Shear Banding and Non-Equilibrium Phase Behavior of Concentrated Wormlike Micellar Solutions

Shear banding is a flow instability encountered in a variety of complex fluids, including highly entangled polymers, colloidal suspensions, and, most prominently, wormlike micelles (WLMs). Although shear banding has been identified in a number of WLM-forming surfactants, its underlying mechanisms are still largely unknown. Here, we present the rheological behavior of concentrated cationic WLMs near an equilibrium isotropic-nematic (I-N) transition as a function of composition and temperature to determine the relationship between shear banding, fluid microstructure and underlying surfactant phase behavior. A novel combination of conventional rheometry, velocimetry, and spatially-resolved flow-small angle neutron scattering reveals that shear banding is due to a first-order, shear-induced transition to a paranematic state. The shear rheology of isotropic WLM solutions are well-described by the Giesekus constitutive model, which provides a quantitative discrimination between banding and non-banding WLMs through the drag anisotropy coupling parameter. This anisotropy parameter is shown to correlate with the order parameter describing the relative distance to the equilibrium I-N transition, as well as the critical flow-alignment required for the onset of shear banding. Combining this information with measurements of the critical shear rates for banding allows the construction of a non-equilibrium state diagram near the I-N transition in terms of the Weissenberg number and the compositional order parameter. This non-equilibrium phase diagram explains a number of experimental observations in shear banding fluids, including spatiotemporal fluctuations and rheo-chaos during shear banding.