A dynamic study of onion phases under shear flow: size changes

It has been shown that lyotropic lamellar phases under shear flow form structures corresponding to a close packed assembly of monodisperse multilamellar vesicles (onions). The size, which is fixed by the shear rate, can vary from a few microns to a tenth of a micron. In this study, we investigate for the first time the transient behaviour of size changes of onions under shear flow by means of small angle light scattering, direct microscopic observations, and conductivity measurements. We evidence two regimes: continuous and discontinuous. The nature of which (continuous or discontinuous) depends on the initial and final shear rate, and can be described by a dynamic phase diagram. Received: 14 November 1997 / Received in final form: 2 March 1998 / Accepted: 9 March 1998     

A Monte-Carlo study of equilibrium polymers in a shear flow

We use an off-lattice microscopic model for solutions of equilibrium polymers (EP) in a lamellar shear flow generated by means of a self-consistent external field between parallel hard walls. The individual conformations of the chains are found to elongate in flow direction and shrink perpendicular to it while the average polymer length decreases with increasing shear rate. The Molecular Weight Distribution of the chain lengths retains largely its exponential form in dense solutions whereas in dilute solutions it changes from a power-exponential Schwartz distribution to a purely exponential one upon an increase of the shear rate. With growing shear rate the system becomes increasingly inhomogeneous so that a characteristic variation of the total monomer density, the diffusion coefficient, and the center-of-mass distribution of polymer chains of different contour length with the velocity of flow is observed. At higher temperature, as the average chain length decreases significantly, the system is shown to undergo an order-disorder transition into a state of nematic liquid crystalline order with an easy direction parallel to the hard walls. The influence of shear flow on this state is briefly examined. Received 22 October 1998 and Received in final form 12 April 1999     

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     

Towards lowering dissipation bounds for turbulent flows

We examine the background flow variational principle for calculating bounds on the energy dissipation rate in turbulent shear flow, and suggest to select this principle's test functions such that they comply with the small-scale smoothness of real turbulent velocity fields. A self-consistent algorithm implementing this requirement then yields an upper bound on the dimensionless dissipation coefficient which shows a weak power-law decrease at high Reynolds numbers, instead of approaching a nonzero constant, as it did in previous estimates. Received 26 October 1998     

Identification of flow mechanisms for a soft crystal

We study the behavior under flow of soft spherical micelles forming a fcc phase at high volume fraction. Due to the size (300 ?) of the elementary objects, the structure can be investigated through X-rays and neutron scattering, at rest and under flow in a Couette cell. Using scattering in two perpendicular directions, different mechanisms of flow are identified. At intermediate shear (around 100 s^-1) the system exhibits the so called layer sliding mechanism where two dimensional hexagonal compact planes of spheres align themselves with the Couette cell walls. At lower shear rate, the fcc structure is locally preserved, and the flow is mediated by defects between crystallites. At high shear rate, we observe the melting of the structure and a liquid-like structure factor. Moreover, we were able to use the existence of the layer sliding regime to generate a fcc monocrystal by annealing the satcking faults between the decorrelated planes created by the layer sliding. Received: 7 July 1997 / Received in final form: 16 January 1998 / Accepted: 5 March 1998     

Fluid membranes in hydrodynamic flow fields: Formalism and an application to fluctuating quasispherical vesicles in shear flow

The dynamics of a single fluid bilayer membrane in an external hydrodynamic flow field is considered. The deterministic equation of motion for the configuration is derived taking into account both viscous dissipation in the surrounding liquid and local incompressibility of the membrane. For quasi-spherical vesicles in shear flow, thermal fluctuations can be incorporated in a Langevin-type equation of motion for the deformation amplitudes. The solution to this equation shows an overdamped oscillatory approach to a stationary tanktreading shape. Inclination angle and ellipticity of the contour are determined as a function of excess area and shear rate. Comparisons to numerical results and experiments are discussed. Received 20 August 1998     

