Slow Transients and Metastability in Wormlike Micelle Rheology

The steady-state nonlinear rheology of wormlike micellar systems is thought to be subject to shear banding (the underlying shear stress vs. strain rate curve $sigma(dot{gamma})$ is nonmonotonic). Shear banding may result in a plateau ($sigma(dot{gamma})=sigma_{ m p}$) in the measured flow curve (at controlled mean strain rate $dot{gamma}$). We present new rheological data for aqueous CPyCl/NaSal (100 mM/60 mM). Steady-state flow curves published previously for this system (Rehage H. and Hoffmann H., Mol. Phys. 74 (1991) 933) have since been interpreted as shear-banded flow with “top-jumping”, in which the steady-state shear rate $dot{gamma}_1$ in the low shear band is the largest possible ($dot{gamma}_1=dot{gamma}_1^{max}$, σp=σmax ). That would rule out the existence of a metastable branch with a stress larger than σp. We show that such a branch does, however, exist (for temperatures in the range 20 – 25 ○C). Similar results are found for a 100 mM/75 mM system. The time scale for relaxation of a metastable state onto true steady state flow, τss, is far longer than the Maxwell time of the fluid; this is consistent with shear banding. We observe $ au_{ m ss}sim (dot{gamma}-dot{gamma}_{ m c})^{-p}$ in the metastable regime $(dot{gamma}geqdot{gamma}_1)$, with p an exponent that depends on composition and temperature. The “critical” shear rate $dot{gamma}_{ m c}$ is in some cases less than $dot{gamma}_1$ so that no actual divergence of τss occurs. In at least one case, though, there is evidence for a physical divergence ($dot{gamma}_{ m c} > dot{gamma}_1$) accompanied by a small window of shear rates, $dot{gamma}_1leqdot{gamma}leqdot{gamma}_{ m c}$, for which τss is effectively infinite. In some respects the observed behaviour resembles that reported previously (Berret J.-F., Roux D.C. and Porte G., J. Phys. II France 4 (1994) 1261) for equimolar CPyCl/NaSal in 0.5 M NaCl. Those results were interpreted in terms of nucleation and growth of a shear-induced nematic phase. However the same explanation is unlikely for the low weight fractions (π≤ 5%) used in our study