Flow-vorticity Plane Research Articles

Shear rheology of a dilute suspension of thin rings

The rheology of suspensions of rings (tori) rotating in an unbounded low Reynolds number simple shear flow is calculated using numerical simulations at dilute particle number densities ( n ≪ 1 ). Suspensions of non-Brownian rings are studied by computing pair interactions that include hydrodynamic interactions modeled using slender body theory and particle collisions modeled using a short-range repulsive force. Particle contact and hydrodynamic interactions were found to have comparable influences on the steady-state Jeffery orbit distribution. The average tilt of the ring away from the flow-vorticity plane increased during pairwise interactions compared to the tilt associated with Jeffery rotation and the steady-state orbit distribution. Particle stresses associated with the increased tilt during the interaction were found to be comparable to the stresses induced directly by particle contact forces and the hydrodynamic velocity disturbances of other particles. The hydrodynamic diffusivity coefficients in the gradient and vorticity directions were also obtained and were found to be two orders of magnitude larger than the corresponding values in fiber suspensions at the same particle concentrations. Rotary Brownian dynamics simulations of isolated Brownian rings were used to understand the shear rate dependence of suspension rheology. The orbit distribution observed in the regime of weak Brownian motion, P e ≫ ϕ T − 3, was surprisingly similar to that obtained from pairwise interaction calculations of non-Brownian rings. Here, the Peclet number P e is the ratio of the shear rate and the rotary diffusivity of the particle and ϕ T is the effective inverse-aspect ratio of the particle (approximately equal to 2 π times the inverse of its non-dimensional Jeffery time period). Thus, the rheology results obtained from pairwise interactions should retain accuracy even for weakly Brownian rings ( n ≪ 1 and ϕ T − 3 ≪ P e ).

Buckling of elastic fibers in a shear flow

Three-dimensional dynamics of flexible fibers in shear flow are studied numerically, with a qualitative comparison to experiments. Initially, the fibers are straight, with different orientations with respect to the flow. By changing the rotation speed of a shear rheometer, we change the ratio A of bending to shear forces. We observe fibers in the flow-vorticity plane, which gives insight into the motion out of the shear plane. The numerical simulations of moderately flexible fibers show that they rotate along effective Jeffery orbits, and therefore the fiber orientation rapidly becomes very close to the flow-vorticity plane, on average close to the flow direction, and the fiber remains in an almost straight configuration for a long time. This ‘ordering’ of fibers is temporary since they alternately bend and straighten while tumbling. We observe numerically and experimentally that if the fibers are initially in the compressional region of the shear flow, they can undergo compressional buckling, with a pronounced deformation of shape along their whole length during a short time, which is in contrast to the typical local bending that originates over a long time from the fiber ends. We identify differences between local and compressional bending and discuss their competition, which depends on the initial orientation of the fiber and the bending stiffness ratio A. There are two main finding. First, the compressional buckling is limited to a certain small range of the initial orientations, excluding those from the flow-vorticity plane. Second, since fibers straighten in the flow-vorticity plane while tumbling, the compressional buckling is transient—it does not appear for times longer than 1/4 of the Jeffery period. For larger times, bending of fibers is always driven by their ends.

Shear driven vorticity aligned flocs in a suspension of attractive rigid rods.

A combination of rheology, optical microscopy and computer simulations was used to investigate the microstructural changes of a semi-dilute suspension of attractive rigid rods in an imposed shear flow. The aim is to understand the relation of the microstructure with the viscoelastic response, and the yielding and flow behaviour in different shear regimes of gels built from rodlike colloids. A semi-dilute suspension of micron sized, rodlike silica particles suspended in 11 M CsCl salt solution was used as a model system for attractive rods' gel. Upon application of steady shear the gel microstructure rearranges in different states and exhibits flow instabilities depending on shear rate, attraction strength, volume fraction and geometrical confinement. At low rod volume fractions, the suspension forms large, vorticity aligned, particle rich flocs that roll in the flow-vorticity plane, an effect that is due to an interplay between hydrodynamic interactions and geometrical confinement as suggested by computer simulations. Experimental data allow the creation of a state diagram, as a function of volume fraction and shear rates, identifying regimes of stable (or unstable) floc formation and of homogeneous gel or broken clusters. The transition is related to dimensionless Mason number, defined as the ratio of shear forces to interparticle attractive force.

