Shear banding fluctuations and nematic order in wormlike micelles

Shear layers and plugs in the capillary flow of wormlike micellar gels

Wormlike micellar solutions formed by long-chained zwitterionic surfactants show gel-like rheology at room temperature and have recently been found to exhibit other complex and interesting rheological features. We study the dynamics of these wormlike micellar gels in a pipe-flow scenario using particle imaging and tracking velocimetry and report the existence of plug flows with strong wall slip and non-parabolic velocity profiles for different surfactant concentrations and imposed flow rates. We rationalize these results as features of a developing transient flow of a viscoelastic solution in space and time. We show that evolution of shear layers is governed by intermittent flows, asymmetric velocity profiles and flow induced heterogeneity. Our experiments shed light on the transient fluid dynamics of wormlike micelles in simple geometries and highlight the complexity of flows involving wormlike micellar gels and similar soft matter systems in canonical flows.

Kinetics of shear banding flow formation in linear and branched wormlike micelles

We investigate the flow evolution of a linear and a branched wormlike micellar solution with matched rheology in a Taylor-Couette (TC) cell using a combination of particle-tracking velocimetry, birefringence, and turbidity measurements. Both solutions exhibit a stress plateau within a range of shear rates. Under startup of a steady shear rate flow within the stress plateau, both linear and branched samples exhibit strong transient shear thinning flow profiles. However, while the flow of the linear solution evolves to a banded structure at longer times, the flow of the branched solution transitions to a curved velocity profile with no evidence of shear banding. Flow-induced birefringence measurements indicate transient birefringence banding with strong micellar alignment in the high shear band for the linear solution. The transient flow-induced birefringence is stronger for the branched system at an otherwise identical Wi. At longer times, the birefringence bands are replaced by a chaotic flow reminiscent of elastic instabilities. Visualization of the flow-induced turbidity in the velocity gradient-vorticity plane reveals quasi-steady banding with a turbidity contrast between high and low shear bands in the linear solution. However, the turbidity evolves uniformly within the gap of the TC cell for the branched solution, corroborating the non-banded quasi-steady velocimetry results. Finally, we show that while elastic instabilities in the linear solution emerge in the high shear band, the flow of branched solution at high Wi becomes unstable due to end effects, with growing end regions that ultimately span the entire axial length of the TC cell.

Flow-Induced Concentration Nonuniformity and Shear Banding in Entangled Polymer Solutions

Recent models have predicted entangled polymer solutions could shear band due to unstable flow-induced demixing. This work provides the first experimental probe of the in situ concentration profile of entangled polymer solutions under shear. At shear rates above a critical value, we show that the concentration and velocity profiles can develop bands, in quantitative agreement with steady-state model predictions. These findings highlight the critical importance of flow-concentration coupling in entangled polymer solutions.

Impact of turbulence-induced asymmetric propagators on the accuracy of phase-contrast velocimetry

Phase-contrast magnetic resonance velocimetry (PC-MRI) has been widely used to investigate flow properties in numerous systems. In a horizontal cylindrical pipe (3 mm diameter), we investigated the accuracy of PC-MRI as the flow transitioned from laminar to turbulent flow (Reynolds number 352-2708). We focus primarily on velocimetry errors introduced by skewed intra-voxel displacement distributions, a consequence of PC-MRI theory assuming symmetric distributions. We demonstrated how rapid fluctuations in the velocity field, can produce broad asymmetric intravoxel displacement distributions near the wall. Depending on the shape of the distribution, this resulted in PC-MRI measurements under-estimating (positive skewness) or over-estimating (negative skewness) the true mean intravoxel velocity, which could have particular importance to clinical wall shear stress measurements. The magnitude of these velocity errors was shown to increase with the variance and decrease with the kurtosis of the intravoxel displacement distribution. These experimental results confirm our previous theoretical analysis, which gives a relationship for PC-MRI velocimetry errors, as a function of the higher moments of the intravoxel displacement distribution (skewness, variance, and kurtosis) and the experimental parameters q and Δ. This suggests that PC-MRI errors in such unsteady/turbulent flow conditions can potentially be reduced by employing lower q values or shorter observation times Δ.

