Dependence of heat transport on the strength and shear rate of prescribed circulating flows

We study numerically the dependence of heat transport on the maximum velocity and shear rate of physical circulating flows, which are prescribed to have the key characteristics of the large-scale mean flow observed in turbulent convection. When the side-boundary thermal layer is thinner than the viscous boundary layer, the Nusselt number (Nu), which measures the heat transport, scales with the normalized shear rate to an exponent 1/3. On the other hand, when the side-boundary thermal layer is thicker, the dependence of Nu on the Peclet number, which measures the maximum velocity, or the normalized shear rate when the viscous boundary layer thickness is fixed, is generally not a power law. Scaling behavior is obtained only in an asymptotic regime. The relevance of our results to the problem of heat transport in turbulent convection is also discussed. Received 28 November 2001 Published online 25 June 2002     

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.     

Hydrodynamic screening of star polymers in shear flow

The mutual effects of the conformations of a star polymer in simple shear flow and the deformation of the solvent flow field are investigated by a hybrid mesoscale simulation technique. We characterize the flow field near the star polymer as a function of its functionality (arm number) f . A strong screening of the imposed flow is found inside the star polymer, which increases with increasing f . To elucidate the importance of hydrodynamic screening, we compare results for hydrodynamic and random solvents. The dependence of the polymer orientation angle on the Weissenberg number shows a power law behavior with super-universal exponent --independent of hydrodynamic and excluded-volume interactions. In contrast, the polymer rotation frequency changes qualitatively when hydrodynamic interactions are switched on.     

Flow birefringence and stress optical law of viscoelastic solutions of cationic surfactants and sodium salicylate

The optical and rheological properties of different viscoelastic solutions of surfactant are studied in order to gather experimental data used to calculate the value of the stress optical coefficient C. Three surfactants of the same family (CTAB) have been chosen; they differ by the length of the hydrocarbon chain; it concerns the dodecyltrimethylammonium bromide (C₁₅H₃₄BrN or DoTAB), the myristyltrimethylammonium bromide (C₁₇H₃₈BrN or MyTAB), and the hexadecyltrimethylammonium bromide (C₁₉H₄₂BrN or CTAB). Different parameters like the temperature of the solution and the salinity of the solvent have been made to vary. Flow birefringence experiments and rheological measurements are performed on these solutions in order to study the dependence of the extinction angle , of the birefringence intensity and of the shear stress with the shear rate . These data are used to check the stress optical law which turns out to be valid in a wide range of shear rates. The stress optical coefficient C is then computed: it is found to vary with the salinity of the solvent and the temperature of the solution for a given surfactant. Then, for all solutions of this work the variations of C are related to the variations of the polarizability anisotropy and the persistence length. Received: 18 February 1998 / Revised: 23 June 1998 / Accepted: 22 July 1998     

Undulation instability of lamellar phases under shear: A mechanism for onion formation?

We consider a lamellar phase of bilayer membranes held between two parallel plates and subject to a steady shear. Accounting for the coupling with the shear flow of the short wavelength undulation modes that are responsible for the membrane excess area, we argue that the flow generates an effective force which acts to reduce the excess area. From the viewpoint of the macroscopic lamellar whose geometric dimensions are fixed, this force translates into an effective lateral pressure. At low shear rates this pressure is balanced by the elastic restoring forces of the lamellar. Above a critical shear rate , where d is the interlayer distance and D is the gap spacing, the lamellar buckles into a harmonic shape modulation, and we predict its wavelength and amplitude . We show that our model is isomorphic to a dilative strain, which is known to induce a similar buckling (undulation) instability. Indeed, at threshold the wavelength is and is identical in both cases. Using a non-linear analysis, we discuss how the wavelength and amplitude vary with shear rate away from the threshold. For we find and . We then focus on the coupling of the buckling modulation itself with the flow, and obtain a criterion for the limit of its stability. Motivated by experiments of D. Roux and coworkers, we assume that at this limit of stability the lamellar breakups into “onion"-like, multilamellar, vesicles. The critical shear rate for the formation of onions is predicted to scale as . The scaling with d is consistent with available experimental data. Received 15 April 1998 and Received in final form 4 March 1999     

Correlation between the viscoelastic properties of a soft crystal and its microstructure

