Fourier decomposition of polymer orientation in large-amplitude oscillatory shear flow

Structural Dynamics
A J GiacominA M Schmalzer

Abstract

In our previous work, we explored the dynamics of a dilute suspension of rigid dumbbells as a model for polymeric liquids in large-amplitude oscillatory shear flow, a flow experiment that has gained a significant following in recent years. We chose rigid dumbbells since these are the simplest molecular model to give higher harmonics in the components of the stress response. We derived the expression for the dumbbell orientation distribution, and then we used this function to calculate the shear stress response, and normal stress difference responses in large-amplitude oscillatory shear flow. In this paper, we deepen our understanding of the polymer motion underlying large-amplitude oscillatory shear flow by decomposing the orientation distribution function into its first five Fourier components (the zeroth, first, second, third, and fourth harmonics). We use three-dimensional images to explore each harmonic of the polymer motion. Our analysis includes the three most important cases: (i) nonlinear steady shear flow (where the Deborah number [Formula: see text] is zero and the Weissenberg number [Formula: see text] is above unity), (ii) nonlinear viscoelasticity (where both [Formula: see text] and [Formula: see text] exceed unity...Continue Reading

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