Flow phase diagrams for concentration-coupled shear banding

After surveying the experimental evidence for concentration coupling in the shear banding of wormlike micellar surfactant systems, we present flow phase diagrams spanned by shear stress Σ (or strain rate ) and concentration, calculated within the two-fluid, non-local Johnson-Segalman (d-JS-φ) model. We also give results for the macroscopic flow curves Σ(ˉ,ˉφ) for a range of (average) concentrations ˉφ. For any concentration that is high enough to give shear banding, the flow curve shows the usual non-analytic kink at the onset of banding, followed by a coexistence “plateau” that slopes upwards, dΣ/dˉ > 0. As the concentration is reduced, the width of the coexistence regime diminishes and eventually terminates at a non-equilibrium critical point [Σ_c,ˉφ_c,ˉ_c]. We outline the way in which the flow phase diagram can be reconstructed from a family of such flow curves, Σ(ˉ,ˉφ), measured for several different values of ˉφ. This reconstruction could be used to check new measurements of concentration differences between the coexisting bands. Our d-JS-φ model contains two different spatial gradient terms that describe the interface between the shear bands. The first is in the viscoelastic constitutive equation, with a characteristic (mesh) length l. The second is in the (generalised) Cahn-Hilliard equation, with the characteristic length ξ for equilibrium concentration-fluctuations. We show that the phase diagrams (and so also the flow curves) depend on the ratio r ≡ l /ξ, with loss of unique state selection at r = 0. We also give results for the full shear-banded profiles, and study the divergence of the interfacial width (relative to l and ξ) at the critical point. Received: 20 December 2002 / Accepted: 24 April 2003 / Published online: 11 June 2003 RID="a" ID="a"e-mail: physf@irc.leeds.ac.uk RID="b" ID="b"e-mail: p.d.olmsted@leeds.ac.uk     

Two-dimensional t-J model at moderate doping

Using the method which retains the rotation symmetry of spin components in the paramagnetic state and has no preset magnetic ordering, spectral and magnetic properties of the two-dimensional t-J model in the normal state are investigated for the ranges of hole concentrations 0 ⩽ x ⩽ 0.16 and temperatures 0.01t ⩽ T ⩽ 0.2t. The used hopping t and exchange J parameters of the model correspond to hole-doped cuprates. The obtained solutions are homogeneous which indicates that stripes and other types of phase separation are not connected with the strong electron correlations described by the model. A series of nearly equidistant maxima in the hole spectral function calculated for low T and x is connected with hole vibrations in the region of the perturbed short-range antiferromagnetic order. The hole spectrum has a pseudogap in the vicinity of (0,π) and (π, 0). For x ≈ 0.05 the shape of the hole Fermi surface is transformed from four small ellipses around (±π/2,±π/2) to two large rhombuses centered at (0, 0) and (π,π). The calculated temperature and concentration dependencies of the spin correlation length and the magnetic susceptibility are close to those observed in cuprate perovskites. These results offer explanations for the observed scaling of the static uniform susceptibility and for the changes in the spin-lattice relaxation and spin-echo decay rates in terms of the temperature and doping variations in the spin excitation spectrum of the model. Received 14 November 2002 Published online 1st April 2003 RID="a" ID="a"e-mail: alexei@fi.tartu.ee     

Viscosity minimum in bimodal concentrated suspensions under shear

We study a model of concentrated suspensions under shear in two dimensions. Interactions between suspended particles are dominated by direct-contact viscoelastic forces and the particles are neutrally bouyant. The bimodal suspensions consist of a variable proportion between large and small droplets, with a fixed global suspended fraction. Going beyond the assumptions of the classical theory of Farris (R.J. Farris, Trans. Soc. Rheol. 12, 281 (1968)), we discuss a shear viscosity minimum, as a function of the small-to-large-particle ratio, in shear geometries imposed by external body forces and boundaries. Within a linear-response scheme, we find the dependence of the viscosity minimum on the imposed shear and the microscopic drop friction parameters. We also discuss the viscosity minimum under dynamically imposed shear applied by boundaries. We find a reduction of macroscopic viscosity with the increase of the microscopic friction parameters that is understood using a simple two-drop model. Our simulation results are qualitatively consistent with recent experiments in concentrated bimodal emulsions with a highly viscous or rigid suspended component. Received 28 June 2002 RID="a" ID="a"e-mail: ernesto@pion.ivic.ve     

