Search for: All records

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. 

We examine linear and nonlinear shear and extensional rheological properties using a “micelle-slip-spring model” [T. Sato et al., J. Rheol. 64, 1045–1061 (2020)] that incorporates breakage and rejoining events into the slip-spring model originally developed by Likhtman [Macromolecules 38, 6128–6139 (2005)] for unbreakable polymers. We here employ the Fraenkel potential for main chain springs and slip-springs to address the effect of finite extensibility. Moreover, to improve extensional properties under a strong extensional flow, stress-induced micelle breakage (SIMB) is incorporated into the micelle-slip-spring model. Thus, this model is the first model that includes the entanglement constraint, Rouse modes, finite extensibility, breakage and rejoining events, and stress-induced micelle breakage. Computational expense currently limits the model to micellar solutions with moderate numbers of entanglements ([Formula: see text]), but for such solutions, nearly quantitative agreement is attained for the start-up of the shearing flow. The model in the extensional flow cannot yet be tested owing to the lack of data for this entanglement level. The transient and steady shear properties predicted by the micelle-slip-spring model for a moderate shear rate region without significant chain stretch are fit well by the Giesekus model but not by the Phan–Thien/Tanner (PTT) model, which is consistent with the ability of the Giesekus model to match experimental shear data. The extensional viscosities obtained by the micelle-slip-spring model with SIMB show thickening followed by thinning, which is in qualitative agreement with experimental trends. Additionally, the extensional rheological properties of the micelle-slip-spring model with or without SIMB are poorly predicted by both the Giesekus and the PTT models using a single nonlinear parameter. Thus, future work should seek a constitutive model able to capture the behavior of the slip-spring model in shear and extensional flows and so provide an accurate, efficient model of micellar solution rheology.