Faraday instability with a polymer solution

We present an experimental study of the Faraday instability in which we compare the behavior of a Newtonian fluid (water-glycerine mixture) with that of a semi-dilute non-Newtonian solution of high molecular weight polymer. We show that although the dispersion relation of surface waves, derived for a layer of inviscid fluid, remains valid in that particular non-Newtonian case, the behavior of the instability threshold with frequency strongly differs from the Newtonian case. We explain this effect as a result of a frequency-dependent viscosity. The linear stability analysis of the non-Newtonian case shows a perfect agreement with the experimental results both for the dispersion relation and for the reduction of the instability threshold. We discuss the use of the characteristics of the Faraday experiment as a measurement tool to determine frequency dependent properties of non-Newtonian fluids. Received 5 January 1999     

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     

Aggregation of particles settling in shear-thinning fluids

We have experimentally studied the coaxial settling of three identical non-Brownian spheres in a shear-thinning fluid at small Reynolds numbers. While settling, the particles create corridors of reduced viscosity in their wake and, if they are initially close enough to one another, they can form stable clusters. By analogy with previous results obtained on two-particle interaction in the first part of this work, we show that the particle velocities can be satisfactorily described using a first-order expression and assuming that the reduced viscosity remains constant. We report systematic experiments performed at different initial separation distances between particles and the use of our simple model allows the prediction of the settling behaviour and in particular the conditions for clusters formation. We thus show that particle aggregation can occur even for large initial distances between particles and within times that are small compared to the time scales in Newtonian fluids. Received 10 July 2002 RID="a" ID="a"e-mail: talini@fast.u-psud.fr     

Echo tracer dispersion in flows of polymer solutions through porous media: A tool for detecting weak permeability heterogeneities?

Tracer dispersion in Newtonian and shear-thinning fluids (scleroglucan-water polymer solutions) flowing through single and double porosity grain packings has been studied experimentally using both classical transmission dispersion and echo dispersion (in the latter, the concentration variation front is pumped back through a detector at the inlet after penetrating for a chosen distance into the sample). Transmission dispersion increases markedly in both types of samples with the shear thinning index of the fluid at all Péclet numbers (except when molecular diffusion is dominant). Echo and transmission experiments give nearly identical dispersivity values for Newtonian fluids while echo dispersivity is lower than transmission for shear thinning ones. The normalized dispersivity difference has same order of magnitude for single and double porosity samples and increases with the shear thinning exponent α (by a factor of 2 between α = 0.35 and α = 0.60). This difference may be due to heterogeneities inducing permeability variations of small amplitude over distances of the order of the sample section : their influence on tracer dispersion is partly reversible with respect to a change of the flow direction and is only detectable if it is amplified by the shear-thinning properties of the fluid. Received 19 September 2001     

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     

Numerical simulation and experiments of a control method to suppress the Bénard von Kármán instability

We report both two-dimensional numerical simulations and experimental results that confirm the robustness of a new method for inhibiting vortex shedding associated to the Bénard-von Kármán (BvK) instability in the wake of a cylinder. Using the SIMPLER algorithm on a 2D channel, we solve the Navier-Stokes equations and we show that pressure suction at the front stagnation point of a circular cylinder, modelled here through a point sink located at the front stagnation point, can completely suppress the Bénard-von Kármán instability for super-critical Reynolds numbers. Comparison with recent experimental results are in close agreement. Received 7 March 2002 / Received in final form 12 September 2002 Published online 29 November 2002     

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     

Pulses of tunable size near a subcritical bifurcation

We show that a nonlinear gradient term can be used to tune the width of pulse-like solutions to a generalized quintic Ginzburg-Landau equation. We investigate the dynamics of these solutions and show that weakly turbulent patches can persist for long times. Analogies with turbulent spots in plane Couette flows are discussed. Received: 29 May 1997 / Revised: 16 March 1998 / Accepted: 30 April 1998     

Free cooling and inelastic collapse of granular gases in high dimensions

The connection between granular gases and sticky gases has recently been considered, leading to the conjecture that inelastic collapse is avoided for space dimensions higher than 4. We report Molecular Dynamics simulations of hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular medium is monitored throughout the cooling process. The behaviour is found to be very similar to that of a two-dimensional system, with a shearing-like instability of the velocity field and inelastic collapse when collisions are inelastic enough, showing that the connection with sticky gases needs to be revised. Received 17 April 2000 and Received in final form 7 June 2000     

A thin-film equation for viscoelastic liquids of Jeffreys type

We derive a novel thin-film equation for linear viscoelastic media describable by generalized Maxwell or Jeffreys models. As a first application of this equation we discuss the shape of a liquid rim near a dewetting front. Although the dynamics of the liquid is equivalent to that of a phenomenological model recently proposed by Herminghaus et al. (S. Herminghaus, R. Seemann, K. Jacobs, Phys. Rev. Lett. 89, 056101 (2002)), the liquid rim profile in our model always shows oscillatory behaviour, contrary to that obtained in the former. This difference in behaviour is attributed to a different treatment of slip in both models.     

