Reverse Brazil nut problem: competition between percolation and condensation

In the Brazil nut problem (BNP), hard spheres with larger diameters rise to the top. There are various explanations (percolation, reorganization, convection), but a broad understanding or control of this effect is by no means achieved. A theory is presented for the crossover from BNP to the reverse Brazil nut problem based on a competition between the percolation effect and the condensation of hard spheres. The crossover condition is determined, and theoretical predictions are compared to molecular dynamics simulations in two and three dimensions.