Intruder trajectory tracking in a three-dimensional vibration-driven granular system: Unveiling the mechanism of the Brazil nut effect

Abstract

We employ a Hall-effect magnetic sensor array to accurately track the trajectory of a single magnetic sphere, referred to as the “intruder,” within a three-dimensional vibro-fluidized granular bed to unravel the underlying physical mechanism governing the motion of the intruder. Within the acceleration range of 3.5 g ≥ Γ ≥ 1.5 g, we find that, regardless of the intruder’s initial position, it consistently reaches the same equilibrium depth when the vibration acceleration (Γ) and frequency (ω) are fixed. For Γ ≤ 2.5 g, the equilibrium position lies on the surface of the granular bed, while for Γ > 2.5 g, it shifts below the surface. Additionally, intruders with different densities exhibit varying equilibrium depths, with higher density resulting in a deeper equilibrium position. To understand the mechanism behind the intruder’s upward or downward motion, we measure its rising or sinking velocities under different vibration parameters. Our findings demonstrate that the rising velocity of the intruder, under varying vibration accelerations (Γ) and frequencies (ω), can be collapsed using the ratio Γ/ω, while the sinking velocity remains unaffected by the vibration strength. This confirms that the upward motion of the larger sphere, associated with the Brazil nut effect, primarily arises from the void-filling mechanism of the bed particles. Furthermore, our experiments reveal that the presence of convection within the bed particles has minimal impact on the motion of the intruder.