Complex dynamics of a sheared nematic fluid

Nonlinearities in constitutive equations of extended objects in shear flow lead to novel phenomena, e.g. 'rheochaos' in solutions of wormlike micelles and 'elastic turbulence' in polymer solutions. Since both phenomena involve anisotropic objects, their contributions to the deviatoric stress are likely to be similar. However, these two fields have evolved rather independently and an attempt at connecting these fields is still lacking. We show that a minimal model in which the anisotropic nature of the constituting objects is taken into account by a nematic alignment tensor field reproduces several statistical features found in rheochaos and elastic turbulence. We numerically analyse the full non-linear hydrodynamic equations of a sheared nematic fluid under shear stress and strain rate controlled situations, incorporating spatial heterogeneity only in the gradient direction. For a certain range of imposed stress and strain rates, this extended dynamical system shows signatures of spatiotemporal chaos and transient shear banding. In the chaotic regime the power spectra of the order parameter stress, velocity fluctuations and the total injected power show power law behavior and the total injected power shows a non-gaussian, skewed probability distribution. These dynamical features bear resemblance to elastic turbulence phenomena observed in polymer solutions. The scaling behavior is independent of the choice of shear rate/stress controlled method.

Rheo-NMR in food science-Recent opportunities

For over 25 years, nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) techniques have been used to study materials under mechanical deformation. Collectively, these methods are referred to as Rheo-NMR. In many cases, it provides spatially and temporally resolved maps of NMR spectra, intrinsic NMR parameters (such as relaxation times), or motion (such as diffusion or flow). Therefore, Rheo-NMR is complementary to conventional rheological measurements. This review will briefly summarize current capabilities and limitations of Rheo-NMR in the context of material science and food science in particular. It will report on recent advances such as the incorporation of torque sensors or the implementation of large amplitude oscillatory shear and point out future opportunities for Rheo-NMR in food science.

Laning, thinning and thickening of sheared colloids in a two-dimensional Taylor-Couette geometry

We investigate the dynamics and rheological properties of a circular colloidal cluster that is continuously sheared by magnetic and optical torques in a two-dimensional (2D) Taylor-Couette geometry. By varying the two driving fields, we obtain the system flow diagram and report the velocity profiles along the colloidal structure. We then use the inner magnetic trimer as a microrheometer, and observe continuous thinning of all particle layers followed by thickening of the third one above a threshold field. Experimental data are supported by Brownian dynamics simulations. Our approach gives a unique microscopic view on how the structure of strongly confined colloidal matter weakens or strengthens upon shear, envisioning the engineering of rheological devices at the microscales.

Shear banding in nematogenic fluids with oscillating orientational dynamics

We investigate the occurrence of shear banding in nematogenic fluids under planar Couette flow, based on mesoscopic dynamical equations for the orientational order parameter and the shear stress. We focus on parameter values where the sheared homogeneous system exhibits regular oscillatory orientational dynamics, whereas the equilibrium system is either isotropic (albeit close to the isotropic-nematic transition) or deep in its nematic phase. The numerical calculations are restricted to spatial variations in shear gradient direction. We find several new types of shear-banded states characterized by regions with regular oscillatory orientational dynamics. In all cases shear banding is accompanied by a non-monotonicity of the flow curve of the homogeneous system; however, only in the case of the initially isotropic system this curve has the typical S-like shape. We also analyze the influence of different orientational boundary conditions and of the spatial correlation length.

Hydrodynamic length-scale selection in microswimmer suspensions

A universal characteristic of mesoscale turbulence in active suspensions is the emergence of a typical vortex length scale, distinctly different from the scale invariance of turbulent high-Reynolds number flows. Collective length-scale selection has been observed in bacterial fluids, endothelial tissue, and active colloids, yet the physical origins of this phenomenon remain elusive. Here, we systematically derive an effective fourth-order field theory from a generic microscopic model that allows us to predict the typical vortex size in microswimmer suspensions. Building on a self-consistent closure condition, the derivation shows that the vortex length scale is determined by the competition between local alignment forces, rotational diffusion, and intermediate-range hydrodynamic interactions. Vortex structures found in simulations of the theory agree with recent measurements in Bacillus subtilis suspensions. Moreover, our approach yields an effective viscosity enhancement (reduction), as reported experimentally for puller (pusher) microorganisms.

