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Article Dans Une Revue Physics of Fluids Année : 2007

Initiation of granular surface flows in a narrow channel

Résumé

We experimentally investigate how a long granular pile confined in a narrow channel destabilizes when it is inclined above the angle of repose. A uniform flow then develops, which is localized at the free surface. It first accelerates before reaching a steady uniform regime. During this process, an apparent erosion is observed and the thickness of the flowing layer increases. We precisely study the evolution of the vertical velocity profile in this transient regime. The measurements are compared with the prediction of a viscoplastic model Jop et al., Nature 441, 727 2006. A characteristic of dry granular materials is that they can behave like a solid or a liquid. A typical situation is obtained when an avalanche is triggered at the surface of a pile. In this case, grains start to move at the free surface, accelerate, and put into motion other grains initially static. Understanding how the flowing part interacts with the static part has motivated many experimental works. Different configurations have been investigated: avalanches propagating on a static layer inclined with respect to the horizontal, 1–3 piles collapsing on a horizontal surface, 4,5 and flows in rotating drums or on a pile. 6–11 However, the dynamics observed in these experiments is complex, since the frontier between flow and no flow evolves both in space and time. Investigating the erosion process in a uniform avalanche, where the flow/no-flow interface varies only in time, is one of the motivations of this Brief Communication. From a theoretical point of view, different approaches have been proposed to describe the solid-liquid transition. A whole class of models is based on depth averaged equations and writes the mass and momentum equation for the flowing layer and the static pile. 12 In this framework, an additional closure equation has to be proposed to describe the evolution of the interface. 13–15 A second approach considers the granu-lar material, such as a mixture of a liquid and solid phase, and writes an empirical equation for the liquid phase fraction. 16 This approach captures some nontrivial features of the transition between static and flowing regions. 16 Recently, it has been shown that for some configurations with sidewalls, the localization of the granular flows on top of a pile is simply related to the nonuniform distribution of stresses. Due to the lateral friction, the ratio between shear and normal stress decreases when going deeper in the pile. At a critical depth, it reaches the yield threshold and the material stops. Using a viscoplastic rheological model, 17,18 quantitative predictions have been obtained for steady uniform flows. One can then wonder if unsteady avalanches, where erosion is observed, can be captured by the same approach. To study initiation of flow, we design an experimental setup where a long pile confined in a narrow channel is suddenly destabilized above the angle of repose. This configuration allows to create an accelerating surface flow, where the interface between flow and no-flow regions is flat and evolves in time only. The experimental setup is presented in Fig. 1. It consists of a long channel with glass sidewalls and a rough bottom to prevent the whole pile from flowing. We use glass beads d = 0.53± 0.05 mm in diameter, and density s = 2450 kg/ m 3. In order to study a quasi-two-dimensional system we choose a narrow channel W = 19d 1 cm. The velocity of the grains measured through the glass sidewall is then representative of the bulk behavior. 17 A long L-shaped wedge closes the channel and defines a rectangular box 110 cm long and 10 cm high. The wedge can rotate around its upper tip. At the beginning of an experiment, the channel is empty and the wedge is in the bottom position. The whole setup is inclined at the desired inclination. The beads are then poured below the wedge from the top. To have reproducible initial conditions we gently tap several times on the setup. Thanks to this setup, a long static pile can be created at any arbitrary inclination Fig. 1a, which allows to study the initiation of flow above the angle of spontaneous avalanches. At t = 0, we release the heap by rapidly lifting the wedge. The time evolution of the pile is sketched in Fig.
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Dates et versions

hal-01432144 , version 1 (11-01-2017)

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Pierre Jop, Yoël Forterre, Olivier Pouliquen. Initiation of granular surface flows in a narrow channel. Physics of Fluids, 2007, 19, pp.88102 - 88102. ⟨10.1063/1.2753111⟩. ⟨hal-01432144⟩
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