Two-fluid rheology model for living polymer solutions*

What happens to wormlike micelle surfactant (living polymer) solutions at high shear rates? Applications of these fluids often require their significant shear thinning across a very wide range of shear. The viscosity and flow birefringence of surfactant solutions has been measured here across 7 decades of shear rate and 5 decades of viscosity, at temperatures ranging from 20 °C to 60 °C. In this temperature range, the resting equilibrium state of these solutions varies between well-entangled coils at low temperature and short dilute semiflexible rods at high temperature, on account of the kinetics of breaking and combination reactions. Under stress, the breaking reaction is accelerated and the average length decreases, and at high enough stress exhibits the short-dilute rod rheology. We have therefore developed a rheological model, based on a modified living-Rolie-Poly entangled-polymer rheology and a dilute reactive-rod rheology, with kinetic exchange between these states. This new model, whose parameters are determined from small-amplitude equilibrium measurements, finally accurately describes the observed non-equilibrium behavior.