Nonlinear dynamics of density waves in granular flows through narrow vertical channels

We study granular flows through narrow channels driven by gravity in the framework of the kinetic theory for dissipative dense gases. We derive equations of motion for quasi-one-dimensional systems. In a certain range of flow density, the steady homogeneous regime is found to be unstable against the formation of density waves. We show moreover that near the onset of the instability, the governing equation for the flow density is a mixture of the Korteweg-de-Vries equation, which leads to soliton, and the Bürger equation which exhibits spatio-temporal chaos. The competition between chaos and solitons may lead either to regular spatially ordered density waves or to chaotic dynamics. We argue that these two types of dynamics can be encountered experimentally according to the channel width and the dissipative properties of the granular media. Received: 11 March 1998 / Revised and Accepted: 3 July 1998     

Noise correlations in shear flows

We consider the effects of a shear on velocity fluctuations in a flow. The shear gives rise to a transient amplification that not only influences the amplitude of perturbations but also their time correlations. We show that, in the presence of white noise, time correlations of transversal velocity components are exponential and that correlations of the longitudinal components are exponential with an algebraic prefactor. Cross correlations between transversal and downstream components are strongly asymmetric and provide a clear indication of non-normal amplification. We suggest experimental tests of our predictions. Received 26 February 2002 / Received in final form 11 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: bruno.eckhardt@physik.uni-marburg.de RID="b" ID="b"Also at: Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India     

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     

Dynamics of spatio-temporal defects in the Taylor-Dean system

The dynamics of defects in a pattern of traveling inclined rolls has been investigated. Two regimes were identified in the neighborhood of defects: a diffusive regime, with a negative phase diffusion coefficient, and a coalescence regime in which the phase gradient diverges in time following a power law behavior. The observed periodic nucleation of defects is related to the frequency inhomogeneity induced by the disymmetry of the wave amplitude. Amplitude holes have been observed in the secondary modulated pattern. Received 23 February 1999 and Received in final form 26 May 1999     

Stripe patterns in the magnetic reorientation of a glass-forming nematic liquid crystal

We study spontaneous pattern formation in a glass-forming nematic liquid crystal during the magnetically induced dynamic Fréedericksz transition. Pattern growth rates and wavelengths as functions of the magnetic field are extracted from optical transmission textures of thin planar cells. The characteristics of the observed stripe pattern can be related to viscoelastic parameters of the nematic by means of a linear stability analysis of director fluctuation modes. The viscous properties of the material allow to vary the time scales of the experiment with temperature by orders of magnitude, leaving the spatial structure of the pattern essentially unchanged. We find that the ratios of shear and rotational viscosity coefficients relevant for the pattern wavelength selection remain constant in the temperature range investigated, whereas their absolute values change by almost two orders. Received 23 November 2001 and Received in final form 19 April 2002     

Hydrodynamic vector potentials

Solving the Navier-Stokes equation for incompressible fluids is greatly simplified by the solution of the vorticity equation. To accomplish this for three-dimensional flows requires vector potentials. These potentials are not only useful to take care of the incompressibility. Their modes are suitable also as test functions since the familiar Galerkin procedure does not work. The new method is checked by examples with known results and its relation to the classical approach with the stream function is clarified. The principle demonstration, however, concerns the transition to turbulence in plane shear flows. A simple layer of long rolls with axes parallel to the basic flow incites the transition. Received 20 August 2001     

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     

Lattice Boltzmann simulation of a binary fluid with different phase viscosities and its application to fingering in two dimensions

A thermodynamically consistent lattice Boltzmann scheme for simulating the flow of a binary fluid is extended to allow the fluid components to have different viscosities. The approach is tested for the shear and Poiseuille flow of layered immiscible fluids and for the dispersion relation and the damping of a capillary wave. We then consider the fingering that results when a fluid is displaced by a less viscous fluid in a two-dimensional channel. The finger widths obtained match the results of Reinelt and Saffman [#!Reinelt85!#], but differ somewhat from those of Halpern and Gaver [#!Halpern94!#] for capillary numbers above 2. A limiting finger width close to 1/2 is obtained for high capillary numbers and high viscosity ratios. Received 25 May 1999 and Received in final form 19 November 1999