Shear banding in polymeric fluids under large amplitude oscillatory shear flow

Abstract

In this thesis, I theoretically explore shear banding of entangled linear polymer solutions and melts in large amplitude oscillatory shear strain (LAOStrain) and stress (LAOStress) protocols. This work moves beyond that of Moorcroft and Fielding [2013, 2014] who showed time-dependent shear banding in shear startup and step stress protocols. These protocols are only transiently time-dependent. LAOStrain and LAOStress have a sustained time-dependence. I consider the criteria derived in [Moorcroft and Fielding 2013] to predict the onset of shear banding in the transient material response for shear startup and step stress, relative to the triggers of shear banding in LAOStrain and LAOStress. I find that stability to the formation of shear banded flow in the LAOS protocols can be understood - to a good approximation - by the known triggers of shear banding in these simpler transiently time-dependent protocols.

I employ the Rolie-Poly (RP) model [Graham et al. 2003] to investigate the existence of shear banding in LAOStrain and LAOStress over a wide range of imposed amplitudes and frequencies. I find shear banding to occur in the alternance state (where time-translational invariance is achieved), even in materials that are known to remain homogeneous at the steady state.

For each protocol I consider the relative influence of the constraint-release stress relaxation RP parameter and entanglement number (Z) on the intensity of shear banding across the phase space. I find significant shear banding to occur in both LAOStrain and LAOStress for experimentally-realistic values of Z, both in materials that shear band to steady state, and those that don't. The main results of these investigations are submitted for publication in the Journal of Rheology [Carter et al. 2016].

Finally, I consider the shortcomings of using a single-mode RP model when characterising the full chain dynamics of entangled linear polymers in flow. I employ a multimode approach and fit a power-law spectrum to experimental linear rheology data and investigate time-dependent shear banding in the presence of higher-order relaxation dynamics. For this, I use the simpler shear startup protocol and investigate the limits under which significant shear banding exists for well-entangled polymers and discuss the possible importance of considering edge fracture as a mechanism for shear banding.