Buckling, crumpling, and tumbling of semiflexible sheets in simple shear flow.

As 2D materials such as graphene, transition metal dichalcogenides, and 2D polymers become more prevalent, solution processing and colloidal-state properties are being exploited to create advanced and functional materials. However, our understanding of the fundamental behavior of 2D sheets and membranes in fluid flow is still lacking. In this work, we perform numerical simulations of athermal semiflexible sheets with hydrodynamic interactions in shear flow. For sheets initially oriented near the flow-vorticity plane, we find buckling instabilities of different mode numbers that vary with bending stiffness and can be understood with a quasi-static model of elasticity. For different initial orientations, chaotic tumbling trajectories are observed. Notably, we find that sheets fold or crumple before tumbling but do not stretch again upon applying greater shear.

Numerical simulations of the motion of ellipsoids in planar Couette flow of Giesekus viscoelastic fluids

The motion of neutrally buoyant ellipsoids in a planar Couette flow of Giesekus viscoelastic fluids between two narrowly set plates is numerically simulated with a fictitious domain method. The aspect ratio of the ellipsoid is 4 (i.e., prolate spheroids) and the Deborah number (De) ranges from 0 to 4.0. For a single ellipsoid initially placed in the mid-plane between the two plates, the ellipsoid major axis rotates around the vorticity axis in a kayaking mode at relatively low Deborah numbers, and is tilted in the flow-vorticity plane when the Deborah number exceeds a critical value, with the orientation being closer to the flow direction for a larger De. For a single ellipsoid initially not placed in the mid-plane, the ellipsoid undergoes lateral migration toward the nearby wall, and it is interesting that the ellipsoid turns its orientation to the vorticity axis at relatively small De and a direction close to the vorticity axis at large De (above 3.0), in contrast to the ellipsoid placed in the mid-plane without lateral migration, whose terminal orientation exhibits a kayaking motion at relatively small De and is close to the flow direction for De > 3. As a result, for the multiple-ellipsoid case, there exists a transient stage where the average orientation of the ellipsoids turns toward the vorticity axis for all nonzero Deborah numbers studied, and the orientation close to the vorticity axis can be often observed for the isolated ellipsoids. Both the particle interactions and the wall effect promote the ellipsoids to align with the flow direction. Particle aggregation and the dynamic aligning structures are observed at large Deborah numbers.

Phase-dependent shear-induced order of nanorods in isotropic and nematic wormlike micelle solutions.

Small angle X-ray scattering with in situ shear was employed to study the assembly and ordering of dispersions of gold nanorods within wormlike micelle solutions formed by the surfactant cetylpyridinium chloride (CPyCl) and counter-ion sodium salicylate (NaSal). Above a threshold CPyCl concentration but below the isotropic-to-nematic transition of the micelles, the nanorods self-assembled under quiescent conditions into isotropically oriented domains with hexagonal order. Under steady shear at rates between 0.5 and 7.5 s-1, the nanorod assemblies acquired macroscopic orientational order in which the hexagonal planes were coincident with the flow-vorticity plane. The nanorods could be re-dispersed by strong shear but re-assembled following cessation of the shear. In the nematic phase of the micelles at higher surfactant concentration, the nanorods did not acquire hexagonal order but instead formed smectic-like layers in the gradient-vorticity plane under shear. Finally, at still higher surfactant concentration, where the micelles form a hexagonal phase, the nanorods showed no translational ordering but did acquire nematic-like order under shear due to alignment in the flow. Depletion forces mediated by the wormlike micelles are identified as the driving mechanism for this sequence of nanorod ordering behaviors, suggesting a novel mechanism for controlled, reconfigurable assembly of nanoparticles in solution.

Steady-shear rheological properties for suspensions of axisymmetric particles in second-order fluids

Following Leal who gave the motion of a slender axisymmetric rod in a second-order fluid, we derived a complete rheological constitutive equation for dilute and semidilute slender rod suspensions in a viscoelastic solvent based on a cell model. Numerical solutions for the Fokker–Planck equation are obtained for simple shear flows at low and large Peclet numbers using a finite volume method, hence avoiding the need for closure approximations. The second normal stress difference coefficient of the solvent plays a non-negligible role in the particle contribution to the stress as well as on the rod orientation dynamics: a spread of the particle orientation in the flow-vorticity plane and an enhancement of the alignment along the vorticity direction are predicted when increasing the second normal stress difference coefficient. Brunn extended the Leal analysis to dumbbells and tri-dumbbells, for which both normal stress difference coefficients have to be considered. The original Pipkin diagram is finally modified to help guide the choice of relevant constitutive equations for particles in viscoelastic fluids.