A flow visualization and superposition rheology study of shear-banding wormlike micelle solutions

In this paper, we use rheometry and flow visualization to study the dynamics of the interface between shear bands in a wormlike micellar solution sheared between concentric cylinders, i.e., in a Taylor-Couette (TC) cell, and to evaluate the stress diffusion coefficient and the stress correlation length in the Johnson-Segalman model. Two wormlike micellar solutions are studied: an aqueous solution of CTAB-NaNO3 and a solution of CPCl-NaSal in brine. These systems are highly elastic, exhibit Maxwellian behavior in linear viscoelasticity experiments, and shear banding in nonlinear experiments [S. Lerouge, et al., Soft Matter, 2008, 4, 1808-1819, M. A. Fardin, et al., Soft Matter, 2012, 8(39), 10072-10089, P. Ballesta, et al., J. Rheol., 2007, 51, 1047]. A large, custom-built, computer controlled TC cell allows us to rotate both cylinders independently and to visualize the flow in the r-z plane using a CCD camera. At low shear rates, the flow is stable and the fluid appears homogeneous throughout the gap between the cylinders. Above a critical shear rate, a shear banding transition occurs. This manifests itself in the formation of two distinct bands in the r-z plane, with an interface between the two bands. For sufficiently high ramp speeds, multiple steps of interface evolution are identified, as noted by Radulescu, Lerouge, and others [O. Redulescu, et al., Europhys. Lett., 2003, 62, 230, S. Lerouge, et al., Soft Matter, 2008, 4, 1808-1819]. We quantify the interface travel using direct visualization and use this measure, as well as superposition rheometry [P. Ballesta, et al., J. Rheol., 2007, 51, 1047], to determine the stress diffusion coefficient D and the stress correlation length ζ in the Johnson-Segalman model. These parameters are evaluated at different temperatures, shear rates, and gap sizes. We find that the stress diffusion coefficient and the stress correlation length exhibit a strong dependence on the gap of the Taylor-Couette cell for both shear-banding systems. For the CTAB-NaNO3 system, we report a linear dependence of the stress diffusion coefficient on temperature for the parameter range considered. In addition, we find that for this system, the stress diffusion coefficient is independent of shear rate. For the CPCl-NaSal system, we observe the same color changes in the sample reported by others on extended light exposure; however, we find that different histories of light exposure do not affect the measured stress diffusion coefficient.

Advances and artefact suppression in RARE-velocimetry for flow with curved streamlines

Method and considerations are presented that allow for an improved quantitative velocity measurement of complex fluids under shear using a fast 2D PGSE-RARE technique. While this contribution is relevant for shear geometries with rotational symmetry in general, the focus here is set on cylindrical Couette cells, a device most commonly used for rheological NMR investigations. The curved nature of the flow within the shearing geometry creates challenges in accurately determining the flow profile, as conventional imaging gradients naturally operate on a Cartesian grid. In particular the appropriate slice thickness in the flow direction and the applied k-space trajectory are discussed. For the latter an MRI simulation program has been written that numerically solves the Bloch equations and allows for the investigation of out-of-pixel flow. Furthermore, we present ways of increasing the spatial resolution across the gap of cylindrical Couette cells while still providing 2D imaging capabilities under certain conditions, thus allowing for a more detailed quantification of flow profiles as necessary for the analysis of complex fluid flow.

Spatial Mapping of Flow-Induced Molecular Alignment in a Noncrystalline Biopolymer Fluid Using Double Quantum Filtered (DQF) (23)Na MRI

Flow-induced molecular alignment was observed experimentally in a non-liquid-crystalline bioplymeric fluid during developed tubular flow. The fluid was comprised of rigid rods of the polysaccharide xanthan and exhibited shear-thinning behavior. Without a requirement for optical transparency or the need for an added tracer, (23)Na magic angle (MA) double quantum filtered (DQF) magnetic resonance imaging (MRI) enabled the mapping of the anisotropic molecular arrangement under flow conditions. A regional net molecular alignment was found in areas of high shear values in the vicinity of the tube wall. Furthermore, the xanthan molecules resumed random orientations after the cessation of flow. The observed flow-induced molecular alignment was correlated with the rheological properties of the fluid. The work demonstrates the ability of (23)Na MA DQF magnetic resonance to provide a valuable molecular-mechanical link.

