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.     

Spatiotemporal dynamics of shear induced bands en route to rheochaos

We show experimentally that the route to rheochaos in shear rate relaxation measurements is via Type-III intermittency and mixed mode oscillations in the shear-thinning wormlike micellar system of cetyltrimethylammonium tosylate in the presence of salt sodium chloride. Depolarised small angle light scattering measurements performed during flow show that scattered intensity temporally follows the shear rate/stress dynamics and portrays the crucial role played by nematic ordering. Direct visualization of the gap of the Couette cell, illuminated by an unpolarised laser sheet, in the (vorticity, velocity gradient) plane shows that the spatiotemporal dynamics of the shear induced structures is closely related to the temporal behaviour of shear rate/stress fluctuations.     

Shear-thickening transition in surfactant solutions: New experimental features from rheology and flow birefringence

We report on the shear-thickening transition observed in dilute aqueous solutions of cetyltrimethylammonium tosylate (CTAT) at concentrations . We have re-examined the kinetics of the shear-thickening transition using start-up experiments at rates above the critical shear rate . Using simple well-defined protocols, we have found that the transient mechanical response depends dramatically on the thermal and on the shear histories. Using the same protocols, flow birefringence experiments were carried out. The gap of a Couette cell containing the sheared solution has been visualized between crossed polarizers in steady shear conditions, as well as in start-up experiments. We show that the birefringent shear-induced phase starts from the inner cylinder and grows along the velocity gradient direction, as in a shear banding situation. However, around we have not observed a regime of phase coexistence (isotropic and birefringent). Received 11 November 1999     

NMR velocimetry studies of the steady-shear rheology of a concentrated hard-sphere colloidal system

NMR velocimetry has been used to observe the steady-shear rheological behaviour of a concentrated suspension of hard-sphere like 370 nm diameter PMMA core-shell latex particles at the volume fraction Φ = 0.46, the liquid core of the spheres rendering possible NMR observation of the particles themselves. Rheological measurements in a cone-and-plate geometry indicate that when aged (i.e. left at rest for two weeks), the material exhibits yield stress behaviour at very low shear rates. For shear rates greater than 1 s ^{- 1} a transition to liquid-like behaviour was observed, leading to a rejuvenated fluid state which exhibits shear-thinning behaviour over a wide range of shear rates. A similar yield stress behaviour was reflected in NMR velocimetry measurements in a Couette geometry, where the solid-to liquid transition could be clearly observed. Under steady-state flow, the fluid state inside the radius at which yield stress was observed, exhibited shear-thinning behaviour with a power law exponent n slowly approaching unity with increasing shear rate. This behaviour has some similarities with a model of Derec et al. in which aging and rejuvenation effects compete. Substantial wall slip was observed both at the inner and at the outer wall, an effect which disappeared as the shear rate was increased. No radial particle migration from the high-shear region at the inner wall was observed.     

A spatio-temporal study of rheo-oscillations in a sheared lamellar phase using ultrasound

We present an experimental study of the flow dynamics of a lamellar phase sheared in the Couette geometry. High-frequency ultrasonic pulses at 36 MHz are used to measure time-resolved velocity profiles. Oscillations of the viscosity occur in the vicinity of a shear-induced transition between a high-viscosity disordered fluid and a low-viscosity ordered fluid. The phase coexistence shows up as shear bands on the velocity profiles. We show that the dynamics of the rheological data result from two different processes: (i) fluctuations of slip velocities at the two walls and (ii) flow dynamics in the bulk of the lamellar phase. The bulk dynamics are shown to be related to the displacement of the interface between the two differently sheared regions in the gap of the Couette cell. Two different dynamical regimes are investigated under applied shear stress: one of small amplitude oscillations of the viscosity ( %) and one of large oscillations ( %). A phenomenological model is proposed that may account for the observed spatio-temporal dynamics.Received: 2 December 2003, Published online: 9 March 2004PACS: 83.10.Tv Structural and phase changes - 43.58. + z Acoustical measurements and instrumentation - 47.50. + d Non-Newtonian fluid flows     

Measurement of diffusion in the presence of shear flow

We demonstrate here a method whereby molecular diffusion coefficients may be measured in the presence of the deformational flow field of a rheo-NMR cell. The method, which uses a repetitive CPMG train of rf pulses interspersed with magnetic field gradient pulses, allows the anisotropic diffusion spectrum to be directly probed. We focus on the cylindrical Couette cell, for which the radial, tangential, and axial directions correspond to the hydrodynamic velocity gradient, velocity, and vorticity directions. While ideal Couette flow does not perturb the vorticity direction, it does perturb diffusion measurements for the velocity gradient direction, and to a lesser extent, the velocity direction. We show that with closely spaced gradient pulses operating in a flow-compensating mode, there exists a diffusion limit below which one cannot measure, that scales as T(2)gamma(4), where gamma is the shear rate and T the gradient pulse repetition period. For a typical rheo-NMR cell, and for the more challenging velocity gradient direction, diffusion rates above 10(-12) m(2) s(-1) can be accurately measured (to 1% error) at shear rates up to 3s(-1). We demonstrate the use of the method in measuring the diffusion spectrum of a lyotropic lamellar phase under shear.     

