Macromolecular tumbling and wobbling in large-amplitude oscillatory shear flow

Abstract

For a suspension of rigid dumbbells, in any simple shear flow, we recently solved for the diffusion equation for the orientation distribution function by a power series expansion in the shear rate magnitude. In this paper, we focus specifically on large-amplitude oscillatory shear flow (LAOS), for which we extend the orientation distribution function to the 6th power of the shear rate amplitude. We arrive at the Fourier solution for each harmonic contribution to the total orientation distribution function, separating each harmonic into its coefficients in and out-of-phase with cosnωt , ′ ψ n and ′′ ψ n , respectively. We plot, for the first time, the evolving normalized alternant macromolecular orientation. Moreover, to deepen our understanding of the macromolecular motions, we distinguish and study the two types of possible rotations, tumbling and wobbling.*Corresponding author (giacomin@queensu.ca) CONTENTS

Hydrodynamic interaction for rigid dumbbell suspensions in steady shear flow

“…The pattern of solution for ψ θ ,φ ( ) has been recently uncovered for any simple shear flow [11], and implemented to yield Eq. (1) up to k = 6 , for oscillatory shear flow [12].…”