Brazil nut effect and excluded volume attraction in vibrofluidized granular mixtures

A two dimensional bi-disperse vibrofluidized granular mixture is studied in the rapid flow regime, where particle interactions occur due to instantaneous collisions. Both experiments and simulations are carried out, and these show the existence of two phenomena which have been observed only in very dense granular flows or in equilibrium systems. The Brazil nut phenomenon, which involves the rise of larger particles in a granular mixture upon vibration, has been observed in dense systems due to the percolation of small particles though the interstitial spaces between the large particles, or due to convection rolls. In the present case, where neither effect is present, it is observed that the fluidization of the smaller particles by vibration results in an exponentially decaying density profile, at heights large compared to the particle diameter, and thereby a pressure field that decreases with height. The larger particles, suspended in this decaying pressure field, experience a larger pressure at the bottom and a smaller pressure on top, and they rise to a height where the net force caused by the decreasing pressure is balanced by the weight of the particle. An attractive force between the large particles, similar to the entropic attraction effect in mixtures of colloids and polymers, is also observed in this nonequilibrium system, because when the distance between the large particles is less than the small particle diameter, the pressure between the large particles is smaller than that on the outside. Analytical results are derived for each of these effects, and these are in agreement with the experimental and simulation results.