Time scales in shear banding of wormlike micelles

– We show the existence of three well defined time scales in the dynamics of wormlike micelles after a step between two shear rates on the stress plateau. These time scales are compatible with the presence of a structured interface between bands of different viscosities and correspond to the isotropic band destabilization during the stress overshoot, reconstruction of the interface after the overshoot and travel of a fully formed interface. The last stage can be used to estimate a stress diffusion coefficient. Introduction. – Depending on the type and concentration of surfactant molecules and added salt, solutions of surfactant wormlike micelles have shear thinning or thickening behavior under shear flow. Unlike most fluids, wormlike micelles often have non-analytic flow curves with sharply-selected plateaus along which strain rate or stress may change discontinuously. In the well documented case of shear thinning solutions the usual explanation of the constant stress plateau is shear banding [1, 3, 2], i.e. a separation of the material into bands of different viscosities, triggered by a constitutive instability (such as an isotropic-to-nematic transition [2]). As shown recently [8, 9, 10, 11, 12], the stress selection and history independence of shear banding can be explained using the inhomogeneities of the relevant mesoscopic order parameter (polymer stress), i.e. by incorporating “diffusive” terms in the constitutive equations. Order parameter diffusion was introduced long time ago by van der Waals in the so-called “gradient theory” of the gas-liquid interface [7], and is obligatory in phase field models for pattern formation. Notwithstanding a few attempts to deal with inhomogeneous stresses [6] the same concept has not obtained full acceptance in the rheological community. While one might argue that diffusion terms are negligibly small, these non-perturbative terms resolve stress selection even for infinitesimal values [11]. However, a small diffusion coefficient should also imply a slow approach to steady state; the main purpose of this letter is to demonstrate these long time scales experimentally and relate them to simple model diffusive behavior.