Flow in an hourglass: particle friction and stiffness matter

Abstract

Granular flow out of a silo is studied experimentally and numerically. The time evolution of the discharge rate as well as the normal force (apparent weight) at the bottom of the container is monitored. We show, that particle stiffness has a strong effect on the qualitative features of silo discharge. For deformable grains with a Young's modulus of about Ym ≈ 40 kPa in a silo with basal pressure of the order of 4 kPa lowering the friction coefficient leads to a gradual change in the discharge curve: the flow rate becomes filling height dependent, it decreases during the discharge process. For hard grains with a Young's modulus of about Ym ≈ 500 MPa the flow rate is much less sensitive to the value of the friction coefficient. Using DEM data combined with a coarse-graining methodology allows us to compute all the relevant macroscopic fields, namely, linear momentum, density and stress tensors. The observed difference in the discharge in the low friction limit is connected to a strong difference in the pressure field: while for hard grains Janssen-screening is effective, leading to high vertical stress near the silo wall and small pressure above the orifice region, for deformable grains the pressure above the orifice is larger and gradually decreases during the discharge process. We have analyzed the momentum balance in the region of the orifice (near the location of the outlet) for the case of soft particles with low friction coefficient, and proposed a phenomenological formulation that predicts the linear decrease of the flow rate with decreasing filling height.

The role of the particle aspect ratio in the discharge of a narrow silo

“…Interestingly, for elongated grains, the plateau is much less pronounced, and the value of F b is larger. This is similar to our previous observations with lubricated (reduced friction) glass beads (see figure 5(d) of reference [24]). This might be an indication that the friction between the rods (which are mostly aligned parallel with boundaries) and the silo wall is smaller than that in the case of glass beads.…”

Modelling silo clogging with non-local granular rheology

“…used compared with the geometry of our system (unlike the experiments which used a much smaller opening relative to the silo width) as well as the aforementioned lack of sidewall friction. Recent studies (Pongó et al 2021) have shown the flow rates are also a function of particle stiffness. Possibly related effects such as layering near boundaries are not presently incorporated in the continuum model, so exploration of boundary conditions and edge effects are natural areas for future work.…”

“…Recent studies (Pongó et al. 2021) have shown the flow rates are also a function of particle stiffness. Possibly related effects such as layering near boundaries are not presently incorporated in the continuum model, so exploration of boundary conditions and edge effects are natural areas for future work.…”

The effect of obstacles near a silo outlet on the discharge of soft spheres

“…The storage of granular materials in silos and their discharge through small orifices in the container bottom has been studied widely since more than one century. The discharge dynamics of hard particles is practically independent of the pressure in the granular bed [1][2][3]. The outflow rate Q of spheres is well described by Beverloo's equation [4,5].…”