(159b) Mechanistic Constitutive Model for Dilute Wormlike Micelle Solutions

Dilute surfactant solutions forming wormlike micelles undergo complex scission and recombination dynamics in flow that manifest in drastic shear thickening and thinning regimes, multivalued shear stress vs. shear rate curves, and elongation of micellar length. We take a mechanistic approach to developing a constitutive model for the flow of these surfactant solutions, treating the solution as a dilute suspension of Brownian rods whose flow and orientation dynamics are coupled to a reversible “reaction” governing the mean micellar length. This approach to describing the evolution of the micelle length considers flow-induced orientation and growth, stress-induced breakage, and spontaneous growth and breakage. We analyze the behavior of this model in steady and transient flow and find that it captures many of the key rheological features of dilute wormlike micelle solutions, including necessary conditions for a vorticity banding instability. We also make comparisons to experimental results in literature and find good agreement of flow curve predictions.