Starting from the hydrodynamic equations of binary granular mixtures, we
derive an evolution equation for the relative velocity of the intruders, which
is shown to be coupled to the inertia of the smaller particles. The onset of
Brazil-nut segregation is explained as a competition between the buoyancy and
geometric forces: the Archimedean buoyancy force, a buoyancy force due to the
difference between the energies of two granular species, and two geometric
forces, one compressive and the other-one tensile in nature, due to the
size-difference. We show that inelastic dissipation strongly affects the phase
diagram of the Brazil nut phenomenon and our model is able to explain the
experimental results of Breu et al. (PRL, 2003, vol. 90, p. 01402).Comment: 5 pages, 2 figure