Role of Micellar Entanglement Density on Kinetics of Shear Banding Flow Formation: Experiments and a Comparison with the VCM model

We investigate the effects of micellar entanglement density on the kinetics of shear banding flow formation in a Taylor-Couette flow via a combination of experiments and simulations of the Vasquez-Cook-McKinley (VCM) model. In experiments, three sets of wormlike micellar solutions, each set with a similar fluid elasticity and zero-shear-rate viscosity, but with varying entanglement densities, are studied under start-up of steady shear. Our experiments indicate that in the set with the low fluid elasticity, the transient shear banding flow is characterized by the formation of a transient flow reversal in a range of entanglement densities. Outside of this range, the transient flow reversal is not observed. For the sets of medium and high elasticities, the transient flow reversals exist for relatively small entanglement densities, and disappear for large entanglement densities. Our analysis shows that wall slip and elastic instabilities do not affect this transient flow feature. Consistent with experiments, simulations of the VCM model predict that as the micellar entanglement density increases, the strength of the transient flow reversal first increases, then, at a higher entanglement density, the transient flow reversal weakens. We identify a correlation between micellar entanglement density, the width of the stress plateau, and the extent of the transient flow reversal. As the micellar entanglement density increases, the width of the stress plateau first increases, then, at a higher micellar entanglement density, plateau width decreases. Therefore, we hypothesize that the transient flow reversal is connected to the micellar entanglement density through the width of the stress plateau.