Viscous fingering of miscible slices

Viscous fingering of a miscible high viscosity slice of fluid displaced by a lower viscosity fluid is studied in porous media by direct numerical simulations of Darcy's law coupled to the evolution equation for the concentration of a solute controlling the viscosity of miscible solutions. In contrast with fingering between two semi-infinite regions, fingering of finite slices is a transient phenomenon due to the decrease in time of the viscosity ratio across the interface induced by fingering and dispersion processes. We show that fingering contributes transiently to the broadening of the peak in time by increasing its variance. A quantitative analysis of the asymptotic contribution of fingering to this variance is conducted as a function of the four relevant parameters of the problem i.e. the log-mobility ratio R, the length of the slice l, the Peclet number Pe and the ratio between transverse and axial dispersion coefficients $\epsilon$. Relevance of the results is discussed in relation with transport of viscous samples in chromatographic columns and propagation of contaminants in porous media.Comment: 10 pages, 13 figure

Dense bubble flow in a silo: an unusual flow of a dispersed medium

The dense flow of air bubbles in a two-dimensional silo (through an aperture D) filled with a liquid is studied experimentally. A particle tracking technique has been used to bring out the main properties of the flow: displacements of the bubbles, transverse and axial velocities. The behavior of the air bubbles is observed to present similarities with non-deformable solid grains in a granular flow. Nevertheless, a correlation between the bubble velocities and their deformations has been evidenced. Moreover, a new discharge law (Beverloo-like) must be considered for such a system, where the flow rate is observed to vary as D^{1/2} and depends on the deformability of the particles.Comment: 5 pages, 6 figure

Dense granular flow around a penetrating object: Experiments and hydrodynamic model

We present in this Letter experimental results on the bidimensional flow field around a cylinder penetrating into dense granular matter together with drag force measurements. A hydrodynamic model based on extended kinetic theory for dense granular flow reproduces well the flow localization close to the cylinder and the corresponding scalings of the drag force, which is found to not depend on velocity, but linearly on the pressure and on the cylinder diameter and weakly on the grain size. Such a regime is found to be valid at a low enough "granular" Reynolds number.Comment: 5 pages, 4 figure

Stability of a granular layer on an inclined "fakir plane"

We present here experimental results on the effect of a forest of cylinder obstacles (nails) on the stability of a granular layer over a rough incline, in a so-called "fakir plane" configuration. The nail forest is found to increase the stability of the layer, the more for the densest array, and such an effect is recovered by a simple model taking into account the additional friction force exerted by the pillar forest onto the granular layer

Dynamical Janssen effect on granular packings with moving walls

Apparent mass measurements at the bottom of granular packings inside a vertical tube in relative motion are reported. They demonstrate that Janssen's model is valid over a broad range of velocities v. The variability of the measurements is lower than for static packings and the theoretical exponential increase of the apparent mass with the height of the packing is precisely followed (the corresponding characteristic screening length is of the order of the tube diameter). The limiting apparent mass at large heights is independent of v and significantly lower than the static value.Comment: 4 pages, 6 figures. accepted for publication in Phys. Rev. Lett. (2003

Downslope granular flow through a forest of obstacles

We investigate the effect of a forest of pillars on a granular layer steadily flowing over a rough inclined plane. We quantify experimentally how the steady flow rate of grains is affected by the inter-pillars distance for different layer thicknesses and slope angles. We then propose a model based on a depth-average approximation associated with $\mu(I)$ rheology that considers the additional force exerted by the pillars on the granular layer. This model succeeds in accounting for most of the observed results when taking into account some inertia due to the nonvanishing Froude number of the flow.Comment: 9 pages, 7 figure

Force de traînée dans un milieu granulaire ""chaud""

Nous étudions expérimentalement le déplacement à vitesse constante d'un disque intrus dans un empilement 2D dense de plus petits disques constituant un milieu granulaire modèle. Nous mesurons la force de traînée sur l'intrus, en variant sa vitesse et sa taille ainsi que la ""température"" du milieu par vibration. Deux régimes sont observés: à basse température (faibles vibrations), la force de traînée ne dépend pas de la vitesse de l'objet tandis qu'à haute température (fortes vibrations), la force de traînée présente une dépendance linéaire avec cette vitesse

Champ de vitesses et de contraintes autour d'intrus en mouvement dans un matériau granulaire

Nous étudions expérimentalement le déplacement horizontal à vitesse constante d’un objet dans une assemblée 2D dense de disques photoélastiques constituant un milieu granulaire modèle. Des études précédentes avaient permis de caractériser un écoulement similaire dans une géométrie verticale et sous gravité [1,2]. Dans cette nouvelle configuration, un capteur d’effort nous permet de mesurer la force exercée par les disques sur l’objet, pendant qu’une caméra enregistre à la fois la position des disques et le réseau des forces de contact entre ces disques. Des techniques de suivi de particules et des mesures optiques utilisant les propriétés de biréfringence des disques permettent d’obtenir les champs de vitesses des disques ainsi que les forces d’interaction. Le tenseur taux de déformation et le tenseur des contraintes peuvent alors être reconstruits localement par l’analyse des images. L’étude de ces tenseurs devrait apporter de nouveaux éléments pour mieux caractériser la rhéologie d’un matériau granulaire. [1] A. Seguin, Y. Bertho, P. Gondret and J. Crassous, Dense Granular Flow around a Penetrating Object: Experiment and Hydrodynamic Model, Phys. Rev. Lett. 107, 048001 (2011) [2] A. Seguin, Y. Bertho, F. Martinez, J. Crassous, and P. Gondret, Experimental velocity fields and forces for a cylinder penetrating into a granular medium, Phys. Rev. E 87, 012201 (2013