We investigate the rheological properties of a cubic fcc phase of micelles obtained by aggregation of a triblock copolymer (PEO)₁₂₇(PPO)₄₈(PEO)₁₂₇ in water as selective solvent. The resulting soft solid is submitted to a range of stresses varying from 20 to 800Pa in Couette geometry. Creep and flow behaviour can be distinguished and interpreted in terms of structural changes previously observed by SAXS under flow. Contrasting with other systems, no discontinuity in the flow behaviour is associated with the structural changes. The strong shear thinning is interpreted from the scattering data, as resulting from the nucleation of a new structure of hexagonal compact planes parallel to the Couette walls. This creates a lubricating domain in the gap, whose size grows with the applied shear rate. We argue moreover that the very existence of flow (as a steady state opposed to creep) is associated with this so-called layer-sliding structure in a fraction, however small, of the sample. Received on 4 June 1999 and Received in final form 6 September 1999     

Swelling kinetics of the onion phase

A theory is presented for the behavior of an array of multi-lamellar vesicles (the onion phase) upon addition of solvent. A unique feature of this system is the possibility to sustain pressure gradients by tension in the lamellae. Tension enables the onions to remain stable beyond the unbinding point of a flat lamellar stack. The model accounts for various concentration profiles and interfaces developing in the onion as it swells. In particular, densely packed “onion cores” are shown to appear, as observed in experiments. The formation of interfaces and onion cores may represent an unusual example of stabilization of curved interfaces in confined geometry. Received 6 September 2000     

Rheological behaviour and shear thickening exhibited by aqueous CTAB micellar solutions

In this experimental work we carefully investigate the rheological behaviour and in particular the shear thickening exhibited by aqueous micellar solutions of CTAB with NaSal as added counterion. We are particularly interested in the evolution of the critical shear rate (at which shear thickening occurs) versus C _D , the surfactant concentration. We show that , at fixed salt concentration C _S , increases with C _D following a power law evolution with a positive exponent of + 5.8. On the other hand we show that if the ratio C _D / C _S is fixed, decreases with C _D with a negative exponent of -2.0. Nevertheless investigations of the zero shear viscosity indicate that in all situations (implying variation of the surfactant concentration C _D , or the salt concentration C _S or the temperature) is a decreasing function of the length of the micelles. All these evolutions are compatible with a gelation mechanism which could possibly be associated with entanglement effects of large interacting flowing structures. Received: 3 March 1998 / Revised: 16 June 1998 / Accepted: 3 July 1998     

Shear banding instability in wormlike micellar solutions

Using NMR velocimetry and mechanical measurements we study the flow dynamics, within a cone-and-plate rheometer, of the wormlike micelle system, cetylpyridinium chloride/sodium salicylate (CPyCl/NaSal) at 100 mM/60 mM concentration in distilled water. Depending on precise conditions within the system, two classes of behaviour are observed, one in which the boundary between different shear rate phases fluctuates rapidly (on the order of tens of milliseconds) and one in which it migrates slowly with a time constant of many seconds. These modes of behaviour may depend on minor solution impurities, which presumably affect the detailed constitutive properties, but also on the externally applied shear rate within a given system. We argue that the slow migrations are governed by stress relaxation effects while the rapid migrations are flow driven and arise from interfacial instability. Received: 2 June 1998 / Received in final form and Accepted: 27 July 1998     

Universal properties of lamellar systems under weak shear

We have observed that different lamellar phases (thermotropic, lyotropic of surfactants or blockcopolymers) share the same rheological properties = A(T)σ^m, m = 1.67±0.1, independently of their chemical nature, in a range of shear rates , shear stresses σ, and temperatures T, where the flow is stationary. It is argued that the key phenomenon is the appearance of screw dislocations whose glide under an applied shear counterbalances plastically the applied vorticity, and stabilizes the layers, whose slip past each other is thus made more feasible. The theory, which makes use in other respects of the high-temperature creep model in solids, reproduces correctly the power law behavior and the values of A(T). Received 18 April 2001 and Received in final form 25 October 2001     

Understanding the sub-critical transition to turbulence in wall flows

In contrast with free shear flows presenting velocity profiles with inflection points which cascade to turbulence in a relatively mild way, wall bounded flows are deprived of (inertial) instability modes at low Reynolds numbers and become turbulent in a much wilder way, most often marked by the coexistence of laminar and turbulent domains at intermediate Reynolds numbers, well below the range where (viscous) instabilities can show up. There can even be no unstable mode at all, as for plane Couette flow (pCf) or for Poiseuille pipe flow (Ppf) that are currently the subject of intense research. Though the mechanisms involved in the transition to turbulence in wall flows are now better understood, statistical properties of the transition itself are yet unsatisfactorily assessed. A widely accepted interpretation rests on non-trivial solutions of the Navier-Stokes equations in the form of unstable travelling waves and on transient chaotic states associated to chaotic repellors. Whether these concepts typical of the theory of temporal chaos are really appropriate is yet unclear owing to the fact that, strictly speaking, they apply when confinement in physical space is effective while the physical systems considered are rather extended in at least one space direction, so that spatiotemporal behaviour cannot be ruled out in the transitional regime. The case of pCf will be examined in this perspective through numerical simulations of a model with reduced cross-stream (y) dependence, focusing on the in-plane (x, z) space dependence of a few velocity amplitudes. In the large aspect-ratio limit, the transition to turbulence takes place via spatiotemporal intermittency and we shall attempt to make a connection with the theory of first-order (thermodynamic) phase transitions, as suggested long ago by Pomeau.      

