  Based on the Boltzmann-Enskog kinetic theory, we develop a hydrodynamic
theory for the well known (reverse) Brazil nut segregation in a vibro-fluidized
granular mixture. Using an analogy with standard fluid mechanics, we have
recently suggested a novel mechanism of segregation in granular mixtures based
on a {\it competition between buoyancy and geometric forces}: the Archimedean
buoyancy force, a pseudo-thermal 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. For a mixture
of perfectly hard-particles with elastic collisions, the pseudo-thermal
buoyancy force is zero but the intruder has to overcome the net compressive
geometric force to rise. For this case, the geometric force competes with the
standard Archimedean buoyancy force to yield a threshold density-ratio,
$R_{\rho 1}=\rho_l/\rho_s < 1$, above which the {\it lighter intruder sinks},
thereby signalling the {\it onset} of the {\it reverse buoyancy} effect. For a
mixture of dissipative particles, the non-zero pseudo-thermal buoyancy force
gives rise to another threshold density-ratio, $R_{\rho 2}$ ($> R_{\rho 1}$),
above which the intruder rises again. Focussing on the {\it tracer} limit of
intruders in a dense binary mixture, we find that the rise-time of the intruder
could vary {\it non-monotonically} with the density-ratio. For a given
size-ratio, there is a threshold density-ratio for the intruder at which it
takes the maximum time to rise, and above(/below) which it rises faster,
implying that {\it the heavier (and larger) the intruder, the faster it
ascends}. Our theory offers a unified description for the (reverse) Brazil-nut
segregation and the non-monotonic ascension dynamics of Brazil-nuts.
