Velocity Profiles in Shear-Banding Wormlike Micelles

Abstract

Using Dynamic Light Scattering in heterodyne mode, we measure velocity profiles in a much studied system of wormlike micelles (CPCl/NaSal) known to exhibit both shear-banding and stress plateau behavior. Our data provide evidence for the simplest shear-banding scenario, according to which the effective viscosity drop in the system is due to the nucleation and growth of a highly sheared band in the gap, whose thickness linearly increases with the imposed shear rate. We discuss various details of the velocity profiles in all the regions of the flow curve and emphasize on the complex, non-Newtonian nature of the flow in the highly sheared band.PACS numbers: 83.80.Qr, 47.50.+d, 83.85.Ei Understanding the correlation between mechanical and structural response in non-Newtonian fluids submitted to high deformation rates is crucial on both fondamental and technological grounds [1]. Among the variety of complex fluids investigated in recent years, a wide class exhibits flow-structure coupling that leads to a strong shear-thinning behavior: along the steady-state flow curve (shear stress σ vs. shear rateγ), a drop of up to three orders of magnitude in the effective viscosity η = σ/γ is observed in a very narrow stress range leading to a stress plateau (for a review, see for instance Refs. [1,2]). In correlation with this stress plateau, bands of different micro-structures and normal to the velocity gradient appear. Such bands correspond to a new shearinduced structure (SIS), whose low viscosity is in general supposed to be responsible for the shear-thinning. This so-called shear-banding behavior has been observed in both ordered mesophases (lamellar, hexagonal, cubic) [3] and transient gels [4].A particularly well-documented example is the group of wormlike micellar systems of self-assembled surfactant molecules [5,6]. They consist of very long cylindrical aggregates whose configurations mimic polymer solutions. However their dynamics is strongly modified by the equilibrium character of the chains, which enables them to break and recombine [7]. Generically, one starts from an isotropic viscoelastic solution of these micelles above the semidilute regime, which behaves like a Maxwell fluid at low shear rates. Upon increasingγ and entering the nonlinear regime, the onset of the stress plateau for a critical shear rateγ 1 is associated with the nucleation and growth of highly birefringent bands, suggesting strong alignment of the micelles along the velocity direction [5,6]. As the shear rate is further increased aboveγ 1 , the new organization progressively fills the gap at almost constant stress, up to a second critical shear rateγ 2 . Aboveγ 2 , the system enters a second regime of apparently homogeneous structure, with a second branch of increasing stress. The flow curve of Fig. 1 is typical of micellar systems like that investigated in the present work. Such a stress plateau has been reported for concentrations close to the equilibrium isotropic-nematic (I-N) transition, where coupling between the order parameter an...

Rheo-PIV of a shear-banding wormlike micellar solution under large amplitude oscillatory shear

“…During the transition from linear to 3-banded profiles (for imposed shear rates ofγ = 0.3 s −1 andγ = 0.45 s −1 ) the material exhibits an intermediate behavior in which the flow profile appears to have two developing shear bands instead of three clearly distinct bands. This is in contrast to some shear banding scenarios which have been observed in other geometries (such as those observed by Salmon et al (2003) in Couette flow) where the shear rate in the highly sheared band remains constant and the interface between the low and high shear rate regions moves as the apparent shear rate is increased. The data presented in Figure 5 was obtained without the plano-concave lens in place, and with the upper and lower geometries being covered by the transparent film.…”

“…This approach is reasonable because it is well known that when viscometric approximations hold, spatial variations in the stress in a cone-plate geometry are very small (Bird et al, 1987). Subsequent velocimetric studies have focused more often on observing banding in cylindrical Couette geometries (Salmon et al, 2003;Manneville et al, 2004a;Miller and Rothstein, 2007). These velocimetry studies have shown that there is a clear difference between the structure of the shear-banded profiles observed in the two cases.…”

“…Many workers have observed this behavior directly using a variety of velocimetric techniques and under a number of different flow configurations (Lettinga and Manneville, 2009;Salmon et al, 2003;Lopez-Gonzalez et al, 2006;Britton and Callaghan, 1997;Callaghan, 2008;Boukany and Wang, 2008). Callaghan (1997, 1999) showed, using NMR velocimetry, that a CPyCl:NaSal 100:60 mM system (identical to the one used in this work) exhibited a three-banded velocity profile, in which a high shear rate band is observed in the middle of the gap, connected to two lower shear rate regions near the upper and lower surfaces.…”

“…All measurements of the rheology of the CPyCl fluid in this paper (rheometry and combined Rheo-PIV) were carried out on a TA instruments ARG2 stress controlled rheometer equipped with a 50mm diameter, 4 • cone and plate geometry (quartz plate and aluminum cone) and with the temperature controlled to 25 • C. This particular test fluid differs from some of the fluids used in other shear banding studies (e.g. those by Salmon et al (2003) and Lettinga and Manneville (2009)) because it is not prepared in brine and does not contain any added sodium chloride. However, an identical fluid composition (i.e.…”

“…Numerous classes of non-Newtonian fluids are known to exhibit shear banding behavior (Olmsted, 2008), from various kinds of yield stress fluids (Møller et al, 2008;Divoux et al, 2010) to entangled polymer melts (Tapadia et al, 2006;Hu, 2010) and wormlike micellar solutions (Britton and Callaghan, 1997;Salmon et al, 2003;Manneville et al, 2004b,a;Lopez-Gonzalez et al, 2006;Boukany and Wang, 2008;Lettinga and Manneville, 2009). Wormlike micelles are a particularly interesting class of shear banding systems because they are widely used in consumer products, and they have become a canonical model system for probing shear banding.…”