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     

An advected-field method for deformable entities under flow

We study dynamics of a deformable entity (such as a vesicles under hydrodynamical constraints). We show how the problem can be solved by means of Green's functions associated with the Stokes equations. A gauge-field invariant formulation makes the study of dynamics efficient. However, this procedure has its short-coming. For example, if the fluids are not Newtonian, then no Green's function is available in general. We introduce a new approach, the advected field one, which opens a new avenue of applications. For example, non-Newtonian entities can be handled without additional deal. In addition problems like budding, droplet break-up in suspensions, can naturally be treated without additional complication. We exemplify the method on vesicles filled by a fluid having a viscosity contrast with the external fluid, and submitted to a shear flow. We show that beyond a viscosity contrast (the internal fluid being more viscous), the vesicle undergoes a tumbling bifurcation, which has a saddle-node nature. This bifurcation is known for blood cells. Indeed red cells either align in a shear flow or tumble according to whether haematocrit concentration is high or low. Received 19 December 2001 / Received in final form 31 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: chaouqi.misbah@ujf-grenoble.fr     

Proton spin-lattice relaxation in aqueous ionic solutions

The proton spin-lattice relaxation time, T ₁, has been measured for aqueous solutions of sodium, potassium, rubidium and magnesium chlorides up to a concentration of about 4N at 25°c. The sodium and the magnesium chloride solutions were also measured at 60°c and 100°c. The variation of 1/T ₁ is not linear with concentration, at least above about ¼N, in contrast with previous reports [1, 2]. The behaviour depends markedly on the nature of the salt and on the temperature. It is shown that almost the whole of the variation of T ₁ as compared with that of water can be directly and simply related to the corresponding changes in the shear viscosity of the solutions. It is noted that the viscosity correction is better the higher the temperature of the solution.     

Dilational rheology of monolayers of a miscible polymer blend: From good- to poor-solvent conditions

The viscoelastic moduli (elasticity and dilational viscosity) of monolayers of PVAc + P4HS has been studied over a broad frequency range (0.1 mHz-200 kHz) using a combination of relaxation and capillary-waves techniques. The analysis of the surface pressure, the elasticity and the viscosity on the semidilute regime show that the air-water interface is a good solvent for the monolayers of PVAc-rich blends, and a poor (near-Θ) solvent for the monolayers of P4HS-rich blends. The solvent quality changes continuously over a broad concentration range. The results of viscoelastic moduli show that there is a broad relaxation process in the low-frequency range ( ω < 1 Hz). While for PVAc-rich monolayers this relaxation process follows the reptation-like behavior described by Noskov, for P4HS-rich monolayers the model does not describe the amplitudes of the different relaxation modes. For PVAc-rich monolayers two processes are clearly distinguished at higher frequencies: one centered at around 500 Hz and another one at around 40 kHz. However, for P4HS-rich monolayers only one broad relaxation mode is found below 1 kHz. The crossover from one type of behavior to the other one takes place in a very narrow blend-composition range, and is not clearly related to the crossover from good- to poor-solvent condition. Received 7 June 2002 and Received in final form 5 November 2002 RID="a" ID="a"Current address: Complex Fluids Lab., Cranbury Res. Ctr., Rhodia Inc., Cranbury, NJ 08512-7500, USA. RID="b" ID="b"e-mail: rgrubio@quim.ucm.es     

A biaxial nematic gel phase in aqueous vanadium pentoxide suspensions

Aqueous suspensions of V₂O₅ ribbons are one of the very few examples of mineral liquid crystals. In the concentrated regime, we show that these ribbons organize in a biaxial nematic gel phase. A Couette shear cell was used to produce a well oriented sample for in situ synchrotron X-ray scattering studies. We observed two perpendicular anisotropic sections of reciprocal space, which proves the biaxial symmetry of the nematic order. The thermodynamic and flow properties of the biaxial nematic are well described by hard-core theories. We suggest the use of a shear geometry to produce and investigate single domains of other biaxial nematics, reported but still questioned in the literature. Received 26 May 1999     

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     

Formation of adhesive contacts: Spreading versus dewetting

A soft bead (radius R _b) is pressed with a force F against a hydrophobic glass plate through a water drop (“wet” JKR set-up). We observe with a fast camera the growth of the contact zone bridging the rubber bead to the glass. Depending on the approach velocity V, two regimes are observed : i) at large V a liquid film is squeezed at the interface and dewets by nucleation and growth of a dry contact; ii) at low velocities, the bead remains nearly spherical. As it comes into contact, the rubber bead spreads on the glass with a characteristic time (in the range of one millisecond) τ ≈ ηR _b ²/F, where η is the liquid viscosity. The laws of spreading are interpreted by a balance of global mechanical and viscous forces. Received: 22 December 2002 / Accepted: 24 March 2003 / Published online: 29 April 2003 RID="a" ID="a"e-mail: brochard@curie.fr     