Understanding steady and dynamic shear banding in a model wormlike micellar solution

Shear banding under steady and dynamic deformation is examined using a combination of rheology and flow-small angle neutron scattering (SANS) in a model wormlike micelle solution comprised of a mixed cationic/anionic surfactant (cetyltrimethylammonium tosylate/sodium dodecyl benzene sulfonate) and sodium tosylate. Flow-vorticity plane rheo-SANS reveals long transients during shear band formation. Flow-gradient plane spatially resolved flow-SANS measurements probe the microstructure during steady and dynamic shear banding. Under large amplitude oscillatory shear (LAOS) deformation, shear banding is dependent on the Deborah and Weissenberg numbers, validating recent theoretical predictions that include shear-induced breakage. Micelle segmental alignment in the flow-gradient plane during LAOS is a nonmonotonic function of cycle time, t/T, and radial position, r/H. The maximum segmental alignment under LAOS often exceeds that of the corresponding shear rate under steady shear, termed “over-orientation,” which can help identify LAOS shear banding. The results of this study present new methods for identifying shear banding under steady and dynamic deformation, while providing an extensive data set for the development and further improvement of constitutive models.

The Connection between Biaxial Orientation and Shear Thinning for Quasi-Ideal Rods.

The complete orientational ordering tensor of quasi-ideal colloidal rods is obtained as a function of shear rate by performing rheo-SANS (rheology with small angle neutron scattering) measurements on isotropic fd-virus suspensions in the two relevant scattering planes, the flow-gradient (1-2) and the flow-vorticity (1-3) plane. Microscopic ordering can be identified as the origin of the observed shear thinning. A qualitative description of the rheological response by Smoluchowski, as well as Doi–Edwards–Kuzuu theory is possible, as we obtain a master curve for different concentrations, scaling the shear rate with the apparent collective rotational diffusion coefficient. However, the observation suggests that the interdependence of ordering and shear thinning at small shear rates is stronger than predicted. The extracted zero-shear viscosity matches the concentration dependence of the self-diffusion of rods in semi-dilute solutions, while the director tilts close towards the flow direction already at very low shear rates. In contrast, we observe a smaller dependence on the shear rate in the overall ordering at high shear rates, as well as an ever-increasing biaxiality.

Transient, near-wall shear-band dynamics in channel flow of wormlike micelle solutions

We report the spatiotemporal dynamics of shear bands in wormlike micelle solutions as generated in the near-wall region of rectangular channel flow. In this system, a very thin (<2µm) high shear rate band is generated, stacked along the gradient axis of the channel flow. By means of confocal microscopy and particle image velocimetry, we observe the effect of this thin band on both the steady-state flow profile and the transient variation in the flow-direction velocity, which is found to be non-uniform in the vorticity direction. The steady-state velocity profiles deviate from a parabolic shape above an applied wall shear rate of 6s−1 (Wi=0.8), in good correspondence with the measured rheology. Kinetically, the deviation from parabolic flow presents as the development of a thin, near-wall band flowing at a high shear rate. The band dynamics along the vorticity (neutral) axis of the flow are observed at distances from 2 to 10µm from the wall. At the smallest near-wall position of 2µm, space-time plots reveal four distinct stages in the variation of the flow-direction velocity with time and with position along the vorticity axis. First, the flow accelerates at all points along the vorticity axis to about one-half of the final, steady-state velocity at that position in the gap. Second, a deceleration – again at all points in the flow-vorticity plane – abruptly slows down the fluid motion at this near-wall region. The total change in velocity resulting from the deceleration is about one-half that of the previous acceleration. Third, the flow partitions into multiple strips along the vorticity direction; these strips have non-uniform flow-direction velocity. The width of these strips is dependent on the wall shear rate; their width is ∼100µm for flow with a wall shear rate of 8.4s−1. Finally, all the fast strips combine to form a single homogeneous flow with a fast velocity at 2µm from the wall. This velocity is ∼50 times that expected for unbanded flow with the same flow rate. We discuss these shear band spatiotemporal dynamics in the context of transient vorticity structuring that occurs at applied wall shear rates within the stress plateau region.

