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We investigate the effects of micellar entanglement number on the kinetics of shear banding flow formation in a Taylor–Couette flow. 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 the startup of steady shear. Our experiments indicate that in the set with 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 the transient flow feature. We identify a correlation between micellar entanglement number, the width of the stress plateau, and the extent of the transient flow reversal. As the micellar entanglement number increases, the width of the stress plateau first increases; then, at a higher micellar entanglement number, the plateau width decreases. Therefore, we hypothesize that the transient flow reversal is connected to the micellar entanglement number through the width of the stress plateau. 

We investigate the flow evolution of a linear and a branched wormlike micellar solution with matched rheology in a Taylor–Couette (TC) cell using a combination of particle-tracking velocimetry, birefringence, and turbidity measurements. Both solutions exhibit a stress plateau within a range of shear rates. Under startup of a steady shear rate flow within the stress plateau, both linear and branched samples exhibit strong transient shear thinning flow profiles. However, while the flow of the linear solution evolves to a banded structure at longer times, the flow of the branched solution transitions to a curved velocity profile with no evidence of shear banding. Flow-induced birefringence measurements indicate transient birefringence banding with strong micellar alignment in the high shear band for the linear solution. The transient flow-induced birefringence is stronger for the branched system at an otherwise identical Wi. At longer times, the birefringence bands are replaced by a chaotic flow reminiscent of elastic instabilities. Visualization of the flow-induced turbidity in the velocity gradient-vorticity plane reveals quasi-steady banding with a turbidity contrast between high and low shear bands in the linear solution. However, the turbidity evolves uniformly within the gap of the TC cell for the branched solution, corroborating the non-banded quasi-steady velocimetry results. Finally, we show that while elastic instabilities in the linear solution emerge in the high shear band, the flow of branched solution at high Wi becomes unstable due to end effects, with growing end regions that ultimately span the entire axial length of the TC cell. 

We report experiments on flow of wormlike micellar solutions past a falling sphere. By increasing the salt-to-surfactant concentration ratio, and beyond a viscosity peak, wormlike micelles experience a transition from linear to branched microstructure. Two viscoelastic wormlike micelles with salt to surfactant concentrations on each side of the viscosity peak are considered. Our results indicate three significant differences in flows of branched and linear micelles. First, while the sphere drag correction factor rapidly decreases upon increasing Weissenberg number in linear micelles, it shows an apparent local maximum at Wi ≈ 3 in branched micelles. Second, despite its high viscoelasticity, the time-averaged flow of branched micelles around the falling sphere exhibits a fore-and-aft symmetry, while a strong negative wake is observed in linear micelles at relatively weaker flows. Third, branched micelles exhibit a stronger flow-induced birefringence than linear micelles in an otherwise identical condition. Our hypothesis is that subject to strong flows around the falling sphere, branched micelles can relax much more efficiently than linear wormlike micelles through sliding of the branched junctions. This additional stress relaxation mechanism may facilitate micellar orientation, produce a marginal sphere drag reduction and a Newtonian-like flow profile around the falling sphere. Finally, unsteady flow is observed in both linear and branched micellar solutions beyond some critical thresholds of the extensional Weissenber number. Our results corroborate a recently proposed criterion for onset of instability in flow of wormlike micelles past a falling sphere, thereby, suggesting that micellar branching does not affect the mechanism of flow instability.