II. Recirculation flow induced by a bubble stream rising in a viscous liquid

The recirculation flow induced by the rising motion of a bubble stream in a viscous fluid within an open-top rectangular enclosure is studied. The three-dimensional volume averaged conservation equations are solved by a control-volume method using a hybrid finite differencing scheme to describe the liquid phase hydrodynamics. The momentum exhange between the bubbles and the liquid phase is modeled with a source term equals to the volumetric buoyancy force acting on the gas in the bubble stream. The volumetric buoyancy force accounts for in line interactions between bubbles through the average gas volume fraction in the gas liquid column which depends on the size and the rising velocity of bubbles. The fluid flow within an open-top rectangular enclosure is further investigated by particle image velocimetry for a bubble stream rising in a water-glycerol solution. The measured fluid velocities in a vertical plane are compared with the predictions of the numerical model over a wide range of fluid viscosity (43 mPa s-800 mPa s) and gas flow rates. Finally, the recirculation flows resulting from the interaction of two neighbouring vertical bubble streams are studied. Received: 23 July 1997 / Revised: 19 December 1997 / Accepted: 11 May 1998     

Change of the scaling behavior of the end-to-end square distance in a two-dimensional polydisperse system

The simulation of a two-dimensional, broadly polydisperse, living polymers system at high concentration reveals an unusual conformational behaviour for the longer chains. Unlike in three dimensions, the longer chains are not swollen but are squeezed by the smaller chains. This observation is discussed in terms of a two dimensional solvent- polymer mixture whose solvent particules are larger than the polymer monomers. Received: 13 December 1996 / Revised: 16 March 1998 / Accepted: 27 March 1998     

Asymptotic analysis of wall modes in a flexible tube

The stability of wall modes in a flexible tube of radius R surrounded by a viscoelastic material in the region R < r < H R in the high Reynolds number limit is studied using asymptotic techniques. The fluid is a Newtonian fluid, while the wall material is modeled as an incompressible visco-elastic solid. In the limit of high Reynolds number, the vorticity of the wall modes is confined to a region of thickness in the fluid near the wall of the tube, where the small parameter , and the Reynolds number is , and are the fluid density and viscosity, and V is the maximum fluid velocity. The regime is considered in the asymptotic analysis, where G is the shear modulus of the wall material. In this limit, the ratio of the normal stress and normal displacement in the wall, , is only a function of H and scaled wave number . There are multiple solutions for the growth rate which depend on the parameter .In the limit , which is equivalent to using a zero normal stress boundary condition for the fluid, all the roots have negative real parts, indicating that the wall modes are stable. In the limit , which corresponds to the flow in a rigid tube, the stable roots of previous studies on the flow in a rigid tube are recovered. In addition, there is one root in the limit which does not reduce to any of the rigid tube solutions determined previously. The decay rate of this solution decreases proportional to in the limit , and the frequency increases proportional to . Received: 5 November 1997 / Revised: 10 March 1998 / Accepted: 29 April 1998     

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     

Tracer dispersion in power law fluids flow through porous media: Evidence of a cross-over from a logarithmic to a power law behaviour

An analytical model is presented to describe the dispersion of tracers in a power-law fluid flowing through a statistically homogeneous and isotropic porous medium. The model is an extension of Saffman's approach to the case of non-Newtonian fluids. It is shown that an effective viscosity depending on the pressure gradient and on the characteristics of the fluid, must be introduced to satisfy Darcy's law. An analytical expression of the longitudinal dispersivity is given as a function of the Peclet number Pe and of the power-law index n that characterizes the dependence of the viscosity on the shear rate . As the flow velocity increases the dispersivity obeys an asymptotic power law: . This asymptotic regime is achieved at moderate Peclet numbers with strongly non-Newtonian fluids and on the contrary at very large values when n goes to 1 ( for n=0.9). This reflects the cross-over from a scaling behaviour for towards a logarithmic behaviour predicted for Newtonian fluids (n=1). Received: 22 July 1997 / Revised and Accepted: 2 July 1998     

I. Formation and rise of a bubble stream in a viscous liquid

The continuous emission of gas bubbles from a single ejection orifice immersed in a viscous fluid is considered. We first present a semi empirical model of spherical bubble growth under constant flow conditions to predict the bubble volume at the detachment stage. In a second part, we propose a physical model to describe the rise velocity of in-line interacting bubbles and we derive an expression for the net viscous force acting on the surrounding fluid. Experimental results for air/water-glycerol systems are presented for a wide range of fluid viscosity and compared with theoretical predictions. An imagery technique was used to determine the bubble size and rise velocity. The effects of fluid viscosity, gas flow rate, orifice diameter and liquid depth on the bubble stream dynamic were analyzed. We have further studied the effect of large scale recirculation flow and the influence of a neighbouring bubble stream on the bubble growth and rising velocity. Received: 23 July 1997 / Revised: 16 December 1997 / Accepted: 11 May 1998     

