Thermodynamic instability of polymeric liquids in large-amplitude oscillatory shear flow from corotational Maxwell fluid

Abstract

When polymeric liquids are subjected to oscillatory shear flow, if the amplitude of the shear rate is high enough, the shear stress response will become aperiodic. This has been variously attributed to fracture, common line ingress, slip, shear-banding and phase change, however, the underlying causes for these is unclear. In this paper we explore the creation of new thermodynamic phases as the trigger for these phenomena. Specifically, we examine two thermodynamic instability criteria that have been suggested for large-amplitude oscillatory shear flow (LAOS). One of these criteria is based on non-equilibrium thermodynamics (the Ziegler criterion), and the other, on equilibrium thermodynamics (the free energy criterion). The advent of exact solutions for stress responses to LAOS provokes this investigation. We use one such exact solution to evaluate these criteria for the simplest relevant constitutive model, the corotational Maxwell fluid. By relevant, we mean at least predicting higher harmonics in LAOS. We find that, in steady shear flow, the Ziegler instability arises when the dimensionless shear rate exceeds the square root of the golden ratio, Applying our results to instability measurements on dissolved polybutadiene, we find the Ziegler criterion to be useful at low frequency, and the free energy criterion to be useful elsewhere.