Universal laws in silo discharge of soft disks

We investigate the effect of particle deformability on the flow behavior in a 2D silo. We use a novel Smoothed Particle Hydrodynamics-Discrete Element Method (SPH-DEM) approach that explicitly models the particles’ deformation. We identify a two-fold mechanism through which particle deformation influences silo flow: (i) the spatial arrangement of particles and (ii) the velocity distribution of particles at the outlet. Specifically, we observe—for orifices larger than five times the particle diameter—that the velocities at the outlet follow the same distribution for both hard and soft particles. Thus, we are able to collapse appropriately scaled velocity profiles at the outlet onto a single master curve. Also, we find that our velocity scaling should take the different spatial organization of soft and hard particles near the orifice into account. Finally, we explore the effect of particle deformation on the silo discharge rate. By introducing a deformability parameter \(\alpha \), we propose an extended version of the Beverloo equation that accounts for the influence of particle deformation on the flow rate. Interestingly, we find that this deformability parameter should be chosen as the ratio of the stress at the bottom of the container and the bulk modulus of the material.