Particle flows in silos, significance of particle shape, stiffness and friction
Authors:   , Pongó Tivadar 
Published: January 2023

Granular flows are frequently observed in nature and appear in many industrial processes as well. In this numerical work the focus is mainly directed at the understanding of how the change of different grain properties, such as shape, friction and stiffness, influences the flow out of a silo. However, the heating dynamics of a granular gas of rods is also analyzed. In all these scenarios, the simulations are paired with experiments to calibrate and validate the results. The numerical analysis indicated that the discharge of soft, low-friction grains from a container exhibits a height-dependent flow rate, which is not usual for granular media. The systematic study mapped the parameter space of particle friction and stiffness, exploring the system’s macroscopic response in detail. Moreover, the examination of the coarse-graining fields helped us to explain when and why the flow rate depends on the column height. The answers include the material response to pressure gradients, but also the way stress is transmitted in the system. The outcomes allowed us to propose simple theoretical arguments, connecting the macroscopic flow rate with the pressure gradient at the orifice. As a result, we have come up with a well-reasoned explanation for the height-dependent discharge flow rate, shown experimentally and numerically by soft low-frictional grains. Our numerical investigation of a 2D silo flow of mixtures of soft and hard grains reproduced the high impact that even 5% of hard frictional grains have on the flow of an ensemble of low-friction, soft particles. Numerical results signaled the importance of the friction between the two types of grains. When the frictional hard grains are added to the soft grains, the flow gets slower, clogging becomes more frequent, and the force measured on the bottom plate decreases. Moreover, we obtained that these effects are enhanced when the interspecies friction is increased. The introduction of a rotational shear through the rotation of the flat silo bottom leads to a surprising effect on the discharge of rods: the flow rate is reduced significantly, by up to 70%. Our simulations and the application of the coarse-graining methods reveal the underlying reasons for this observation. The exit velocity of particles is the main contributing factor to this drop, which is in correlation with the vertical orientation of the grains. Our numerical tool allowed the exploration of the dependence of flow rate 𝑄 on the orifice size 𝐷. In the limit of large orifices, the classical power-law correlation 𝑄 ∼ 𝐷5/2 was reproduced. For small apertures, however, we obtained a power-law relation but with a notably larger exponent. Furthermore, the size of the so-called free fall arch region is also found to decrease due to the rotation. Finally, granular gas made up of rods and heated by the walls has been studied numerically. Our study provides additional insight into the process for instance by describing the system behavior in the non-symmetrically heated direction, which was not accessible experimentally. The velocity distributions of the particles are examined and found to be well-fitted by stretched exponential distributions, in agreement with previous experiments. Moreover, in the experimentally not accessible direction, we obtained asymmetrical distribution tails. Additionally, the collapsing of the velocity distributions lead us to conclude that the energy scales with the square of the characteristic velocity of the wall.