Linear versus branched: flow of a wormlike micellar fluid past a falling sphere

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.