A tale of two micelles: The analysis and simulation of a two-species scission/reforming model for wormlike micellar solutions

Wormlike micellar mixtures are surfactant solutions consisting of long self-assembled aggregates which can entangle exhibiting viscoelastic properties. These aggregates can break and reform in equilibrium due to thermal fluctuations, and in flow due to stress. In shearing flows, many wormlike micellar solutions exhibit a shear-banding with regions of high and separately low shear-rate. The VCM (Vasquez, Cook, McKinley) model was developed to describe the physics of concentrated solutions of wormlike micelles. This two-species microstructural network model describes the coupled evolution of two wormlike micellar species, long species which can break in half to form shorter species which can recombine to form a long species. The VCM constitutive equations comprise a coupled, nonlinear partial differential equation system, which allows for reptative and Rouse-like stress-relaxation mechanisms in addition to breakage. Using computational, asymptotic and analytic methods this initial/boundary value system is studied and predictions are compared with experiments.;In pressure-driven rectilinear channel flow, the VCM velocity profile exhibits a complex spatial structure including a wall boundary layer and, above a critical pressure drop, an interior interfacial layer. At a critical pressure drop the flow transitions to a shear-banded flow, and volumetric spurt is observed. An adaptive spectral method is developed to track and resolve the spatial and temporal evolution of the thin interior layer. Linear stability analysis of the steady pressure driven flow shows that an interfacial instability can arise resulting in a 2D sinuous ('snake-like') perturbation flow in the flow/gradient plane, with local fluctuations along the interface between bands. Decreasing the channel height leads to a critical height at which the flow stabilizes.;In homogeneous uniaxial extensional flow, the VCM model exhibits a non-montonic elastic tensile stress versus extension rate curve. Linear stability analysis of this curve shows that within the multi-valued region the model is extremely unstable to perturbations along the filament. A thin film Lagrangian formulation is used to simulate inhomogeneous filament stretching. Simulations show that elongating filaments can exhibit a dramatic and sudden rupture event accompanied by a mass breakage of the long species similar to that observed in experiments of wormlike micelles.