Yann Bertho

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 e. Relevance of the results is discussed in relation with transport of visc...

Influence of confinement on granular penetration by impact.

We study experimentally the influence of confinement on the penetration depth of impacting spheres into a granular medium contained in a finite cylindrical vessel. The presence of close lateral walls reduces the penetration depth, and the characteristic distance for these lateral wall effects is found to be of the order of one sphere diameter. The influence of the bottom wall is found to have a much shorter range.

Dynamical Janssen effect on granular packing with moving walls.

Apparent mass (M(app)) measurements at the bottom of granular packings inside a vertical tube in relative motion are reported. They demonstrate that Janssens 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 M(app) 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.

Sphere penetration by impact in a granular medium: A collisional process

The penetration by a gravity-driven impact of a solid sphere into a granular medium is studied by two-dimensional simulations. The scaling laws observed experimentally for both the final penetration depth and the stopping time with the relevant physical parameters are here recovered numerically without the consideration of any microscopic solid friction but with dissipative collisions only. Dissipative collisional processes are thus found as essential in catching the penetration dynamics in granular matter whereas microscopic frictional processes can only be considered as secondary effects.

Powder flow down a vertical pipe: the effect of air flow

The dynamics of dry granular flows down a vertical glass pipe of small diameter have been studied experimentally. Simultaneous measurements of pressure proles, air and grain flow rates and volume fractions of particles have been realized together with spatio-temporal diagrams of the grain distribution down the tube. At large grain flow rates, one observes a stationary flow characterized by high particle velocities, low particle fractions and a downflow of air resulting in an underpressure in the upper part of the pipe. A simple model assuming a free fall of the particles slowed down by air friction and taking into account nite particle fraction eects through Richardson{ Zaki’s law has been developed: it reproduces pressure and particle fraction variations with distance and estimates friction forces with the wall. At lower flow rates, sequences of high-density plugs separated by low-density bubbles moving down at a constant velocity are observed. The pressure is larger than outside the tube and its gradient reflects closely the weight of the grains. Writing mass and momentum conservation equations for the air and for the grains allows one to estimate the wall friction, which is less than 10% of the weight for grains with a clean smooth surface but up to 30% for grains with a rougher surface. At lower flow rates, oscillating-wave regimes resulting in large pressure fluctuations are observed and their frequency is predicted.

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 nondeformable 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.

Local rheological measurements in the granular flow around an intruder.

The rheological properties of granular matter within a two-dimensional flow around a moving disk is investigated experimentally. Using a combination of photoelastic and standard tessellation techniques, the strain and stress tensors are estimated at the grain scale in the time-averaged flow field around a large disk pulled at constant velocity in an assembly of smaller disks. On the one hand, one observes inhomogeneous shear rate and strongly localized shear stress and pressure fields. On the other hand, a significant dilation rate, which has the same magnitude as the shear strain rate, is reported. Significant deviations are observed with local rheology that justify the need of searching for a nonlocal rheology.

Intermittent dry granular flow in a vertical pipe

The intermittent compact flow of glass beads in a vertical glass pipe of small diameter is studied experimentally by combining particle fraction, pressure, and air, and grain flow rates measurements with a spatiotemporal analysis of the flow. At the onset of the flow, a decompaction front is observed to propagate from the bottom to the top of the tube at a velocity much larger than that of the grains. The blockage front also propagates upward and at a still higher velocity. The decompaction induces a decreasing pressure wave strongly amplified as it propagates upward toward the top of the tube. Pressure variations of 3000 Pa or more are detected in this region while particle fraction variations are of the order of 0.02. Grain velocities during the flow period also increase strongly at the top of the tube while the corresponding fraction of total time decreases. A one-dimensional numerical model based on a simple relation between the effective acceleration of the grains and the particle fraction variations reproduces the amplification effect and provides predictions for its dependence on the permeability of the packing.

Influence of humidity on granular packings with moving walls

A significant dependence on the relative humidity H for the apparent mass (Mapp) measured at the bottom of a granular packing inside a vertical tube in relative motion is demonstrated experimentally. While the predictions of Janssens model are verified for all values of H investigated (25% ≤ H ≤ 80%), Mapp increases with time towards a limiting value at high relative humidities (H ≥ 60%), but remains constant at lower ones (H = 25%). The corresponding Janssen length λ is nearly independent of the tube velocity for H ≥ 60% but decreases markedly for H = 25%. Other differences are observed on the motion of individual beads in the packing: for H = 25%, they are almost motionless, while the mean particle fraction of the packing remains constant; for H ≥ 60% the bead motion is much more significant and the mean particle fraction decreases. The dependence of these results on the bead diameter and their interpretation in terms of the influence of capillary forces are discussed.

Penetration of a Projectile by Impact into a Granular Medium

When a solid sphere drops in a granular medium, an impact crater is created. The penetration of the projectile in the granular bed as a function of the impact energy is evaluated theoretically using a simple model including a friction law between the projectile and the grains, a viscous dissipation in the bed and a force from the collisions between the projectile and the granular material. This model is observed to be in agreement with our quasi-2D experimental results and suggests that the penetration depth is a power law of the total drop distance.