Average outpouring velocity and flow rate of grains discharged from a tilted quasi-2D silo

The flow of granular materials through constricted openings is important in many natural and industrial processes. These complex flows – featuring dense, dissipative flow in the bulk but low-dissipation, low density outpouring in the vicinity of the orifice – have long been characterized empirically by the Beverloo rule and, recently, modeled successfully using energy balance [J. R. Darias, et. al., Phys. Rev. E 101, 052905 (2020)]. The dependence of flow rate on the silo's angle with respect to gravity, however, is not captured by current models. We experimentally investigate the role of tilt angle in this work using a quasi-2D monolayer of grains in a silo. We measure mass flow rate, the average exit velocities of grains, and the packing fraction along the orifice with varying tilt angles. We propose a model that describes our results (and findings with 3D systems [H. G. Sheldon and D. J. Durian, Granul. Matter 12, 579 (2010)]) by considering the dependence of outpouring speed and angle with respect to the orifice angle and, importantly, the angle of stagnant zones adjacent to the orifice. We conclude by posing questions about possible extensions of our model in order to describe spatial variations of exit velocity and density along the orifice.