Brazil nut effect: Influence of friction and jamming on the transition line

We report a molecular dynamics study of the behavior of a bidimensional system consisting of a large disk (the intruder) immersed in a bed of many small disks. All collisions are instantaneous and inelastic and all possible parameters of the system are kept fixed except for two dimensionless parameters determining the frequency and amplitude of the vibrating base. A systematic exploration of this parameter space leads to determining a transition line separating a zone in which the Brazil nut effect is observed and one in which it is not. It is observed for the BNE to be present it is necessary that the characteristic velocity of the vibrating base is above a certain threshold. This threshold increases as the characteristic acceleration of the base gets larger. The results strongly suggest that, in the region of the parameter space in which the study is made, there is a minimum amplitude and a maximum frequency for the Brazil nut effect to take place. The shape of the transition line is understood in connection with the friction of the system with the lateral walls and with jamming. Friction with the lateral walls produces a net downward force, eventually leading to a convective current that pushes the intruder up. Although the energy injection rate, that helps the development of the convective current, is proportional mainly to the square of the velocity of the base, it is found that the average frictional force decreases when increasing the base acceleration. Therefore, for large base accelerations, higher values of the base velocity are needed to produce a convective current sufficiently strong. But if the system is not excited enough the friction which would produced convective currents are balanced by the reaction forces that result from jamming.