Modified inelastic bouncing ball model of the segregation of binary granular mixture: Numerical simulation

Abstract

In a vertically vibrated binary granular mixture, the larger grains rise to top (Brazil Nut Effect, BNE), sink to bottom (Reverse BNE), or remain mixed depending on the grain properties and vibration parameter. Previously, we introduced a model considering the mixture components as two non-interacting inelastic bouncing balls. In particular, segregation is determined from the times-of-flight of the balls, which in turn, depend on the intrinsic properties of the grains represented by transmissibility, Tᵣ, and on the vibration’s dimensionless acceleration Γ. Here, we simulated and tracked the times-of-flight τ of two bouncing balls of different Tᵣ. We determined the segregation phases from the probability-weighted difference ω〈 δ t 〉 between branches of the bifurcation diagrams (dimensionless τ versus Γ). The segregation phases, represented by the segregation phase diagram (ω〈 δ t 〉 versus Γ and Tᵣ) replicated our previous results.