Refractive indices and thermo-optical properties of dye laser solvents

By measuring the wavelength tuning of a distributed feedback dye laser, solvent refractive-index changes as small as 0.0002 may be determined. This technique hence allows precise measurement of refractive-index dependence on temperature (dn/dT) and therefore enables the thermo-optical properties of solvents used in dye lasers to be assessed. In addition to single component solvents, the thermo-optical properties of solvent mixtures and additives are reported here. The refractive-index change with temperature (dn/dT) is related to solvent density change with temperature (dq/dT) through molecular polarizability.     

Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν² L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η^3/2(1 - η)^-7/4 R ^3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50 . These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity fluctuations are also provided. Received 7 June 2001 and Received in final form 7 December 2001     

The large amplitude oscillatory strain response of aqueous foam: Strain localization and full stress Fourier spectrum

The stochastic motion of a two-dimensional vesicle in linear shear flow is studied at finite temperature. In the limit of small deformations from a circle, Langevin-type equations of motion are derived, which are highly nonlinear due to the constraint of constant perimeter length. These equations are solved in the low-temperature limit and using a mean-field approach, in which the length constraint is satisfied only on average. The constraint imposes non-trivial correlations between the lowest deformation modes at low temperature. We also simulate a vesicle in a hydrodynamic solvent by using the multi-particle collision dynamics technique, both in the quasi-circular regime and for larger deformations, and compare the stationary deformation correlation functions and the time autocorrelation functions with theoretical predictions. Good agreement between theory and simulations is obtained.     

Slip elastography: a novel method for visualising and characterizing adherence between two surfaces in contact

Identification of the anatomical location and mechanical properties such as adherence at the tissue tumour interface may be of clinical benefit in determination of tumour resectability and prognosis. There are currently no imaging modalities in routine clinical practice that can provide this information. This paper presents the development of a new imaging technique based on ultrasound elastography, called slip elastography, for determination of the anatomical location and measurement of the adherence between two surfaces. The theoretical basis of slip and its definition in relation to shear are described. In vitro testing with gelatine phantoms to determine the optimal parameters for shear strain estimation and slip boundary measurement and to test reliability are also described.The results suggest that slip elastography can reliably identify the anatomical location of a slip boundary and can measure the externally applied axial force required to initiate slip at that boundary in vitro. The vector based shear strain estimator was the most robust and worked with minimal angular dependence with minimal non-slip shearing artefact.     

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     

Lattice-Boltzmann study of spontaneous emulsification

We study the dynamics of spontaneous emulsification of an initially planar oil-water interface when surfactants are added. The thermodynamic properties of the ternary oil-water-surfactant system are modeled by a Ginzburg-Landau-type free energy. The lattice Boltzmann method is used to solve the dynamic equations. The dynamics is found to be governed by a complicated interplay of convection and diffusion as the two relevant transport mechanisms. As long as the interface is almost flat, we find the interfacial area to grow first exponentially and then linearly in time. Later finger-like structures form which grow with a constant velocity. The tip velocity is found to increase roughly linearly with the mobility of the amphiphile, and to decrease as with the solvent viscosity . Received 5 January 1999     

Molecular origin and dynamic behavior of slip in sheared polymer films

The behavior of the slip length in thin polymer films subject to planar shear is investigated using molecular dynamics simulations. At low shear rates, the slip length extracted from the velocity profiles correlates well with that computed from a Green-Kubo analysis. Beyond chain lengths of about N=10, the molecular weight dependence of the slip length is dominated strongly by the bulk viscosity. The dynamical response of the slip length with increasing shear rate is well captured by a power law up to a critical value where the momentum transfer between wall and fluid reaches its maximum.     

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.     

On the boundary slip of fluid flow

For hundreds of years, in all the textbooks of classical fluid mechanics and lubrica- tion mechanics it is assumed that there was no wall slip (boundary slip) at a liquid-solid interface, i.e. no relative motion between liquid and solid at the interface. This is the no-slip boundary condition. It has been widely applied to engineering and experiments and to almost all the rheology or viscosity measurements of fluids. Rheology is one of the most important bases for fluid mechanics and lubricati…