Shear-induced transitions and instabilities in surfactant wormlike micelles

In this review, we report recent developments on the shear-induced transitions and instabilities found in surfactant wormlike micelles. The survey focuses on the non-linear shear rheology and covers a broad range of surfactant concentrations, from the dilute to the liquid-crystalline states and including the semi-dilute and concentrated regimes. Based on a systematic analysis of many surfactant systems, the present approach aims to identify the essential features of the transitions. It is suggested that these features define classes of behaviors. The review describes three types of transitions and/or instabilities : the shear-thickening found in the dilute regime, the shear-banding which is linked in some systems to the isotropic-to-nematic transition, and the flow-aligning and tumbling instabilities characteristic of nematic structures. In these three classes of behaviors, the shear-induced transitions are the result of a coupling between the internal structure of the fluid and the flow, resulting in a new mesoscopic organization under shear. This survey finally highlights the potential use of wormlike micelles as model systems for complex fluids and for applications.Comment: 64 pages, 31 figures, 2 table

Gradient and vorticity banding

"Banded structures" of macroscopic dimensions can be induced by simple shear flow in many different types of soft matter systems. Depending on whether these bands extend along the gradient or vorticity direction, the banding transition is referred to as "gradient banding" or "vorticity banding," respectively. The main features of gradient banding can be understood on the basis of a relatively simple constitutive equation. This minimal model for gradient banding will be discussed in some detail, and its predictions are shown to explain many of the experimentally observed features. The minimal model assumes a decrease of the shear stress of the homogeneously sheared system with increasing shear rate within a certain shear-rate interval. The possible microscopic origin of the severe shear-thinning behaviour that is necessary for the resulting nonmonotonic flow curves is discussed for a few particular systems. Deviations between experimental observations and predictions by the minimal model are due to obvious simplifications within the scope of the minimal model. The most serious simplifications are the neglect of concentration dependence of the shear stress (or on other degrees of freedom) and of the elastic contributions to the stress, normal stresses, and the possibility of shear-induced phase transitions. The consequences of coupling of stress and concentration will be analyzed in some detail. In contrast to predictions of the minimal model, when coupling to concentration is important, a flow instability can occur that does not require strong shear thinning. Gradient banding is sometimes also observed in glassy- and gel-like systems, as well as in shear-thickening systems. Possible mechanisms that could be at the origin of gradient-band formation in such systems are discussed. Gradient banding can also occur in strongly entangled polymeric systems. Banding in these systems is discussed on the basis of computer simulations. Vorticity banding is less well understood and less extensively investigated experimentally as compared to gradient banding. Possible scenarios that are at the origin of vorticity banding will be discussed. Among other systems, the observed vorticity-banding transition in rod-like colloids is discussed in some detail. It is argued, on the basis of experimental observations for these colloidal systems, that the vorticity-banding instability for such colloidal suspensions is probably related to an elastic instability, reminiscent of the Weissenberg effect in polymeric systems. This mechanism might explain vorticity banding in discontinuously shear-thickening systems and could be at work in other vorticity-banding systems as well. This overview does not include time-dependent phenomena like oscillations and chaotic behaviour

Phase Coexistence of Complex Fluids in Shear Flow

We present some results of recent calculations of rigid rod-like particles in shear flow, based on the Doi model. This is an ideal model system for exhibiting the generic behavior of shear-thinning fluids (polymer solutions, wormlike micelles, surfactant solutions, liquid crystals) in shear flow. We present calculations of phase coexistence under shear among weakly-aligned (paranematic) and strongly-aligned phases, including alignment in the shear plane and in the vorticity direction (log-rolling). Phase coexistence is possible, in principle, under conditions of both common shear stress and common strain rate, corresponding to different orientations of the interface between phases. We discuss arguments for resolving this degeneracy. Calculation of phase coexistence relies on the presence of inhomogeneous terms in the dynamical equations of motion, which select the appropriate pair of coexisting states. We cast this condition in terms of an equivalent dynamical system, and explore some aspects of how this differs from equilibrium phase coexistence.Comment: 16 pages, 10 figures, submitted to Faraday Discussion