NMR study of the dissolution of laser-polarized xenon

NMR of laser-polarized xenon is used to probe the dissolution behaviour of the noble gas in different liquids. The dissolution and self-relaxation rates are extracted via a macroscopic model, and comparison of the decay rate of the xenon magnetization in deuterated and non-deuterated solvent pairs allows the determination of the pure dipole-dipole contribution to relaxation. A transient convective effect, tentatively assigned to the xenon concentration gradient, is observed and characterized by diffusion encoding MRI experiments. The flow of xenon penetrates inside the solvent near the walls of the NMR tube, the longitudinal images showing a “” shape, the transverse ones a “O” shape. This convection effect has implications for delivery conditions of laser-polarized xenon in continuous flow experiments and magnetic resonance imaging. Received 29 April 2002 / Received in final form 26 July 2002 Published online 22 October 2002 RID="a" ID="a"e-mail: hdesvaux@cea.fr RID="b" ID="b"URA CNRS/CEA 331     

Structure and rheology of concentrated wormlike micelles [4]at the shear-induced isotropic-to-nematic transition

We have investigated the simple shear flow behavior of wormlike micelles using small-angle neutron scattering and mechanical measurements. Ternary surfactant solutions made of cetylpyridinium chloride, hexanol and brine (0.2 M NaCl) and hereafter abbreviated as CPCl-Hex were studied in the concentrated regime, . In a preliminary report (Berret et al. [#!ref16!#]), the discontinuity of slope observed in the shear stress versus shear rate curve was interpreted in terms of first-order phase transition between an isotropic state and a shear-induced nematic state ( transition). At the transition rate, , the solution exhibits a macroscopic phase separation into viscous and fluid layers (inhomogeneous shear flow). Above a second characteristic shear rate, the flow becomes homogeneous again, the sheared solution being nematic only. The neutron patterns obtained in the two-state inhomogeneous region have been re-examined. Based on a consistent analysis of both orientational and translational degrees of freedom related to the wormlike micelles, we emphasize new features for the transition. In the present paper, the shear rate variations of the relative proportions of each phase in the two-state region, as well as the viscosity ratio between isotropic and nematic phases are derived. We demonstrate in addition that slightly above the transition rate, the shear induced nematic phase is already strongly oriented, with an order parameter P ₂ = 0.65. The orientational state is that of a nematic flow-oriented monodomain. Finally, from the locations of the neutron scattering maxima for each isotropic and nematic contributions, we evaluate the concentrations for each phase and and derived a dynamical phase diagram of CPCl-Hex, in terms of the stress versus and . According to the classification by Schmitt et al. [#!ref22!#], the transition observed in CPCl-Hex micellar solutions could result from a positive flow-concentration coupling, in agreement with the observed monotonically increasing shear stress in the two-phase region. Received: 16 February 1998 / Revised: 18 February 1998 / Accepted: 24 May 1998     

Hydromagnetic transverse instability of two highly viscous fluid-particle flows with finite ion Larmor radius corrections

A linear analysis of the combined effect of viscosity, finite ion Larmor radius and suspended particles on Kelvin-Helmholtz instability of two superposed incompressible fluids in the presence of a uniform magnetic field is carried out. The magnetic field is assumed to be transverse to the direction of streaming. A general dispersion relation for such a configuration has been obtained using appropriate boundary conditions. The stability analysis is discussed analytically, and the obtained results are numerically confirmed. Some special cases are recovered and corrected. The limiting cases of absence of suspended particles (or fluid velocities) and finite Larmor radius, absence of suspended particles are discussed in detail. In both cases, all other physical parameters are found to have stabilizing as well as destabilizing effects on the considered system. In the former case, the kinematic viscosity is found to has a stabilizing effect, while in the later case, the finite Larmor radius is found to has a stabilizing influence for a vortex sheet. It is shown also that both finite Larmor radius and kinematic viscosity stabilizations for interchange perturbations are similar to the stabilization effect due to a magnetic field for non-interchange perturbations. Received 13 January 2003 Published online 24 April 2003 RID="a" ID="a"Also at: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt. e-mail: m.elsayed@uaeu.ac.ae     

On N-wave type systems and their gauge equivalent

The class of nonlinear evolution equations (NLEE) - gauge equivalent to the N-wave equations related to the simple Lie algebra are derived and analyzed. They are written in terms of (x, t) ∈ satisfying r = rank nonlinear constraints. The corresponding Lax pairs and the time evolution of the scattering data are found. The Zakharov-Shabat dressing method is appropriately modified to construct their soliton solutions. Received 20 October 2001 / Received in final form 30 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg     

