Nonlinear rheology of wormlike micelles

Certain viscoelastic surfactant solutions show unusual nonlinear rheology: In steady shear, the shear stress saturates to a constant value while the first normal stess increases roughly linearly with shear rate over several decades. Here we explain this behavior in terms of the ‘‘reptation-reaction’’ model for the dynamics of reversibly breakable, polymerlike micelles. The constitutive equation for this model leads to a flow instability of shear-banding type. The limiting shear stress is predicted to be ${\mathrm{\sigma }}^{\mathrm{*}}$=0.67${\mathit{G}}_0$ (with ${\mathit{G}}_0$ the plateau modulus), in quantitative agreement with experiment.