The intruder motion in a cubic granular container

Abstract

The Brazil nut effect is a key issue impeding the uniform distribution of particles in a mixed granular system. Extensive research was conducted on this segregation phenomenon in the 1990s and 2000s to identify the mechanisms and influencing factors involved. However, due to limitations in experimental techniques, the scope and effectiveness of research have been restricted. In this study, the Hall-effect magnetic sensing technique was utilized to track the motion of a single magnetic sphere (referred to as the intruder) within a cubic granular bed. This tracking method allowed for the measurement of the intruder's equilibrium positions as well as its trajectories. In a vibration-fluidized cubic granular container, an interesting phenomenon was observed: the intruder displayed a unique periodic helical oscillatory motion near the corner of the cubic container, with the oscillation amplitude gradually attenuating until stabilizing at its equilibrium position. A discrete element method simulation was carried out, revealing that the granular convection flow ascends from the center and descends near the container walls, with a faster flow rate at the four corners. An equation of motion was established accordingly for an intruder in such a convective granular flow, providing a comprehensive explanation for the observed intruder behavior. As a result of this comprehensive approach, we have uncovered the unique phenomenon of different mechanisms collectively driving the periodic spiral oscillation of the intruder before it eventually rested in its equilibrium position, a phenomenon whose mechanism has not previously been investigated in the literature.