Time of flight of intruder in a vertically vibrated granular material: Brazil Nut Effect and its reverse

Abstract

The Brazil Nut Effect (BNE) is the phenomenon where the larger grains in a vertically vibrated granular mixture rise to the top. The reverse, where the larger grains sink to the bottom, is the Reverse Brazil Nut Effect (RBNE). Previously, using the modified Inelastic Bouncing Ball Model (mIBBM), we proposed that these effects could be described by comparing the bifurcation diagrams (BD, time of flight τ versus the dimensionless acceleration Γ) of the center of mass (CM) of mixture components. Here, we investigate the model for the case when one component of the mixture consists of just a single intruder particle. Using the discrete element method (DEM), we analyze the possible movement of the intruder in a vertically vibrated granular bed (GB) made of 2160 smaller particles. We vary the density, size, and initial position of the intruder, and compare the BD of the intruder with that of the CM of the GB as BNE or RBNE occurs. Although the simulation generates BNE or RBNE, the mIBBM only indicates BNE, and therefore, is not effective in distinguishing between the two phenomena. This is because mIBBM only considers the CM of the GB, and the intruder is assumed to move only along the z-direction of periodic vertical vibration.