The flow of a very concentrated slurry in a parallel-plate device: influence of gravity

We investigate, both experimentally and theoretically, the fow and structure of a slurry when sheared between 2 horizontal plates. The slurry, otherwise called a "wet granular material", is made of non-Brownian particles immersed in a viscous fluid. The particles are heavier than the fluid, consequently, gravity influences the structure and flow profiles of the sheared material. Experiments are carried out in a plane Couette device, with a model slurry composed of approximately monodisperse spherical PMMA particles in oil, at high average solid concentration (about 58%). Optical observation reveals a typical 2-phase configuration, with a fluidized layer in contact with the upper plate and on top of an amorphous solid phase. We provide data on velocity profiles, wall-slip and shear stress versus the average shear rate. To interpret the data, we propose a model for the ideal case of infinite horizontal flat plates. The model, of mean field type, is based on local constitutive equations for the tangential and normal components of the stress tensor and on expressions relating the material viscometric coefficients (the shear viscosity eta and the normal viscosity psi) with the local concentration (phi) and the local shear rate. 1-,2- and 3-phase configurations are predicted, with non linear flow and concentration profiles. We conclude that the model equations correctly describe the experimental data, provided that appropriate forms are chosen for the divergence of eta and psi near the packing concentration (phi_max), namely a (phi_max-phi)^-1 singularity.Comment: 26 pages, 12 figures ; submitted to Physics of Fluid

Measurement of the Crab Flux Above 60 GeV with the CELESTE Cherenkov Telescope

We have converted the former solar electrical plant THEMIS (French Pyrenees) into an atmospheric Cherenkov detector called CELESTE, which records gamma rays above 30 GeV (7E24 Hz). Here we present the first sub-100 GeV detection by a ground based telescope of a gamma ray source, the Crab nebula, in the energy region between satellite measurements and imaging atmospheric Cherenkov telescopes. At our analysis threshold energy of 60 +/- 20 GeV we measure a gamma ray rate of 6.1 +/- 0.8 per minute. Allowing for 30% systematic uncertainties and a 30% error on the energy scale yields an integral gamma ray flux of I(E>60 GeV) = 6.2^{+5.3}_{-2.3} E-6 photons m^-2 s^-1. The analysis methods used to obtain the gamma ray signal from the raw data are detailed. In addition, we determine the upper limit for pulsed emission to be <12% of the Crab flux at the 99% confidence level, in the same energy range. Our result indicates that if the power law observed by EGRET is attenuated by a cutoff of form e^{-E/E_0} then E_0 < 26 GeV. This is the lowest energy probed by a Cherenkov detector and leaves only a narrow range unexplored beyond the energy range studied by EGRET.Comment: 34 pages, accepted by the Astrophysical Journa

Rheology and Structure of Concentrated Suspensions of Hard Spheres. Shear Induced Particle Migration

The apparent shear viscosity, in the non-Brownian limit, for a homogeneous suspension of monodispersed hard spheres in systems ranging from dilute to concentrated was previously established. From an estimation of the viscous dissipation. We use the inter-particle distance dependence of the shear viscosity for determining the components of a local stress tensor associated with the transient network of particles for the volume fraction above the percolation threshold. For this purpose, we develop a model based on lubrication forces between colliding particles for coupling the particle stress tensor to the stress tensor of the suspension considered as an effective medium. In the case of non-uniform flows with low shear rate regions, it is necessary to introduce a non-local stress tensor since the stress can be directly transmitted by the network of particles over a correlation length larger than the particle diameter. This approach shows ...A partir d'une estimation de la dissipation visqueuse, nous avons précedemment évalué la viscosité apparente de cisaillement des suspensions homogènes de sphères dures monodisperses et non Browniennes dans les systèmes dilués ou concentrés. Nos utilisons la dépendance de la viscosité de cisaillement avec la distance moyenne entre les particules pour déterminer les composantes d'un tenseur local de contraintes associé à l'amas transitoire de particlues au dessus de la fraction volumique critique de percolation. Nous developpons pour cela un modèle basé sur les forces de lubrification s'exerçant au cours des collisions entre les particules afin de coupler le tenseur local de contraintes associé aux particules et le tenseur des contraintes dans la suspension assimilée à un milieu effectif. Dans le cas des écoulements non uniformes présentant des zones de faible cisaillement, il est nécessaire de considérer un tenseur non local des contraintes car les forces peuvent alors se transmettre directement à travers l'amas de particules sur une longueur de corrélation supérieure au diamètre des particules. Cette approche montre que la migration des particules dans un écoulement est induite par les variations spatiales de la contrainte tangentielle. Les prévisions du modèle relatives aux profils de concentrations en particules dans un écoulement de Couette ou dans un écoulement de Poiseuille plan sont en bon accord avec les données expérimentales de la littérature