Direct visualization of flow-induced conformational transitions of single actin filaments in entangled solutions.

While semi-flexible polymers and fibres are an important class of material due to their rich mechanical properties, it remains unclear how these properties relate to the microscopic conformation of the polymers. Actin filaments constitute an ideal model polymer system due to their micron-sized length and relatively high stiffness that allow imaging at the single filament level. Here we study the effect of entanglements on the conformational dynamics of actin filaments in shear flow. We directly measure the full three-dimensional conformation of single actin filaments, using confocal microscopy in combination with a counter-rotating cone-plate shear cell. We show that initially entangled filaments form disentangled orientationally ordered hairpins, confined in the flow-vorticity plane. In addition, shear flow causes stretching and shear alignment of the hairpin tails, while the filament length distribution remains unchanged. These observations explain the strain-softening and shear-thinning behaviour of entangled F-actin solutions, which aids the understanding of the flow behaviour of complex fluids containing semi-flexible polymers.

Rotational motion of a thin axisymmetric disk in a low Reynolds number linear flow

The motion of thin, torque-free axisymmetric rigid particles with fore-aft symmetry in low Reynolds number linear flows is investigated. The rotational motion of such a particle is fully determined by the effective aspect ratio (κe), defined as the aspect ratio of a spheroid having the same period of rotation as that of the particle. We determine the effective aspect ratio for a family of shapes given by, y(ρ) = κ(1 − ρ2)α where α is a positive parameter, ρ is the radial distance from the particle center in polar coordinates, y is half the thickness of the particle, κ is the aspect ratio of the particle defined as the ratio of the thickness (L) of the particle parallel to the axis of symmetry to its diameter (d) perpendicular to the axis of symmetry. This family includes an oblate spheroid (\documentclass[12pt]{minimal}\begin{document}$\alpha =\frac{1}{2}$\end{document}α=12) and the shape approaches a blunt circular cylinder shape as α → 0. For a thin particle, the effective aspect ratio scales like \documentclass[12pt]{minimal}\begin{document}$\smash{G_{A}^{\frac{1}{2}}}$\end{document}GA12, where GA is the torque non-dimensionalized by μγd3 acting on a particle held in a fixed alignment in a simple shear flow with its longer dimensions in the flow-vorticity plane. Here, μ is the fluid viscosity and γ is the shear rate. Starting with the integral representation of the Stokes flow, an analysis based on a matched asymptotic expansions approach is performed to determine the scaling of the torque acting on a stationary particle in simple shear flow with κ as the small parameter. Using boundary element method simulations, the exact torques are calculated and the scaling obtained from the analysis is verified. We find that there are two regions of interest that contribute to the torque, a flat outer region covering most of the disk area and a boundary layer region of large slope at the edge. For \documentclass[12pt]{minimal}\begin{document}$\alpha &amp;gt;\frac{1}{4}$\end{document}α&amp;gt;14, the torque is dominated by the stresses acting on the flat surface of the particle and is O(κ2) to the leading order. For these shapes, the effective aspect ratio scales like the aspect ratio of the particle. On the other hand, for \documentclass[12pt]{minimal}\begin{document}$\alpha \le \frac{1}{4}$\end{document}α≤14, the leading order torque contribution comes from the boundary layer region. To the leading order, the torque scales as O(κ2logκ) for \documentclass[12pt]{minimal}\begin{document}$\alpha =\frac{1}{4}$\end{document}α=14 and as \documentclass[12pt]{minimal}\begin{document}$O(\kappa ^\frac{3}{2(1-\alpha )})$\end{document}O(κ32(1−α)) for \documentclass[12pt]{minimal}\begin{document}$\alpha &amp;lt;\frac{1}{4}$\end{document}α&amp;lt;14. In general, a particle with a blunt edge is found to rotate faster than a particle of the same aspect ratio for which the slope of the edge varies slowly. The fastest rotating particle is identified to be a cylindrical disk for which κe = 1.12κ3/4.

