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 model to study the relationships between fluid rheology and microstructure of micelles, our results show that branches change the scaling law exponents for viscosity vs micelle strand length. This contrasts with the longstanding 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. 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 tool to help extract branching information from rheology.