Role of Micellar Entanglement Density on Kinetics of Shear Banding Flow Formation

We investigate the effects of micellar entanglement number on the kinetics of shear banding flow formation in a Taylor-Couette flow. Three sets of wormlike micellar solutions, each set with a similar fluid elasticity and zero-shear-rate viscosity, but with varying entanglement densities, are studied under start-up of steady shear. Our experiments indicate that in the set with the low fluid elasticity, the transient shear banding flow is characterized by the formation of a transient flow reversal in a range of entanglement densities. Outside of this range, the transient flow reversal is not observed. For the sets of medium and high elasticities, the transient flow reversals exist for relatively small entanglement densities, and disappear for large entanglement densities. Our analysis shows that wall slip and elastic instabilities do not affect the transient flow feature. We identify a correlation between micellar entanglement number, the width of the stress plateau, and the extent of the transient flow reversal. As the micellar entanglement number increases, the width of the stress plateau first increases, then, at a higher micellar entanglement number, plateau width decreases. Therefore, we hypothesize that the transient flow reversal is connected to the micellar entanglement number through the width of the stress plateau

Phase Separation of Rigid-Rod Suspensions in Shear Flow

We analyze the behavior of a suspension of rigid rod-like particles in shear flow using a modified version of the Doi model, and construct diagrams for phase coexistence under conditions of constant imposed stress and constant imposed strain rate, among paranematic, flow-aligning nematic, and log-rolling nematic states. We calculate the effective constitutive relations that would be measured through the regime of phase separation into shear bands. We calculate phase coexistence by examining the stability of interfacial steady states and find a wide range of possible ``phase'' behaviors.Comment: 23 pages 19 figures, revised version to be published in Physical Review

Recent experimental probes of shear banding

Recent experimental techniques used to investigate shear banding are reviewed. After recalling the rheological signature of shear-banded flows, we summarize the various tools for measuring locally the microstructure and the velocity field under shear. Local velocity measurements using dynamic light scattering and ultrasound are emphasized. A few results are extracted from current works to illustrate open questions and directions for future research.Comment: Review paper, 23 pages, 11 figures, 204 reference

Spatiotemporal dynamics of multiple shear-banding events for viscoelastic micellar fluids in cone-plate shearing flows

We characterize the transient response of semi-dilute wormlike micellar solutions under an imposed steady shear flow in a cone-plate geometry. By combining conventional rheometry with 2-D Particle Image Velocimetry (PIV), we can simultaneously correlate the temporal stress response with time-resolved velocimetric measurements. By imposing a well defined shear history protocol, consisting of a stepped shear flow sweep, we explore both the linear and nonlinear responses of two surfactant solutions: cetylpiridinium chloride (CPyCl) and sodium salicylate (NaSal) mixtures at concentrations of [66:40] mM and [100:60] mM, respectively. The transient stress signal of the more dilute solution relaxes to its equilibrium value very fast and the corresponding velocity profiles remain linear, even in the strongly shear-thinning regime. The more concentrated solution also exhibits linear velocity profiles at small shear rates. At large enough shear rates, typically larger than the inverse of the relaxation time of the fluid, the flow field reorganizes giving rise to strongly shear-banded velocity profiles. These are composed of an odd number of shear bands with low-shear-rate bands adjacent to both gap boundaries. In the non-linear regime long transients (much longer than the relaxation time of the fluid) are observed in the transient stress response before the fluid reaches a final, fully-developed state. The temporal evolution in the shear stress can be correlated with the spatiotemporal dynamics of the multiple shear-banded structure measured using RheoPIV. In particular our experiments show the onset of elastic instabilities in the flow which are characterized by the presence of multiple shear bands that evolve and rearrange in time resulting in a slow increase in the average torque acting on the rotating fixture