Granular Avalanches in Fluids

Abstract

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...

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“…In both cases, the maximal velocity at the surface agrees with the characteristic velocity of the regime [14]:…”

“…[10,11,13,[28][29][30]. To compare and discuss more in details those velocity profiles, we will first refer to the work carried out by Courrech du Pont et al [14] who have defined three flow regimes for a granular avalanche in a fluid based on the fall under gravity of one grain in fluid: a free fall regime for which there is no fluid influence (i.e. the classical dry regime) and two regimes where the avalanche dynamics is controlled by the fluid drag force and for which the grain motion reaches respectively a viscous and an inertial limit regime.…”

“…Following their definitions of the relevant dimensionless groups, namely Stokes number and grain/fluid density ratio, our experiments appear to be situated in the close vicinity of the boundary between viscous and inertial limit regime with a particle Reynolds number Re 2 ≈ . But, for such values of Re close to unity in this case, we can no more use the Stokes drag force (valid only for Re 1 ≪ ) in the whole viscous regime or a constant drag coefficient (valid only for Re 1 ≫ ) in the whole inertial regime as was done in [14]. To clarify this point, we propose to connect the two limit regimes with the following empirical expression of the drag coefficient derived from [31]: With an analysis analogous to [14], the rheology obtained for dry granular flows [13] has been extended to steady granular flows down an inclined plane taking into account the influence of the interstitial fluid [15].…”

“…But, for such values of Re close to unity in this case, we can no more use the Stokes drag force (valid only for Re 1 ≪ ) in the whole viscous regime or a constant drag coefficient (valid only for Re 1 ≫ ) in the whole inertial regime as was done in [14]. To clarify this point, we propose to connect the two limit regimes with the following empirical expression of the drag coefficient derived from [31]: With an analysis analogous to [14], the rheology obtained for dry granular flows [13] has been extended to steady granular flows down an inclined plane taking into account the influence of the interstitial fluid [15]. Specific rheological laws are achieved for the three regimes which predict in particular that the velocity profiles in both free fall and inertial limit regimes are qualitatively similar.…”

“…According to the definition of three regimes of avalanches in fluids [14], the local rheology has been subsequently extended to the case of submarine granular flows down inclined planes [15].…”