Rigid ring-shaped particles that align in simple shear flow

AbstractMost rigid, torque-free, low-Reynolds-number, axisymmetric particles undergo a time-periodic tumbling motion in a simple shear flow, with their axes of symmetry following a set of closed Jeffery orbits. We have identified a class of rigid, ring-like particles whose axes of symmetry instead reach a permanent alignment near the velocity gradient direction with the plane of the particle aligning near the flow–vorticity plane. An asymptotic analysis for small particle aspect ratio (ratio of length parallel to the axis of symmetry to diameter perpendicular to the axis) shows that an appropriate asymmetry of the ring cross-section with a thinner outer edge and thicker inner edge leads to a tendency to rotate in a direction opposite to the vorticity; this tendency can balance the usual rotation rate associated with the finite thickness of the particle. Boundary integral computations for finite particle aspect ratios are used to determine the conditions of aspect ratio and degree of asymmetry that lead to the aligning behaviour and the final orientation of the axis of symmetry of the aligned particles. The aligning particle follows an equation of motion similar to the Leslie–Erickson equation for the director of a small-molecule nematic liquid crystal. However, whereas the alignment of the director arises from intermolecular interactions, the ring-like particle aligns solely due to its intrinsic rotational motion in a low-Reynolds-number flow.

Evaluation of steerable filter for detection of fibers in flowing suspensions

Steerable filters are concluded to be useful in order to determine the orientation of fibers captured in digital images. The fiber orientation is a key variable in the study of flowing fiber suspensions. Here, digital image analysis based on a filter within the class of steerable filters is evaluated for suitability of finding the position and orientation of fibers suspended in flowing suspensions. In sharp images with small noise levels, the steerable filter succeeds in determining the orientation of artificially generated fibers with well-defined angles. The influence of reduced image quality on the orientation has been quantified. The effect of unsharpness and noise is studied and the results show that the error in orientation is less than 1° for moderate levels. Images from two flow cases, one laminar shear flow and one turbulent, are also analyzed. The fiber orientation distribution is determined in the flow-vorticity plane. For the laminar case a comparison is made to a robust, but computationally more expensive, method involving convolutions with an oriented elliptic filter. A good agreement is found when comparing the resulting fiber orientation distributions obtained with the two methods. For the turbulent case, it is demonstrated that correct results are obtained and that the method can handle overlapping fibers.

Ordering fluctuations in a shear-banding wormlike micellar system

We present a first investigation about the non-linear flow properties and transient orientational-order fluctuations observed in the shear-thinning lecithin-water-cyclohexane wormlike micellar system at a concentration near to the zero-shear isotropic-nematic phase transition. From rheological measurements the stress plateau was found shifted to very low values of the applied shear rate gamma, compared to most of the concentrated living polymer systems reported in the literature. Rheo-small angle neutron scattering (Rheo-SANS) experiments performed in the flow-vorticity plane revealed periodical fluctuations of both the order parameter P(2) and the angular deviation phi from the vorticity axis as determined from the scattering peaks. The periods of the oscillations were not found to depend on imposed gamma. A theoretical model was also developed to explain the oscillatory dynamics of the shear-induced nematic order parameter in terms of the presence of standing waves of the director orientation profile along the circumference of the Couette cell. The experimental results of the periodic order parameter fluctuations together with their theoretical modelling shed significant new insights on the shear banding phenomenon, particularly its microscopic mechanism.

Orientation dynamics in multiwalled carbon nanotube dispersions under shear flow

We report studies of the orientation state of multiwalled carbon nanotubes (MWNTs) dispersions in steady and transient shear flows. Uncured epoxy was used as a viscous Newtonian suspending medium and samples were prepared from "aligned" MWNTs using methods previously reported [S. S. Rahatekar et al., J. Rheol. 50, 599 (2006)]. Orientation measurements were performed in both the flow-gradient (1-2) and flow-vorticity (1-3) plane of simple shear flow using in situ x-ray scattering techniques. Steady state measurements in the 1-2 plane indicate that the MWNT orientation is shear rate dependent, with the MWNTs orienting closer to the flow direction at higher shear rates. During steady shear, anisotropy was measured to be higher in the 1-2 plane than in the 1-3 plane, demonstrating that the nanotube orientation state is not unaxially symmetric in shear. It is hypothesized that the steady state MWNT orientation is governed primarily by a rate-dependent state of nanotube aggregation/disaggregation, which was separately characterized by optical microscopy of the same samples under shear. High flux synchrotron radiation allowed for time-resolved structural studies in transient flows. A partial relaxation of flow-induced anisotropy was observed following flow cessation, despite the very small rotational diffusivity estimated for these nanotubes. Long transients are observed in step-down experiments, as the orientation state changes in response to the slow tube aggregation process.