Surfactant micelles: model systems for flow instabilities of complex fluids

Complex fluids such as emulsions, colloidal gels, polymer or surfactant solutions are all characterized by the existence of a "microstructure" which may couple to an external flow on time scales that are easily probed in experiments. Such a coupling between flow and microstructure usually leads to instabilities under relatively weak shear flows that correspond to vanishingly small Reynolds numbers. Wormlike micellar surfactant solutions appear as model systems to study two examples of such instabilities, namely shear banding and elastic instabilities. Focusing on a semidilute sample we show that two-dimensional ultrafast ultrasonic imaging allows for a thorough investigation of unstable shear-banded micellar flows. In steady state, radial and azimuthal velocity components are recovered and unveil the original structure of the vortical flow within an elastically unstable high shear rate band. Furthermore thanks to an unprecedented frame rate of up to 20,000 fps, transients and fast dynamics can be resolved, which paves the way for a better understanding of elastic turbulence.

Microstructural evolution of a model, shear-banding micellar solution during shear startup and cessation

We present direct measurements of the evolution of the segmental-level microstructure of a stable shear-banding polymerlike micelle solution during flow startup and cessation in the plane of flow. These measurements provide a definitive, quantitative microstructural understanding of the stages observed during flow startup: an initial elastic response with limited alignment that yields with a large stress overshoot to a homogeneous flow with associated micellar alignment that persists for approximately three relaxation times. This transient is followed by a shear (kink) band formation with a flow-aligned low-viscosity band that exhibits shear-induced concentration fluctuations and coexists with a nearly isotropic band of homogenous, highly viscoelastic micellar solution. Stable, steady banding flow is achieved only after approximately two reptation times. Flow cessation from this shear-banded state is also found to be nontrivial, exhibiting an initial fast relaxation with only minor structural relaxation, followed by a slower relaxation of the aligned micellar fluid with the equilibrium fluid's characteristic relaxation time. These measurements resolve a controversy in the literature surrounding the mechanism of shear banding in entangled wormlike micelles and, by means of comparison to existing literature, provide further insights into the mechanisms driving shear-banding instabilities in related systems. The methods and instrumentation described should find broad use in exploring complex fluid rheology and testing microstructure-based constitutive equations.

Interface instabilities and chaotic rheological responses in binary polymer mixtures under shear flow

The numerical results of RP–FH model reveal another possible cause of the rheochaos: a vortex structure emerges within the central band.

Recent advances in flow MRI

The past five years have seen exciting new developments in Flow MRI. Two-dimensional images are now routinely acquired in 100-200 ms and, in some cases, acquisition times of 5-10 ms are possible. This has been achieved not only by advances in the implementation of existing pulse sequences but also in data acquisition strategies, such as Compressed Sensing and Bayesian approaches, and technical advices in parallel imaging and signal enhancement methods. In particular, the short imaging timescales that are now achieved offer significant opportunities in the study of transient flow phenomena.

Instabilities in wormlike micelle systems. From shear-banding to elastic turbulence

Shear-banding is ubiquitous in complex fluids. It is related to the organization of the flow into macroscopic bands bearing different viscosities and local shear rates and stacked along the velocity gradient direction. This flow-induced transition towards a heterogeneous flow state has been reported in a variety of systems, including wormlike micellar solutions, telechelic polymers, emulsions, clay suspensions, colloidal gels, star polymers, granular materials, or foams. In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In wormlike micelle solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations. Different candidates have been identified, the main ones being wall slip, interfacial instability between bands or bulk instability of one of the bands. In this review, we present experimental evidence for a purely elastic instability of the high shear rate band as the main origin for fluctuating shear-banding flows.

Azimuthal instability of the interface in a shear banded flow by direct visual observation

The stability of the shear banded flow of a Maxwellian fluid is studied from an experimental point of view using rheology and flow visualization with polarized light. We show that the one-layer homogeneous flow cannot sustain shear rates corresponding to the end of the stress plateau. The high shear rate branch is not found and the shear stress oscillates at the end of the plateau. An azimuthal instability appears: the shear induced band becomes unstable and the interface between the two bands undulates in time and space with a period τ, a wavelength λ and a wave vector k parallel to the direction of the tangential velocity.

