Modified inelastic bouncing ball model of the Brazil nut effect and its reverse

We developed the modified inelastic bouncing ball model (mIBBM) to describe the emergence of the Brazil nut effect (BNE) and its reverse (RBNE) in a vertically-vibrated binary granular mixture. The mIBBM incorporates the container-to-grains force-transmission efficiency (transmissibility) T (r) to quantify the dimensionless mean void lifetime that acts as the segregation phase indicator where omega is the vibration angular frequency. The mixture is represented as two non-interacting inelastic balls, Ball A and Ball B. Each ball bounces with a time-of-flight tau (A) (or tau (B) ) that depends on transmissibility T (rA) (or T (rB) ) and the dimensionless container acceleration I, i.e., tau (A) = tau (A) (I, T (rA) ) and tau (B) = tau (B) (I, T (rB) ). The ball dynamics are described by the bifurcation diagrams of the dimensionless times-of-flight, omega tau (A) (I, T (rA) ) and omega tau (B) (I, T (rB) ). The probability-weighted difference between branches of the two diagrams is computed and interpreted as follows: (occurrence of BNE), (RBNE) and = 0 (no segregation). Segregation phases are revealed as varying shifts and widths of across the I axis. The phase boundaries in the -versus-I diagram are sensitive to changes in T (rA) , T (rB) and Delta T (r) = (T (rA) - T (rB) ). The mIBBM explains why the BNE is a more likely than the RBNE and predicts a segregation phase sequence that is generally consistent with related experimental results taken over a limited omega-range. Additional experiments are needed to enable a more comprehensive and precise evaluation of the mIBBM.