We investigate experimentally the bouncing motion of solid spheres onto a solid plate in an ambient fluid which is either a gas or a liquid. In particular, we measure the coefficient of restitution e as a function of the Stokes number, St, ratio of the particle inertia to the viscous forces. The coefficient e is zero at small St, increases monotonically with St above the critical value Stc and reaches an asymptotic value at high St corresponding to the classical “dry” value emax measured in air or vacuum. This behavior is observed for a large range of materials and a master curve e/emax=f(St) is obtained. If gravity is sufficient to describe the rebound trajectory (after the collision) in a gas, this is not the case in a liquid where drag and added-mass effect are important but not sufficient: History forces are shown to be non-negligible even at large Reynolds number.

Three regimes of granular avalanches in fluids are put in light depending on the Stokes number St which prescribes the relative importance of grain inertia and fluid viscous effects, and on the grain/fluid density ratio r. In gas (r ≫ 1 and St > 1, e.g., the dry case), the amplitude and time duration of avalanches do not depend on any fluid effect. In liquids (r ∼ 1), for decreasing St, the amplitude decreases and the time duration increases, exploring an inertial regime and a viscous regime. These regimes are described by the analysis of the elementary motion of one grain. Granular matter has received much attention from physicists over the past few years [1]. Beyond the fundamental interest in the physics of granular systems which can present some features of either solids, liquids or even gases, the understanding of granular materials is essential in many industrial activities such as pharmacology, chemical engineering, food, agriculture, and so on. Many studies concern the avalanches that may arise on the slope of a granular pile in air. Such granular avalanches occur in various places in Nature, from small scale, as for the building of any sand pile, to large scale, as the event observed after the Mont St-Helen eruption in 1980. Two angles can be defined when building a pile: the maximum angle of stability θ m at which an avalanche starts and the angle of repose θ r at which the avalanche stops. Between these two angles is a region of bistability where the grains can either be flowing ("liquid state") or at rest ("solid state"). Many experiments performed with dry grains in a rotating cylinder [2,3,4,5,6] showed clearly the existence of these two angles.To date, no detailed study has focused on the influence of the interstitial fluid for a totally immersed grain assembly. This influence is certainly important in granular avalanche processes, as evidenced by the marked differences observed by geologists between subaqueous and eolian cross strata [7]. As a matter of fact, the propagation of subaqueous dunes differs in general from the propagation of eolian dunes even if the slope angles are quite similar: When the transport rate of sand particles is large enough, the flow is continuous in the lee side of the structure in the immersed case, but occurs by successive avalanches in the dry case [7]. This observation prompted geologists to accumulate data on avalanches of sand or beads in rotating drums filled with air or water [8] or even with glycerol mixtures [9], that seemed to show that the amplitude of avalanches decreases and the time duration increases with the fluid viscosity. We have performed an extensive series of experiments to investigate the influence of the interstitial fluid on the packing stability and the avalanche dynamics. The analysis of our results obtained with a rotating drum set-up indicate the existence of three regimes: (i) a free-fall regime for which there is no fluid influence and that corresponds to the classical dry regime, and two regimes where the interstitial fluid governs the a...

We study experimentally the parallel flow in a Hele-Shaw cell of two immiscible fluids, a gas and a viscous liquid, driven by a given pressure gradient. We observe that the interface is destabilized above a critical value of the gas flow and that waves grow and propagate along the cell. The experimental threshold corresponds to a velocity difference of the two fluids in good agreement with the inviscid Kelvin-Helmholtz instability, while the wave velocity corresponds to a pure viscous theory deriving from Darcy's law. We report our experimental results and analyze this instability by the study of a new equation where the viscous effects are added to the Euler equation through a unique drag term. The predictions made from the linear stability analysis of this equation agree with the experimental measurements.

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.

The destabilization of the stationary basic flow occurring between two disks enclosed by a cylinder is studied experimentally when the radius of the disks is large compared to the spacing. In the explored range of the cell aspect ratio, when one disk only is rotating, circular vortices propagating to the centre are observed above a critical angular velocity. These structures occur naturally but can also be forced by small modulations of the angular velocity of the disk. For each rotation rate the dispersion relation of the instability is experimentally reconstructed from visualizations and it is shown that this dispersion relation can be scaled by the boundary layer thickness measured over the disk at rest. The bifurcation is found to be of supercritical nature. The effect of the forcing amplitude is in favour of a linear convective nature of this instability of the non-parallel inward flow existing above the stationary disk. The most unstable temporal frequency is found to be about four times the frequency of the rotating disk. The evolution of the threshold of this primary instability is described for different aspect ratios of the cell. Finally, two sets of experiments made under transient conditions are presented: one in order to investigate further a possible convective/absolute transition for the instability, and the other to compare with the impulsive spin-down-to-rest experiments of Savas (1983).

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.

The transport inception of immersed grains is studied experimentally with laminar flow conditions in a Hele-Shaw cell when varying the tilt angle of the cell and the water flow rate. Varying these two parameters, grains are either motionless, rolling on the bed surface, or avalanching downwards. This paper focuses on the determination of the onset for grain motion either by erosion or by avalanche. For a horizontal interface, onset for erosion corresponds to a constant critical Shields number θc=0.14 at small particle Reynolds number (Red<1) but decreases as Red−1 at larger particle Reynolds number (Red>1). For tilted bed, the onset of erosion increases when the flow is opposed to gravity. Both results are compared to a standard model based on a balance of the forces acting on a single grain lying on a tilted plane. When tilt angles are large, avalanches occur. The maximum angle of stability is modified by the flow and increases slightly when the flow acts against gravity. This behavior is compared to a continuous model where a few layers of grains are about to slide.

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.