Flow in an hourglass: particle friction and stiffness matter

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 modulus of about Y-m approximate to 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 modulus of about Y-m approximate to 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.

Automated summary

This study investigated the discharge process of granular flow from a silo through experimental and numerical methods. It found that particle stiffness significantly affects the discharge characteristics, with differences in discharge behavior observed between deformable and hard grains at different friction coefficients. The study also analyzed the pressure fields during discharge and proposed a formulation to predict the flow rate decrease with decreasing filling height for soft particles with low friction coefficient.