Forced silo discharge: Simulation and theory

We study, through discrete element simulations, the discharge of granular materials through a circular orifice on the base of a cylindrical silo forced by a surcharge. At the beginning of the discharge, for a high granular column, the flow rate $Q_{\rm ini}$ scales as in the Beverloo equation for free discharge. However, we find that the flow rate $Q_{\rm end}$ attained at the end of the forced discharge scales as $\sqrt{\rho_{\rm b} P}D_{\rm o}^3/D_{\rm s}$, with $\rho_{\rm b}$ the bulk density, $P$ the pressure applied by the overweight, $D_{\rm o}$ the orifice diameter and $D_{\rm s}$ the silo diameter. We use the work--energy theorem to formulate an equation for the flow rate $Q_{\rm end}$ that predicts the scalings only in part. We discuss the new challenges offered by the phenomenology of strongly forced granular flows.