I. Rheology of Weakly Flocculated Suspensions of Rigid Particles

A rheological law for hard spheres in purely hydrodynamic interaction is used to describe the steady state viscosity of weakly aggregated suspensions of rigid particles. The shear viscosity only involves the volume fraction and the maximum packing concentration of particles. Particle aggregation influences the parameters of the reference viscosity law. Within the framework of fractal aggregation, we introduce the volume fraction of aggregates and we derive the equilibrium mean radius of clusters from an effective medium approximation. The proposed rheological equation is close to the phenomenological Casson equation for soft clusters of fractal dimensionality $D=2$. In a second part, we present rheo-optical experiments for studying the break-up of red cell aggregates in a shear flow and for determining the critical disaggregation shear stress of the flowing suspension mainly representative of the surface adhesive energy between particles. The proposed microrheological model well describes viscometric data in the low shear regime and allows information about the shear induced restructuration and the lifetime of clusters.Nous utilisons une loi de viscosité pour des suspensions concentrées de sphères dures en interaction purement hydrodynamique pour décrire le comportement rhéologique des suspensions faiblement agrégées de particules rigides. La viscosité de cisaillement fait intervenir la fraction volumique et la concentration d'empilement des particules. La floculation des particules modifie les paramètres de la loi rhéologique. Dans le cadre de structures fractales, nous introduisons la fraction volumique effective des agrégats et nous déterminons la taille de d'équilibre des amas à partir d'une hypothèse de milieu effectif. La loi de viscosité se rapproche de la loi phénoménologique de Casson pour des aggrégats mous de dimension fractale $D=2$. Dans une seconde partie, nous présentons des expériences de réflectométrie sous cisaillement pour étudier la rupture des agrégats de globules rouges dans un écoulement et estimer la contrainte critique de désagrégation de la suspension représentative de l'énergie d'adhésion des particules. Le modèle rhéologique décrit les expériences de viscosimétrie à faible cisaillement et renseigne sur la restructuration des agrégats en écoulement et sur le temps de vie des amas réversibles

Settling and fluidization of non Brownian hard spheres in a viscous liquid

A mean field approach is used to estimate the energy dissipation during the homogeneous sedimentation or the particulate fluidization of non Brownian hard spheres in a concentrated suspension of infinite extent. Depending on inertial screening and the range of the hydrodynamic interactions, the effective buoyancy force is determined either from the average suspension density in a Stokes flow or from the fluid density in the turbulent flow regime. An energy balance then yields a settling or fluidization law depending on the particle Reynolds number in reasonable agreement with the Richardson and Zaki correlation and recent experimental results for particle settling or fluidization. We further estimate the energy dissipation in the turbulent boundary layers around the particles to precise the Reynolds number dependence of the hindered settling function in the intermediate flow regime

II. Rheology of Weakly Flocculated Suspensions of Viscoelastic Particles

A microrheological model is proposed to estimate the steady state shear viscosity of concentrated suspensions of viscoelastic particles. We first present a Kelvin Voigt model to describe the deformation and stable orientation of a viscoelastic particle in a simple shear field. We then use a viscosity law for concentrated suspensions of hard particles in purely hydrodynamic interactions and we relate the maximum packing concentration to the component of the particle deformation tensor in the direction of the flow. We analyse the steady state viscometric behavior of red cell suspensions in saline solution and we show the influence of the nonlinear viscoelectric properties of the cell membrane. In a second part, we consider a flocculation of deformable particles and we deduce a viscosity law taking into account both the aggregation phenomena and the deformation-orientation of particles in the shear field. The rheological law describes the viscosity behavior of aggregated deformable red cells in dextran saline solution only for negligible shear induced restructuration of the aggregates.Nous proposons un modèle microrhéologique pour estimer la viscosité de cisaillement des suspensions concentrées de particules viscoélastiques. Dans un premier temps, nous présentons un modèle de Kelvin Voigt tournant afin de décrire la déformation et l'orientation stable d'une particule de viscoélastique dans un écoulement de cisaillement simple. Nous utilisons alors une loi de viscosité valable pour des suspensions concentrées de sphères dures en interaction purement hydrodynamique et nous relions la concentration maximale d'empilement à la composante du tenseur de déformation des particules dans la direction de l'écoulement. Nous analysons ensuite le comportement rhéologique des suspensions de globules rouges et nous montrons le rôle des propriétés viscoélastiques non linéaires de la membrane cellulaire. Dans une seconde partie, nous introduisons une floculation des particules viscoélastiques et déduisons une loi de viscosité prenant en compte les phénoménes de floculation et de déformation des particules dans le champ de cisaillement. La loi rhéologique proposée décrit la rhéologie des suspensions de globules rouges aggrégés en présence de dextrane dans la mesure où nous pouvons négliger les phénomènes de restructuration des aggrégats sous l'action des contraintes hydrodynamiques

Multiple light scattering in random systems: Analysis of the backscattering spot image

This study concerns the multiple scattering of light in random granular systems and the analysis of the image formed by the light scattered by a random medium. We developed an imagery method with high grey level resolution for visualization and analysis of the intensity profile in the backscattering spot image. We further present statistical models for the radiative transfer in granular media only involving the photon mean path length, the asymmetry factor and the absorption probability of photons. A renormalization of the photon trajectory in the medium gives a photon transport equation for anisotropic scattering and leads to an analytical expression for the intensity profile in the backscattering spot. We finally compare the results from imagery experiments with the predictions from numerical simulations and statistical models

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 $\rm (43 mPa s - 800 mPa s)$ 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