Macromolecular Origins of Fifth Shear Stress Harmonic in Large-Amplitude Oscillatory Shear Flow

Abstract

This study examines the simplest relevant molecular model of a polymeric liquid in large-amplitude oscillatory shear (LAOS) flow: the suspension of rigid dumbbells in a Newtonian solvent. For such suspensions, the viscoelastic response of the polymeric liquid depends exclusively on the dynamics of dumbbell orientation. We have previously derived explicit analytical expressions for the shear rate amplitude and frequency dependences of the first and third harmonics of the alternating shear stress response in LAOS. Higher harmonics sculpt the shear stress, distorting it from its sinusoidal shape. In this work, we derive the polymer contribution to the shear stress response up to and including the next higher, fifth harmonic. For this, we use the fourth order term in the expansion of the orientation distribution to calculate the shear stress response. Our analysis employs the general method of Bird and Armstrong [J Chem Phys, 56, 3680 (1972)]. Our expression is the only one to have been derived from a molecular theory for a fifth harmonic. Our paper thus provides the first glimpse of the molecular origins of a shear stress harmonic higher than the third.