Shear-Induced Alignment of Smectic Side Group Liquid Crystalline Polymers

Large amplitude oscillatory shear (LAOS) is frequently capable of generating macroscopic alignment from an initially random orientation distribution in ordered polymer fluids. Side-group liquid crystalline polymers are of special interest in that the flow field may couple differently to the polymer backbone and the mesogen ordering. We report combined rheological and in situ X-ray scattering investigations of LAOS-induced alignment in smectic side-group LCPs. Synchrotron X-ray scattering is used to study orientation development using a rotating disk shear cell in which orientation is tracked within the flow-vorticity (1−3) plane. In all cases, we find that shear promotes anisotropic orientation states in which the lamellar normal tends to align along the vorticity direction of the shear flow (“perpendicular” alignment). We examine the effects of shear strain amplitude and polymer backbone molecular weight on the ability of LAOS to induce alignment. Rheological measurements of the dynamic moduli reveal that large amplitude shearing in the smectic phase causes a notable decrease in the modulus. X-ray and rheological data demonstrate that increasing strain promotes higher degrees of orientation, while increasing molecular weight impedes development of smectic alignment.

Stacking fault structure in shear-induced colloidal crystallization

We report measurements of the spatial distribution of stacking faults in colloidal crystals formed by means of an oscillatory shear field at a particle volume fraction of 52% in a system where the pair potential interactions are mildly repulsive. Stacking faults are directly visualized via confocal laser scanning microscopy. Consistent with previous scattering studies, shear orders the initially amorphous colloids into close-packed planes parallel to the shearing surface. Upon increasing the strain amplitude, the close-packed direction of the (111) crystal plane shifts from an orientation parallel to the vorticity direction to parallel the flow direction. The quality of the layer ordering, as characterized by the mean stacking parameter, decreases with strain amplitude. In addition, we directly observe the three-dimensional structure of stacking faults in sheared crystals. We observe and quantify spatial heterogeneity in the stacking fault arrangement in both the flow-vorticity plane and the gradient direction, particularly at high strain amplitudes (gamma> or =3). At these conditions, layer ordering persists in the flow-vorticity plane only over scales of approximately 5-10 particle diameters. This heterogeneity is one component of the random layer ordering deduced from previous scattering studies. In addition, in the gradient direction, the stacking registry shows that crystals with intermediate global mean stacking probability are comprised of short sequences of face-centered cubic and hexagonal close-packed layers with a stacking that includes a component that is nonrandom and alternating in character.

Effect of oscillatory shear on polymer solutions.

We consider the effects of oscillatory shear flow on small concentration fluctuations in polymer solutions, which we model as highly asymmetric entangled polymer blends. A simple model that enables us to predict the scattering patterns in the flow-vorticity plane is presented. It is shown that peaks in the patterns occur in the flow direction at a finite wave vector, their position strongly depends on the angular frequency of oscillatory shear flow, whereas the intensity of these peaks is rather controlled by the amplitude of the flow. The model reproduces characteristic double-winged anisotropic scattering patterns called "butterfly," which are stable and thus represent concentration fluctuations rather than phase separation.

Shear Orientation of a Hexagonal Lyotropic Triblock Copolymer Phase As Probed by Flow Birefringence and Small-Angle Light and Neutron Scattering

The shear orientation of the hexagonal liquid crystalline phase of a poloxamer-type triblock copolymer (poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) (Pluronic L64))/water mixture was investigated by means of different techniques, namely, flow birefringence (Δn), small-angle light scattering, and small-angle neutron scattering (SALS, SANS). The evolution of birefringence is discussed for different types of shear. Oscillatory shear showed that birefringence displayed small oscillations during the first cycles until the sample was shear aligned. Then the same Δn value was obtained as in creep experiments. The degree of orientation depended on the strain. On a microscopic length scale probed by SANS, the shear flow results in an alignment of rodlike micelles along the flow direction. SANS experiments with the incident beam along the flow direction revealed that the 10 plane of the hexagonal lattice was aligned parallel to the flow-vorticity plane. On a mesoscopic length scale, studied by microscopy and SALS, a stripe texture was observed. SALS showed that the texture was similar to that obtained in low molar mass surfactants.