External pressure dependence of Granular Orifice Flow: transition to Beverloo flow

TL;DR

This study investigates how external pressure influences granular flow through an orifice, revealing a transition to Beverloo flow when the pressure effect diminishes beyond a critical size ratio, with implications for microgravity applications.

Contribution

The paper introduces a suspended-wall silo setup to directly measure pressure dependence of granular flow, identifying a critical size ratio where external pressure effects vanish.

Findings

Flow rate Q varies linearly with external pressure when Janssen effect is removed.

The slope of this linear relation decays exponentially with the size ratio {\

,

Abstract

In this paper, we have designed and employed a suspended-wall silo to remove Janssen effect in order to explore directly the local pressure dependence of Granular Orifice Flow (GOF) systematically. We find that as Janssen effect is removed, the flow rate Q changes linearly with the external pressure. The slope {\alpha} of the linear change decays exponentially with the ratio of the silo size and the size of the orifice {\Phi}/D, which suggests the existence of a characteristic ratio {\lambda} (~2.4). When {\Phi}/D > {\lambda}, {\alpha} gradually decays to zero, and the effect of external pressure on the GOF becomes negligible, where the Beverloo law retrieves. Our results show that 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 {\Phi}/D. In small {\Phi}/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.