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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.
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Mesoscopic modeling of the effect of branching on the viscoelasticity of entangled wormlike micellar solutions
The effect of branches on the linear rheology of entangled wormlike micelle solutions is modeled by tracking the diffusion of micellar material through branch points. The model is equivalent to a Kirchhoff circuit model with the sliding of an entangled branch along an entanglement tube due to the constrained diffusion of micellar material analogous to the flux of current in the Kirchhoff circuit model. When combined with our previous mesoscopic pointer algorithm for linear micelles that can both break and fuse, the model adds a branch sprouting process and therefore enables simulation of the dynamics of structural change and stress relaxation in ensembles of micelle clusters of different topologies. Applying this new model to study the relationships between fluid rheology and microstructure of micelles, our results show that branches change the scaling law exponents for viscosity versus micelle strand length. This contrasts with the long-standing hypothesis that branches affect viscosity and relaxation in the same way that micelle ends do. The model also suggests a process for inferring branching density from salt-dependent linear rheology. This is exemplified by mixed surfactant solutions over a range of salt concentrations with flow properties measured using both mechanical rheometry and diffusing wave spectroscopy (DWS). By elucidating the connection between the branching characteristics, such as strand length and branching density, with the nonmonotonic variation of solution viscosity, the above model provides a powerful new tool to help extract branching information from rheology.
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- Award ID(s):
- 1907517
- PAR ID:
- 10548456
- Editor(s):
- Liétor-Santos, J-J
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Research
- Edition / Version:
- 2
- Volume:
- 5
- Issue:
- 4
- ISSN:
- 2643-1564
- Page Range / eLocation ID:
- 043024
- Subject(s) / Keyword(s):
- Fluid Dynamics Polymers and Soft Matter
- Format(s):
- Medium: X Size: 1.4 MB Other: pdf
- Size(s):
- 1.4 MB
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevResearch.5.043024
