(240a) Constitutive Modeling of Dilute Wormlike Micelle Solutions: Shear-Induced Structure, Transient Dynamics, and Inhomogeneous Flows

We present a reformulation of the 'reactive rod model' (RRM) of Dutta and Graham [Dutta, Sarit and Graham, Michael D., JNNFM 251 (2018)], a constitutive model for describing the behavior of dilute wormlike micelle (WLM) solutions that treats solutions as dilute suspensions of rigid Brownian rods undergoing reversible scission and growth in flow. Evolution equations for micelle orientation and stress contribution are coupled to a kinetic reaction equation for a collective micelle length, producing dynamic variations in the length and rotational diffusivity of the rods. We improve on the previous framework by reformulating the kinetic equation for micelle growth on a more microstructural (though still highly idealized) basis, in particular by allowing for micelle growth associated with strong alignment of rods and breakage due to tensile stresses along the micelles. We show that this model is able to capture many of the critical steady-state and transient rheological features of dilute wormlike micelle solutions, particularly shear-thickening and -thinning, non-zero normal stress differences, and stress-overshoot; moreover, this formulation is able to predict the formation of shear-induced structures that give rise to reentrant (i.e., a multivalued shear-stress vs. shear rate curve) shear-thickening. We further demonstrate excellent agreement between model predictions and experiments for both steady and transient shear and extensional rheology. We then use the reformulated reactive rod model (RRM-R) to analyze the dynamics and behavior of dilute WLM solutions in circular Couette flow, in which a number of instabilities and rheological properties can manifest. We focus on critical conditions for viscoelastic and elastic instability formation, paying close attention to parameter regimes in which the RRM-R predicts a reentrant flow curve (a necessary condition for vorticity banding).