On the occurrence of even harmonics in the shear stress response of viscoelastic fluids in large amplitude oscillatory shear

The non-linear response of polymeric liquids observed experimentally in large amplitude oscillatory shear (LAOS) is generally characterized by the presence of odd harmonics of the excitation frequency in the Fourier spectrum for the shear stress. Even harmonics of relatively smaller amplitude have also been observed, whose appearance is usually attributed to wall slip phenomena. In the: present work, we show that wall slip is not a necessary condition for the occurrence of even harmonics. To this end, we perform a non-linear study of planar LAOS flow between two infinite parallel plates using either a monotone or non-monotone viscoelastic constitutive equation (i.e., respectively, the Giesekus and Johnson-Segalman models). The analysis allows for spatially non-homogeneous velocity and stress fields. We assume no-slip boundary conditions, and investigate the combined effects of inertia, elasticity, and shear thinning by means of spectral methods. A regular perturbation analysis is also conducted in the inertialess monotone case. Results for the Giesekus model show that combination of elasticity and shear thinning yields transient even harmonics in shear stress whose life span and intensity are considerably increased by inertia. Furthermore, the one-dimensional flow is unstable to finite two-dimensional perturbations under inertia and at high elasticity. This results in the development of secondary flows and saturation of even harmonics into small but finite values. Simulations for the non-monotone Johnson-Segalman model predict even harmonics of relatively larger amplitude that settle in dynamic equilibrium. Furthermore, the fluid's response is quasi-periodic with the appearance of incommensurate frequencies. (C) 2004 Elsevier B.V. All rights reserved.