A novel dimensionless number for the characterisation of densification and segregation in a vibrationally excited granular system

Reliable production of densely packed, homogeneous powders is of significant interest to a range of industrial applications. Vibration-based excitation is frequently employed to increase the density of granular packings. However, this same vibration can lead to segregation – especially pronounced in systems of wide size distribution – which is generally undesirable. Existing research primarily focuses on densification and segregation individually, but the simultaneous optimisation of both phenomena remains underexplored. Discrete Element Method (DEM) simulations were conducted in LIGGGHTS to investigate the densification and segregation in a bidisperse-by-size granular system over a broad range of vibration frequencies and amplitudes, comparing continuous and tap-settle excitation in both vertical and horizontal directions. To test the generality of the proposed tap characterisation, additional horizontal tapping datasets were also generated for two further binary size ratios and for a polydisperse continuous PSD (Weibull) system. It was found that discrete, horizontal ‘taps’ provide the best packing density for the principal binary system explored, and the optimal conditions for the densest and most homogeneous steady-state packing do not correspond to the most rapid packing. There is therefore a small trade-off between steady-state packing density and the speed at which it is achieved. Two distinct densification behaviours were identified, reflecting stable densification and slow segregation-driven density loss. A novel dimensionless number, the ‘dimensionless action,’ is proposed and shown to outperform the commonly used control parameters tested here in collapsing packing-density and segregation-intensity data for three bidisperse systems and a polydisperse continuous-PSD system.