Temporal oscillations of the shear stress and scattered light in a shear-banding-shear-thickening micellar solution

The results of optical and rheological experiments performed on a viscoelastic solution (cetyltrimethylammonium bromide + sodium salicylate in water) are reported. The flow curve has a horizontal plateau extending between two critical shear rates characteristic of heterogeneous flows formed by two layers of fluid with different viscosities. These two bands which also have different optical anisotropy are clearly seen by direct observation in polarized light. At the end of the plateau, apparent shear thickening is observed in a narrow range of shear rates; in phase oscillations of the shear stress and of the first normal stress difference are recorded in a shearing device operating under controlled strain. The direct observation of the annular gap of a Couette cell in a direction perpendicular to a plane containing the vorticity shows that the turbidity of the whole sample also undergoes time dependent variations with the same period as the shear stress. However no banding is observed during the oscillations and the flow remains homogeneous.     

Arch generated shear bands in granular systems

We propose an arch based model, on cubic and square lattices, to simulate the internal mobility of grains, in a dense granular system under shear. In this model, the role of the arches in granular transport presents a non-linear dependence on the local values of the stress components that can be modeled geometrically. This non-linearity is very important since a linear dependence on the stress will make the models behave similarly to viscous fluids, which will not reproduce highly interesting properties of the sheared systems such as shear bands. In particular, we study a modified Couette flow and find the appearance of shear bands in accordance with the literature.     

Spatiotemporal rheochaos in nematic hydrodynamics

Motivated by recent observations of rheochaos in sheared wormlike micelles, we study the coupled nonlinear partial differential equations for the hydrodynamic velocity and order-parameter fields in a sheared nematogenic fluid. In a suitable parameter range, we find irregular, dynamic shear banding and establish by decisive numerical tests that the chaos we observe in the model is spatiotemporal in nature.     

Intermittency route to rheochaos in wormlike micelles with flow-concentration coupling

We show experimentally that the route to chaos is via intermittency in a shear-thinning wormlike micellar system of cetyltrimethylammonium tosylate, where the strength of flow-concentration coupling is tuned by the addition of salt sodium chloride. A Poincaré first return map of the time series and the probability distribution of laminar lengths between burst events shows that our data is consistent with type-II intermittency. The coupling of flow to concentration fluctuations is evidenced by the "butterfly" intensity pattern in small angle light scattering (SALS) measurements performed simultaneously with the rheological measurements. The scattered depolarized intensity in SALS, sensitive to orientational order fluctuations, shows the same time dependence (like intermittency) as that of shear stress.     

Towards local rheology of emulsions under Couette flow using Dynamic Light Scattering

We present local velocity measurements in emulsions under shear using heterodyne Dynamic Light Scattering. Two emulsions are studied: a dilute system of volume fraction φ = 20% and a concentrated system with φ = 75%. Velocity profiles in both systems clearly show the presence of wall slip. We investigate the evolution of slip velocities as a function of shear stress and discuss the validity of the corrections for wall slip classically used in rheology. Focussing on the bulk flow, we show that the dilute system is Newtonian and that the concentrated emulsion is shear-thinning. In the latter case, the curvature of the velocity profiles is compatible with a shear-thinning exponent of 0.4 consistent with global rheological data. However, even if individual profiles can be accounted for by a power law fluid (with or without a yield stress), we could not find a fixed set of parameters that would fit the whole range of applied shear rates. Our data, thus, raise the question of the definition of a global flow curve for such a concentrated system. These results show that local measurements are a crucial complement to standard rheological tools. They are discussed in the light of recent works on soft glassy materials. Received 1 November 2002 and Received in final form 8 January 2003 / Published online: 1 April 2003 RID="a" ID="a"e-mail: salmon@crpp.u-bordeaux.fr     

Turbulent structures in an optimal Taylor–Couette flow between concentric counter-rotating cylinders

