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

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 Gamma, rotation angle velocity omega, 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 lambda(z) and lambda(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 Gamma mainly. BN tendency is enhanced when f increases at a constant Gamma, but is reduced when Gamma increases at a constant f, and vice versa. When omega increases at constant f and Gamma, the value of lambda(z) first rises as a result of enhanced BN tendency and then drops in response to vertical rotation. As omega increases, the surface of the particle mixture becomes hollow, and the lambda(z)-omega curve is partly dispersed. After the hollow touches the container bottom, the curve becomes fully dispersed. omega, f, Gamma, 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 omega, f, Gamma, and m on the final separation results in delicate mathematical descriptions. This model agreed well with the experimental outcomes.