Banded spatiotemporal chaos in sheared nematogenic fluids

We present the results of a numerical study of a model of the hydrodynamics of a sheared nematogenic fluid, taking into account the effects of order-parameter stresses on the velocity profile but allowing spatial variations only in the gradient direction. When parameter values are such that the stress from orientational distortions is comparable to the bare viscous stress, the system exhibits steady states with the characteristics of shear banding. In addition, nonlinearity in the coupling of extensional flow to orientation leads to the appearance of a new steady state in which the features of both spatiotemporal chaos and shear banding are present.

Conductivity measurements in a shear-banding wormlike micellar system

Shear banding in the cetylpyridinium chloride/sodium salicylate micellar system is investigated using electrical conductivity measurements parallel to the velocity and parallel to the vorticity in a cylindrical Couette cell. The measurements show that the conductivity parallel to the velocity (vorticity) increases (decreases) monotonically with applied shear rate. The shear-induced anisotropy is over one order of magnitude lower than the anisotropy of the N(c) nematic phase. The steady-state conductivity measurements indicate that the anisotropy of the shear induced low-viscosity (high shear rate) phase is not significantly larger than the anisotropy of the high viscosity (low shear rate) phase. We estimate that the micelles in the shear induced low viscosity band are relatively short, with a characteristic length to diameter ratio of 5-15. The relaxation behavior following the onset of shear is markedly different above and below the first critical value γ1, in agreement with results obtained by other methods. The transient measurements show that the overall anisotropy of the sample decreases as the steady state is approached, i.e., the micellar length/the degree of order decrease.

Competition between shear banding and wall slip in wormlike micelles

The interplay between shear band (SB) formation and boundary conditions (BC) is investigated in wormlike micellar systems (CPyCl-NaSal) using ultrasonic velocimetry coupled to standard rheology in Couette geometry. Time-resolved velocity profiles are recorded during transient strain-controlled experiments in smooth and sandblasted geometries. For stick BC standard SB is observed, although depending on the degree of micellar entanglement temporal fluctuations are reported in the highly sheared band. For slip BC wall slip occurs only for shear rates larger than the start of the stress plateau. At low entanglement, SB formation is shifted by a constant Delta gamma, while for more entangled systems SB constantly "nucleate and melt." Micellar orientation gradients at the walls may account for these original features.

Flow velocity profiles and shear banding onset in a semidilute wormlike micellar system under Couette flow

Velocity profiles in Couette flow are measured in a wormlike micellar solution made of cetyltrimethylammonium bromide (CTAB), sodium salicylate (NaSal), and water, at R (= [NaSal]/[CTAB]) = 2 and at R = 4; [CTAB] = 100 mM. Velocity profiles were obtained by using a two-incident beam laser Doppler technique. Profiles reveal that one of the micellar solutions (R = 2) becomes heterogeneous a long time after flow inception, even at very low imposed shear rates. However, profiles do not correspond to what is expected for gradient shear banding, because the fluid splits in one section close to the moving cylinder where the local mean velocity depends linearly on the gap position and in a second section presenting important velocity fluctuations. Close to the static cylinder, there is a third section where the fluid does not flow; it behaves like a slipping block. On the other hand, at high imposed shear rates, the former slipping block flows and presents a linear profile. Here, velocity profiles are consistent with gradient shear banding. The onset of shear banding was observed. The picture of two stable shear bands separated by a thin steady interface is not always valid. Inhomogeneous flow could be observed, although it cannot be classified as shear banding. In addition, conditions can be found where, as shear rate is increased and before shear banding appears, instead of a thin interface, a fluctuating intermediate band can be observed. On the contrary, for the R = 4 solution, the flow never becomes heterogeneous even at high shear rates. Flow curves were measured in a Couette cell under shear rate control in two cases, when stress is sensed with the moving cylinder and when it is sensed with the static cylinder of the cell. Differences between the flow curves can be explained by using the velocity profiles for both solutions.

Two-dimensional perturbations in a scalar model for shear banding

We present an analytical study of a toy model for shear banding, without normal stresses, which uses a piecewise linear approximation to the flow curve (shear stress as a function of shear rate). This model exhibits multiple stationary states, one of which is linearly stable against general two-dimensional perturbations. This is in contrast to analogous results for the Johnson-Segalman model, which includes normal stresses, and which has been reported to be linearly unstable for general two-dimensional perturbations. This strongly suggests that the linear instabilities found in the Johnson-Segalman can be attributed to normal stress effects.

