer that escapes rheological measurement. Our analysis focuses on the nonlinear viscoelastic regime, and specifically, where both λω and λγ˙0 are unity. We learn that all orientation contributions to the normal stresses also contribute to the shear stress. The parts of the orientation distribution contributing to the shear stress take on the familiar peanut shapes of the total orientation distribution. The parts of the orientation distribution causing the normal stress differences are subsets of the part of the orientation distribution contributing to the shear stress.