The turbulent structures formed in a Taylor–Couette (TC) flow established between two concentric counter-rotating cylinders were explored numerically. The shear Reynolds number was set to Re_shear = 8000 and the radius ratio was set to r_i/r_o = 0.5. An optimal flow corresponding to the maximal angular velocity transport between the cylinders was selected for the TC flow. The mean velocity profile reached its steepest value near the cylinders in the optimal TC flow. The streamwise velocity correlations at the outer cylinder in the gap exceeded those at the inner cylinder. The large convective transport of angular velocity in the gap generated a maximal angular velocity flux to achieve the optimal flow. The angular velocity flux generated by the momentum source exceeded that generated by the momentum sink. The vorticity dispersion was larger near the inner cylinder than near the outer cylinder, but vorticity stretching near the outer cylinder exceeded than that near the inner cylinder. The skin friction coefficient budgets were plotted using the velocity–vorticity correlation. The vortex stretching contributions dominated the skin friction budgets. The area near the inner cylinder was populated by stronger vortices, but their population density was smaller than the population density of the vortices near the outer cylinder. The probability density functions of the wall-normal and streamwise velocity fluctuations delineated the presence of the large wall-normal velocity fluctuations near the outer cylinder.     

Shear Stress in a Couette Flow of Liquid-Particle Suspensions

The mechanisms of momentum transfer and shear stress of liquid-particle suspensions in two-dimensional Couette flow are studied using direct numerical simulation by lattice-Boltzmann techniques. The results obtained display complex flow phenomena that arise from the two-phase nature of the fluid including a nonlinear velocity profile, layering of particles, and apparent slip near the solid walls. The general rheological behaviour of the suspension is dilatant. A detailed study of the various momentum transfer mechanisms that contribute to the total shear stress indicates that the observed shear thickening is related to enhanced relative solid phase stress for increasing shear rates.     

Observation and control of transverse energy-transport barrier due to the formation of an energetic-electron layer with sheared ExB flow

Off-axis electron-cyclotron heating in an axisymmetric barrier mirror produces a cylindrical layer with energetic electrons, which flow through the central cell and into the end region. The layer, producing a localized bumped ambipolar potential Phi(C), forms a strong shear of radial electric fields E(r) and peaked vorticity with the direction reversal of E(r)xB sheared flow near the Phi(C) peak. Intermittent vortexlike turbulent structures near the layer are suppressed in the central cell by this actively produced transverse energy-transport barrier; this results in T(e) and T(i) rises surrounded by the layer.     

Broad bandwidth optical and mechanical rheometry of wormlike micelle solutions

We characterize the linear viscoelastic shear properties of an aqueous wormlike micellar solution using diffusing wave spectroscopy (DWS) based tracer microrheology as well as various mechanical techniques such as rotational rheometry, oscillatory squeeze flow, and torsional resonance oscillation covering the frequency range from 10(-1) to 10(6) rad/s. Since DWS as well as mechanical oscillatory squeeze flow and torsional resonance oscillation cover a sufficiently high frequency range, the persistence length of wormlike micelles could be determined directly from rheological measurements for the first time.     

Nonlocal effects in flows of wormlike micellar solutions

The flow curve of wormlike micelles usually exhibits a stress plateau sigma* separating high and low viscosity branches, leading to shear-banded flows. We study the flow of semidilute wormlike micellar systems in a confined geometry: a straight microchannel. We characterize their local rheology thanks to particle image velocimetry. We show that flow curves cannot be described by a simple constitutive equation linking the local shear stress to the local shear rate. We demonstrate the existence of nonlocal effects in the flow of wormlike micellar systems and make use of a theoretical framework allowing the measurement of correlation lengths.     

Velocity profiles in shear-banding wormlike micelles

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 the complex, non-Newtonian nature of the flow in the highly sheared band.     

Shear-thinning-induced chaos in taylor-couette flow

The effect of weak shear thinning on the stability of the Taylor-Couette flow is explored for a Carreau-Bird fluid in the narrow-gap limit. The Galerkin projection method is used to derive a low-order dynamical system from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional nonlinear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the base (Couette) flow, becomes lower as the shear-thinning effect increases. That is, shear thinning tends to precipitate the onset of Taylor vortex flow. Similar to Newtonian fluids, there is an exchange of stability between the Couette and Taylor vortex flows, which coincides with the onset of a supercritical bifurcation. However, unlike the Newtonian model, the Taylor vortex cellular structure loses its stability in turn as the Taylor number reaches a critical value. At this point, a Hopf bifurcation emerges, which exists only for shear-thinning fluids.     

A minimal model for vorticity and gradient banding in complex fluids

A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress relation for the reactant and product species. Multivalued reaction terms allow for different homogeneous phases to coexist with each other, resulting in banded composition and shear rate profiles. The one-dimensional equation of motion is evolved from a random initial state to its final steady state. We find that the system chooses banded states over homogeneous states, depending on the shape of the stress constitutive curve and the magnitude of the diffusion coefficient. Banding in the flow gradient direction under shear rate control is observed for shear-thinning transitions, while banding in the vorticity direction under stress control is observed for shear-thickening transitions. Received 1 April 2001 and Received in final form 16 June 2001