External pressure dependence of granular orifice flow: Transition to Beverloo flow

Abstract

In this paper, we have designed and employed a suspended-wall silo to remove the Janssen effect in order to explore directly the local pressure dependence of granular orifice flow (GOF) systematically. We find that as the Janssen effect is removed, the flow rate Q changes linearly with the external pressure. The slope α of the linear change decays exponentially with the ratio of the silo size and the size of the orifice φ/D, which suggests the existence of a characteristic ratio λ (∼2.4). When φ/D > λ, α gradually decays to zero, and the effect of external pressure on the GOF becomes negligible, where the Beverloo law retrieves. Our results show that the Janssen effect is not a determining factor of the constant rate of GOF, although it may contribute to shield the top load. The key parameter in GOF is φ/D. In small φ/D, the flow rate of GOF can be directly adjusted by the external pressure via our suspended-wall setup, which may be useful to the transportation of granules in microgravity environment where the gravity-driven Beverloo law is disabled.