Modeling the transition between stable and unstable operation while emptying a silo

In this paper we have examined the stable and unstable states of the operation during the emptying of the silo. Here the state of stable operation of the silo is understood as a smooth mass outflow. The unstable state is manifested by funnel flow or arching. This issues from a moistured granular material. We have focused on the two extreme experimental cases. The first option was considered as a mass flow and the second one was considered as arching. Based on experimental data we have simulated the silo emptying by DEM. Considering the transition between stable and unstable operation we proposed a novel mathematical model of the silo emptying. This model involves a fractional-differential oscillator equation. Analyzing the solution of this equation we have presented how to recognize the state of stable and unstable operation during silo emptying.