Taylor-like vortices in shear-banding flow of giant micelles

Using flow visualizations in Couette geometry, we demonstrate the existence of Taylor-like vortices in the shear-banding flow of a giant micelles system. We show that vortices stacked along the vorticity direction develop concomitantly with interfacial undulations. These cellular structures are mainly localized in the induced band and their dynamics is fully correlated with that of the interface. As the control parameter increases, we observe a transition from a steady vortex flow to a state where pairs of vortices are continuously created and destroyed. Normal stress effects are discussed as potential mechanisms driving the three-dimensional flow.

High resolution shear profile measurements in entangled polymers

We use confocal microscopy and particle image velocimetry to visualize motion of 250-300 nm. fluorescent tracer particles in entangled polymers subject to a rectilinear shear flow. Our results show linear velocity profiles in polymer solutions spanning a wide range of molecular weights and number of entanglements (8< or =Z< or =56), but reveal large differences between the imposed and measured shear rates. These findings disagree with recent reports that shear banding is a characteristic flow response of entangled polymers, and instead point to interfacial slip as an important source of strain loss.

Spatiotemporal nematodynamics in wormlike micelles en route to rheochaos

We show through polarized light scattering experiments the spatially inhomogeneous orientational dynamics for shear-thinning wormlike micellar gels (cetyltrimethylammonium tosylate+sodium chloride+H2O ) en route to rheochaos. For shear rates in the plateau of the flow curve, we see alternating bright and dark birefringent stripes stacked along the vorticity. The orientational order in adjacent bands is predominantly oriented at +45 degrees and -45 degrees to the flow (v) in the (v,nablav) plane, respectively. We have made an attempt to correlate the observed orientational ordering in terms of the two-dimensional Taylor-like velocity rolls in a gradient banding fluid. The bands show spatial motion along the vorticity, and the orientation dynamics of the interface delineating adjacent bands completely correlates with the temporal dynamics of the stress. Furthermore, the observed spatial dynamics of the interfaces of the rolls depends crucially on the gap width of the Couette cell.

Shear banding and yield stress in soft glassy materials

Shear localization is a generic feature of flows in yield stress fluids and soft glassy materials but is incompletely understood. In the classical picture of yield stress fluids, shear banding happens because of a stress heterogeneity. Using recent developments in magnetic resonance imaging velocimetry, we show here for a colloidal gel that even in a homogeneous stress situation shear banding occurs, and that the width of the flowing band is uniquely determined by the macroscopically imposed shear rate rather than the stress. We present a simple physical model for flow of the gel showing that shear banding (localization) is a flow instability that is intrinsic to the material, and confirm the model predictions for our system using rheology and light scattering.

A rheo-optical study of shear rate and optical anisotropy in wormlike micelles solutions

The flow behaviour of wormlike micelles solutions composed of the surfactant cetylpyridinium chloride (CPCl) and counter-ion sodium salicylate (NaSal) at a molar ratio [CPCl]/[NaSal] = 2 in brine [NaCl] = 0.5 M in a cylindrical Couette geometry was examined using homodyne PCS and ellipsometry. Homodyne PCS was used to profile local shear rate and ellipsometry to concurrently profile local optical anisotropy of the fluid. Shear thinning was observed and was correlated to an increase in turbidity and a breakdown in the stress-optic law. A stress plateau observed in mechanical measurements was correlated with the partitioning of the fluid into regions of low shear rate/low turbidity/high birefringence and high shear rate/high turbidity/low birefringence. The partitioning observed was inconsistent with a simple interpretation of the lever rule.

Alternating vorticity bands in a solution of wormlike micelles

We report on structural characterization of vorticity bands formed in a wormlike micellar solution by Rheo--small-angle neutron scattering and video imaging experiments. Below a critical shear stress tau{c} in Newtonian and shear-thinning regime, only a minor flow alignment of the micelles is observed. Above tau{c}, in the shear-thickening regime, alternating transparent and turbid bands are formed. Triggered small-angle neutron scattering shows different anisotropic patterns in both bands indicating strongly aligned structures. By high-speed video imaging, we show that such an alignment of micelles does not correspond to a phase of lower viscosity.

