Slow Transients and Metastability in Wormlike Micelle Rheology

C. Grand; J. Arrault; M.E. Cates

doi:doi:10.1051/jp2:1997172

Numéro		J. Phys. II France Volume 7, Numéro 8, August 1997


Page(s)		1071 - 1086
DOI		https://doi.org/10.1051/jp2:1997172

DOI: 10.1051/jp2:1997172
J. Phys. II France 7 (1997) 1071-1086

Slow Transients and Metastability in Wormlike Micelle Rheology

C. Grand^{1, 2}, J. Arrault¹ and M.E. Cates¹

¹ Department of Physics and Astronomy, University of Edinburgh, JCMB King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK
² Centre de Recherche Paul Pascal (CNRS), avenue Schweitzer, 33600 Pessac, France

(Received 28 February 1997, accepted 5 May 1997)

Abstract
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 ( $\sigma(\dot{\gamma})=\sigma_{\rm p}$ ) 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 ( $\dot{\gamma}_1=\dot{\gamma}_1^{\max}$ , $\sigma_{\rm p}=\sigma_{\max}$ ). That would rule out the existence of a metastable branch with a stress larger than $\sigma_{\rm p}$ . We show that such a branch does, however, exist (for temperatures in the range 20 - 25 $^{\circ}$ 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, $\tau_{\rm ss}$ , is far longer than the Maxwell time of the fluid; this is consistent with shear banding. We observe $\tau_{\rm ss}\sim (\dot{\gamma}-\dot{\gamma}_{\rm c})^{-p}$ in the metastable regime $(\dot{\gamma}\geq\dot{\gamma}_1)$ , with p an exponent that depends on composition and temperature. The "critical" shear rate $\dot{\gamma}_{\rm c}$ is in some cases less than $\dot{\gamma}_1$ so that no actual divergence of $\tau_{\rm ss}$ occurs. In at least one case, though, there is evidence for a physical divergence ( $\dot{\gamma}_{\rm c} > \dot{\gamma}_1$ ) accompanied by a small window of shear rates, $\dot{\gamma}_1\leq\dot{\gamma}\leq\dot{\gamma}_{\rm c}$ , for which $\tau_{\rm ss}$ 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 ( $\pi\le$ 5%) used in our study.