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. Using a camera and scale composed of load cells, we measure mass flow rate, the average exit velocities of grains, and the packing fraction along the orifice with varying tilt angles during steady-state flow of grains. We compare our results with a simple model that takes into account the angle of stagnant zones adjacent to the orifice in steady-state flow. 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.