Complex dynamics of shear banded flows

Many complex fluids undergo a flow induced transition to a state of coexisting bands of differing viscosities and internal structuring. This effect, which is called "shear banding", is widely observed in wormlike micellar surfactants, onion surfactants, colloidal suspensions and polymer solutions. According to a rapidly accumulating body of experimental evidence, shear bands often exhibit complex dynamics, which can be either oscillatory or chaotic in nature. This can be seen in the unsteady response of the bulk rheological signals, and in the motion of the interface between the bands. After giving a brief overview of this experimental evidence, we review in some detail recent efforts to address it theoretically.

Wormlike micelles: where do we stand? Recent developments, linear rheology and scattering techniques

Wormlike micelles are elongated flexible self-assembly structures formed by the aggregation of amphiphiles. Above a threshold concentration, they entangle into a dynamic network, reminiscent of polymer solutions, and display remarkable visco-elastic properties, which have been exploited in numerous industrial and technological fields. Relating the microstructure of these intricate structures with their bulk properties is still an ongoing quest. In this review, we present a classification of wormlike micelles, with a focus on novel systems and applications. We describe the current state of understanding of their linear rheology and give a detailed account of recent progress in small-angle neutron scattering, a particularly powerful technique to elucidate their microstructure on a wide range of length-scales.

Evidence for three-dimensional unstable flows in shear-banding wormlike micelles

We report on an experimental study of the shear-banding phenomenon in the concentrated wormlike micellar system CTAB at 20wt.% in D2O . Time-resolved velocity profiles are recorded using ultrasonic velocimetry simultaneously to global rheological data. Our results confirm the studies performed previously by Fischer and Callaghan [Phys. Rev. E 64, 011501 (2001)]. Time averaged velocity profiles display an unsheared "nematic gel." In the range of applied shear rate, the flow field exhibits very fast temporal fluctuations. Suspicions for the presence of three-dimensional flow are evidenced and possible causes for a three-dimensional instability are discussed together with the coupling of wall slip to bulk dynamic.

Wormlike micelle formation and flow alignment of a pluronic block copolymer in aqueous solution

The self-assembly into wormlike micelles of a poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) triblock copolymer Pluronic P84 in aqueous salt solution (2 M NaCl) has been studied by rheology, small-angle X-ray and neutron scattering (SAXS/SANS), and light scattering. Measurements of the flow curves by controlled stress rheometry indicated phase separation under flow. SAXS on solutions subjected to capillary flow showed alignment of micelles at intermediate shear rates, although loss of alignment was observed for high shear rates. For dilute solutions, SAXS and static light scattering data on unaligned samples could be superposed over three decades in scattering vector, providing unique information on the wormlike micelle structure over several length scales. SANS data provided information on even shorter length scales, in particular, concerning "blob" scattering from the micelle corona. The data could be modeled based on a system of semiflexible self-avoiding cylinders with a circular cross-section, as described by the wormlike chain model with excluded volume interactions. The micelle structure was compared at two temperatures close to the cloud point (47 degrees C). The micellar radius was found not to vary with temperature in this region, although the contour length increased with increasing temperature, whereas the Kuhn length decreased. These variations result in an increase of the low-concentration radius of gyration with increasing temperature. This was consistent with dynamic light scattering results, and, applying theoretical results from the literature, this is in agreement with an increase in endcap energy due to changes in hydration of the poly(ethylene oxide) blocks as the temperature is increased.

Wall slip, shear banding, and instability in the flow of a triblock copolymer micellar solution

The shear flow of a triblock copolymer micellar solution (PEO-PPO-PEO Pluronic P84 in brine) is investigated using simultaneous rheological and velocity profile measurements in the concentric cylinder geometry. We focus on two different temperatures below and above the transition temperature T{c} which was previously associated with the apparition of a stress plateau in the flow curve. (i) At T=37.0 degrees C<T{c}, the bulk flow remains homogeneous and Newtonian-like, although significant wall slip is measured at the rotor that can be linked to an inflexion point in the flow curve. (ii) At T=39.4 degrees C>T{c}, the stress plateau is shown to correspond to stationary shear-banded states characterized by two high shear rate bands close to the walls and a very weakly sheared central band, together with large slip velocities at the rotor. In both cases, the high shear branch of the flow curve is characterized by flow instability. Interpretations of wall slip, three-band structure, and instability are proposed in light of recent theoretical models and experiments.

