The modeling of free-fall arch formation in granular flow through an aperture

In this study, to predict the formation of the free-fall arch via granular flow through an aperture, an analytical model has been developed based on the particle-scale force equilibrium. This model calculates the size and location of the meta-stable arch and can be extended to predict the granular flow rate. According to the developed analytical model, the formation of a free-fall arch is independent of granular height and stress state above the arch, where only granular particle size, aperture size, and granular friction influence the development of the arch. Besides, this proposed model can predict the formation of the meta-stable arch without empirical parameters. In comparison with experimental results, the predicted granular flow rate based on the model exhibits high accuracy for uniform-sized granular flow. According to numerical simulations, the free-fall arch appears above the aperture; however, the particle velocity at the arch is low and can be considered negligible. Gravity will cause the granular particles under the arch to fall freely. This mathematical model offers an efficient method to predict the formation of the free-fall arch and calculate the granular flow rate through an aperture.