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     

Compression induced phase transitions in PEO brushes: the n-cluster model

The compression of brushes of terminally anchored chain within the de Gennes n-cluster model is analysed. This model was developed for Poly(ethylene oxide) in water but may apply to other systems. Brushes described by this model exhibit discontinuous concentration profile associated with the coexistence of an inner dense “phase” and an outer, dilute, one. The compression induces growth of the dense, weakly compressible region. This, in turn, gives rise to distinctive force profiles associated with changes of slope. When the dilute region disappears, the compression of two brushes can give rise to a transient attraction. Received: 4 November 1997 / Revised: 29 January 1998 / Accepted: 24 March 1998     

Nonperturbative renormalization group approach to turbulence

We suggest a new, renormalization group (RG) based, nonperturbative method for treating the intermittency problem of fully developed turbulence which also includes the effects of a finite boundary of the turbulent flow. The key idea is not to try to construct an elimination procedure based on some assumed statistical distribution, but to make an ansatz for possible RG transformations and to pose constraints upon those, which guarantee the invariance of the nonlinear term in the Navier-Stokes equation, the invariance of the energy dissipation, and other basic properties of the velocity field. The role of length scales is taken to be inverse to that in the theory of critical phenomena; thus possible intermittency corrections are connected with the outer length scale. Depending on the specific type of flow, we find different sets of admissible transformations with distinct scaling behaviour: for the often considered infinite, isotropic, and homogeneous system K41 scaling is enforced, but for the more realistic plane Couette geometry no restrictions on intermittency exponents were obtained so far. Received: 28 December 1997 / Accepted: 6 August 1998     

Depinning of a domain wall in the 2d random-field Ising model

We report studies of the behaviour of a single driven domain wall in the 2-dimensional non-equilibrium zero temperature random-field Ising model, closely above the depinning threshold. It is found that even for very weak disorder, the domain wall moves through the system in percolative fashion. At depinning, the fraction of spins that are flipped by the proceeding avalanche vanishes with the same exponent as the infinite percolation cluster in percolation theory. With decreasing disorder strength, however, the size of the critical region decreases. Our numerical simulation data appear to reflect a crossover behaviour to an exponent at zero disorder strength. The conclusions of this paper strongly rely on analytical arguments. A scaling theory in terms of the disorder strength and the magnetic field is presented that gives the values of all critical exponent except for one, the value of which is estimated from scaling arguments. Received: 13 February 1998 / Accepted: 30 March 1998     

Modeling film flows down inclined planes

A new model of film flow down an inclined plane is derived by a method combining results of the classical long wavelength expansion to a weighted-residuals technique. It can be expressed as a set of three coupled evolution equations for three slowly varying fields, the thickness h, the flow-rate q, and a new variable that measures the departure of the wall shear from the shear predicted by a parabolic velocity profile. Results of a preliminary study are in good agreement with theoretical asymptotic properties close to the instability threshold, laboratory experiments beyond threshold and numerical simulations of the full Navier-Stokes equations. Received: 16 April 1998 / Revised: 29 June 1998 / Accepted: 2 July 1998     

Chain radius dependence on concentration in a 2D living polymer system

A living polymer system is used to study the effect of concentration on a broad, polydisperse two-dimensional polymer system. It is found that the mean squared end-to-end radius of a chain of L monomers does not decrease by following a simple power law of the concentration but by a function of the form . An origin for such a behaviour is proposed. Received: 21 November 1997 / Received in final form: 21 April 1998 / Accepted: 24 April 1998     

Kinematic segregation of granular mixtures in sandpiles

We study the segregation of granular mixtures in two-dimensional silos using a recently proposed set of coupled equations for surface flows of grains. We study the thick flow regime, where the grains are segregated in the rolling phase. We incorporate this dynamical segregation process, called kinematic sieving, free-surface segregation or percolation, into the theoretical formalism and calculate the profiles of the rolling species and the concentration of grains in the bulk in the steady state. Our solution shows the segregation of the mixture with the large grains being found at the bottom of the pile in qualitative agreement with experiments. Received: 6 July 1998 / Revised and Accepted: 13 August 1998