Granger causality and cross recurrence plots in rheochaos

Our stress relaxation measurements on wormlike micelles using a Rheo-SALS (rheology + small angle light scattering) apparatus allow simultaneous measurements of the stress and the scattered depolarized intensity. The latter is sensitive to orientational ordering of the micelles. To determine the presence of causal influences between the stress and the depolarized intensity time series, we have used the technique of linear and nonlinear Granger causality. We find there exists a feedback mechanism between the two time series and that the orientational order has a stronger causal effect on the stress than vice versa. We have also studied the phase space dynamics of the stress and the depolarized intensity time series using the recently developed technique of cross recurrence plots (CRPs). The presence of diagonal line structures in the CRPs unambiguously proves that the two time series share similar phase space dynamics.

Tuning rheochaos by temperature in wormlike micelles

We investigate the critical role played by the mean micellar length during the route to rheochaos for wormlike micellar gels of surfactant cetyltrimethylammonium tosylate in the presence of salt sodium chloride that show coupling of flow to concentration fluctuations. To this end, we have carried out stress/shear rate relaxation experiments at a fixed shear rate/stress but at different temperatures to take the sample through the route to rheochaos. We see the type-II intermittency route to rheochaos in stress relaxation measurements and the type-III intermittency route to rheochaos in shear rate relaxation measurements. We have also carried out linear rheology measurements at different temperatures to estimate the mean micellar length (-)L, the reptation time tau(rep), and the breaking time tau(break). It is shown that (-)L changes by approximately 58%, as the sample goes through the route to rheochaos.

Rheo-NMR phenomena of wormlike micelles

Using a combination of rheology and nuclear magnetic resonance (NMR) spectroscopy/velocimetry we demonstrate the existence of shear banding fluctuations under Couette flow of the micellar system 10% w/v cetylpyridinium chloride and sodium salicylate (CPyCl-NaSal) molar ratio 2 : 1 in 0.5 M NaCl in either HO or HO, using both time-averaged and real-time measurements. These shear banding fluctuations are consistent not only with the shear stress fluctuations observed in rheological measurements but also with fluctuations in the change of the constrained fraction of the amphiphile chain (Δ) observed in H-NMR spectroscopy experiments. Using H-NMR spectroscopy on a deuterated probe molecule (-decane) located in the wormlike micellar interior, direct measurement of the shear-induced nematic phase transition is reported.

Fast magnetic resonance imaging and velocimetry for liquids under high flow rates

We here demonstrate the use of NMR velocity imaging techniques to measure flow in a free falling jet of water at speeds up to and on the order of 1m/s. In particular, we show how to adapt the RARE imaging method, based on a CPMG multiple rf pulse train, so that the real and imaginary parts of the signal may be suitably acquired, enabling pulsed gradient spin echo encoding for flow. We term this method "soft-pulse-quadrature-cycled PGSE-RARE" or SPQC-PGSE-RARE. We further demonstrate the use of a one-dimensional (slice selective) imaging method which takes advantage of the cylindrical symmetry of the flow, and considerably shortens the image acquisition time.

Minimal model for chaotic shear banding in shear thickening fluids

We present a minimal model for spatiotemporal oscillation and rheochaos in shear thickening complex fluids at zero Reynolds number. In the model, a tendency towards inhomogeneous flows in the form of shear bands combines with a slow structural dynamics, modeled by delayed stress relaxation. Using Fourier-space numerics, we study the nonequilibrium "phase diagram" of the fluid as a function of a steady mean (spatially averaged) stress, and of the relaxation time for structural relaxation. We find several distinct regions of periodic behavior (oscillating bands, traveling bands, and more complex oscillations) and also regions of spatiotemporal rheochaos. A low-dimensional truncation of the model retains the important physical features of the full model (including rheochaos) despite the suppression of sharply defined interfaces between shear bands. Our model maps onto the FitzHugh-Nagumo model for neural network dynamics, with an unusual form of long-range coupling.