Forced flow of granular media: Breakdown of the Beverloo scaling

Abstract

The Beverloo scaling for the gravity flow of granular materials through orifices has two distinct universal features. On the one hand, the flow rate is independent of the height of the granular column. On the other hand, less well-known yet more striking, the flow rate is fairly insensitive to the material properties of the grains (density, Young's modulus, friction coefficient, etc.). We show that both universal features are lost if work is done on the system at a high rate. In contrast to viscous fluids, the flow rate increases during discharge if a constant pressure is applied to the free surface of a granular column. Moreover, the flow rate becomes sensitive to the material properties. Nevertheless, a new universal feature emerges: the dissipated power scaled by the mean pressure and the flow rate follows a master curve for forced and unforced conditions and for all material properties studied. We show that this feature can be explained if the granular flow in the silo is assumed to be a quasistatic shear flow under the μ(I)-rheology.

Role of particle size in the kinematic properties of silo flow

“…In fact, materials of diverse nature, such as cereals, drugs, or minerals, are stored in granular form and have to be processed accordingly. Even so, given the complexity of discrete media, the silo discharge continues to be an open problem from the point of view of its underlying physics and is, indeed, a topic under very active research [3][4][5][6][7]. The most widely accepted expression to predict the mass flow rate W of granular matter in a silo was proposed by Beverloo et al [8] in 1961,…”

Velocity profiles in forced silo discharges

“…A discussion on the relation between pressure, flow rate and dissipated power can be found in Ref. [18]. In this paper we focus only on velocity profiles and leave the discussion on pressure profiles for a future work.…”

“…Recently, it has been shown that the use of an overweight on top of the granular column of a discharging silo induces an increase of the flow at the final stages of the discharge [18]. This is once again in contrast to viscous fluids since these decrease their flow rate during discharge from a tank even if a constant overpressure is applied to the free surface.…”

“…[7]. However, experimental observations are against this prediction [18]. One may expect that the use of an overweight is equivalent to the addition of extra granular material on top of the original granular column.…”

“…The basic mechanism to explain the increase in flow rate due to an overweight is based on energy balance [18]. In a dense granular system, the collision rate is very high, which leads to inelastic collapse.…”