Method of group foliation and non-invariant solutions of partial differential equations

Using the heavenly equation as an example, we propose the method of group foliation as a tool for obtaining non-invariant solutions of PDEs with infinite-dimensional symmetry groups. The method involves the study of compatibility of the given equations with a differential constraint, which is automorphic under a specific symmetry subgroup and therefore selects exactly one orbit of solutions. By studying the integrability conditions of this automorphic system, i.e. the resolving equations, one can provide an explicit foliation of the entire solution manifold into separate orbits. The new important feature of the method is the extensive use of the operators of invariant differentiation for the derivation of the resolving equations and for obtaining their particular solutions. Applying this method we obtain exact analytical solutions of the heavenly equation, non-invariant under any subgroup of the symmetry group of the equation. Received 13 September 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: sheftel@gursey.gov.tr     

Microphase separation in weakly charged hydrophobic polyelectrolytes

Aqueous solutions of a well-defined poly(N-isopropylacrylamide-co-sodium 2-acrylamido-methylpropanesulfonate) (NIPAM/NaAMPS in a 95/5 molar ratio) have been investigated by means of small-angle neutron scattering (SANS) and rheological experiments as a function of temperature ( 25^° C T 60^° C) and polymer concentration ( 0.5wt% C 12wt%). The solutions remain optically transparent and isotropic over the whole temperature range, in contrast with the homopolyNIPAM which precipitates above its lower critical solution temperature (LCST = 32^° C). Upon addition of salt, the systems undergo a micro-macrophase separation. At temperatures above 45^° C, the SANS spectra exhibit a sharp peak at a scattering wave vector, q _max, which increases slightly with temperature. At high temperature ( T∼ 60^° C), the scattered intensity follows a power law I(q) ∼q ^-4 in the asymptotic regime, characteristic of two-density media with sharp interfaces, and q _max is found to vary with polymer concentration as q _max∼C ^0.22. Estimates of the typical sizes give values between 40 ? and 200 ?. These results provide a strong evidence of a thermally induced microphase separation, which is corroborated by the very sharp increases of the viscosity (over 2 decades) and of the stress relaxation time of the solutions, occurring in the temperature range where the scattering peak is observed. The results are discussed and compared with the theoretical models proposed for weakly charged polyelectrolytes in a poor solvent. Received 1 October 2001     

High-spin structure of the neutron-rich odd-odd 106, 108 45Rh and 110, 112 47Ag isotopes

The ^{106, 108}Rh and ^{110, 112}Ag nuclei have been produced as fission fragments following the fusion reaction ²⁸Si + ¹⁷⁶Yb at 145 MeV bombarding energy and studied with the Eurogam2 array. The yrast high-spin states of these four odd-odd nuclei, which are observed for the first time, consist of rotational bands in which the odd proton occupies the πg _9/2 subshell and the odd neutron the νh _11/2 subshell. Their behaviour as a function of spin values does not vary with the number of neutrons: as observed in the odd-N neighbouring nuclei, the motion of the odd neutron remains decoupled from the motion of the core, from N = 61 to N = 65. Moreover, the staggering observed in the yrast bands of odd-odd isotopes is strongly reduced as compared to the large values displayed by the rotational bands built on the πg _9/2 subshell in the odd-A Rh and Ag isotopes. The results of particle-rotor calculations indicate that this reduction is related to a change of the core deformation. Received: 1 June 2001 / Accepted: 23 July 2002 / Published online: 10 December 2002 RID="a" ID="a"e-mail: porquet@csnsm.in2p3.fr RID="b" ID="b"Present address: CSNSM IN2P3-CNRS and Université Paris-Sud 91405 Orsay, France. RID="c" ID="c"Present address: NAC, Faure, ZA 7131, South Africa. RID="d" ID="d"Present address: Department of Nuclear Physics, ANU, Canberra ACT 0200, Australia. Communicated by D. Schwalm     

Quasi-periodic and periodic solutions for dynamical systems related to Korteweg-de Vries equation

We consider quasi-periodic and periodic (cnoidal) wave solutions of a set of n-component dynamical systems related to Korteweg-de Vries equation. Quasi-periodic wave solutions for these systems are expressed in terms of Novikov polynomials. Periodic solutions in terms of Hermite polynomials and generalized Hermite polynomials for dynamical systems related to Korteweg-de Vries equation are found. Received 15 October 2001 / Received in final form 6 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: nakostov@ie.bas.bg     

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