Behaviour of a binary particle system under the effects of simultaneous vertical vibration and rotation

Abstract

We performed experiments to investigate the effects of simultaneous vertical vibration and rotation (around a vertical axis) on a binary particle system. In particular, the effects of vibration frequency f, dimensionless acceleration Γ, rotation angle velocity ω, and the total mass m of the particle system on the final separation results are investigated. The system exhibited transitional Brazilian Nut (BN) separation patterns in both the vertical and axial directions. The coupling of vertical and axial separation mechanisms determined the final spatial separation state. We defined the vertical and axial separation parameters λ_z and λ_r between −1 for Complete Reversed BN (RBN) and 1 for Complete BN to describe the separation states quantitatively. These experiments suggested that when no rotation is applied, the system exhibits mono-directional relations with f and Γ mainly. BN tendency is enhanced when f increases at a constant Γ, but is reduced when Γ increases at a constant f, and vice versa. When ω increases at constant f and Γ, the value of λ_z first rises as a result of enhanced BN tendency and then drops in response to vertical rotation. As ω increases, the surface of the particle mixture becomes hollow, and the λ_z–ω curve is partly dispersed. After the hollow touches the container bottom, the curve becomes fully dispersed. ω, f, Γ, and m all have significant effects on the final vertical and axial separation patterns. Stronger vibration generally increases RBN/Axial RBN, whereas stronger rotation helps form BN/Axial BN. We also established a geometrical model of the separation states to study the effect of ω, f, Γ, and m on the final separation results in delicate mathematical descriptions. This model agreed well with the experimental outcomes.