Two-species 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, which we find is accomplished by microstructural transformation, from one type of fluid to another. 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 15 °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. These fluids are therefore modeled in a set of equations as the sum of two distinct and independent fluids: one portion that is semidilute entangled polymer (following living-Rolie-Poly rheology) and another that is dilute reactive rods, with kinetic exchange between the two species. This new model, whose parameters are determined mainly from small-amplitude equilibrium measurements, finally accurately describes the observed non-equilibrium viscosity and orientation behavior.