Shocks in sand flowing in a silo

We study the formation of shocks on the surface of a granular material draining through an orifice at the bottom of a quasi-two-dimensional silo. At high flow rates, the surface is observed to deviate strongly from a smooth linear inclined profile, giving way to a sharp discontinuity in the height of the surface near the bottom of the incline, the typical response of a choking flow such as encountered in a hydraulic jump in a Newtonian fluid like water. We present experimental results that characterize the conditions for the existence of such a jump, describe its structure and give an explanation for its occurrence. The flow of granular materials presents a multitude of experimental and theoretical challenges in many-body physics, as manifested in the unusual collective behaviour of a large assembly of macroscopic grains that interact with each other through collisions and friction. The phenomena of interest in quasi-static motion range from jamming transitions, and the formation and evolution of shear bands, to the transmission of In the dynamical regime associated with technological applications such as silo flows, other questions of interest include the origin and maintenance of fluctuations and their relation to mean flows in the bulk, and the nucleation and evolution of avalanche-like behaviour in the vicinity of the A system of long-standing technological interest in this last situation is associated with flow in a silo. Building on an understanding of simple properties such as the flow rate as a function of the draining orifice size and the shape of the silo (Nedderman 1992), recent work has focused on details such as the form of the velocity profile of the bulk flowing regions. In Samadani, Pradhan & Kudrolli (1999) we studied the flow in the vicinity of the orifice of a silo. The predominant flow is restricted to a parabolic region centred at the origin and may be interpreted in terms of simple diffusion models (Nedderman & Tuzun 1979; Mullins 1974). Here, we complement those studies by considering the dynamical evolution of the form of the free surface in a quasi-two-dimensional silo flow. Our system consists of a flat-bottomed silo that is quasi-two-dimensional: 89 cm wide, 45 cm high and 2.54 cm deep, the last being 25–1000 times the typical grain size. The orifice itself has a square cross-section of width equal to that of the silo, with an attached valve to control the flow rate Q (see …