  It is well-recognized that granular media under rapid flow conditions can be
modeled as a gas of hard spheres with inelastic collisions. At moderate
densities, a fundamental basis for the determination of the granular
hydrodynamics is provided by the Enskog kinetic equation conveniently adapted
to account for inelastic collisions. A surprising result (compared to its
molecular gas counterpart) for granular mixtures is the failure of the energy
equipartition, even in homogeneous states. This means that the partial
temperatures $T_i$ (measuring the mean kinetic energy of each species) are
different to the (total) granular temperature $T$. The goal of this paper is to
provide an overview on the effect of different partial temperatures on the
transport properties of the mixture. Our analysis addresses first the impact of
energy nonequipartition on transport which is only due to the inelastic
character of collisions. This effect (which is absent for elastic collisions)
is shown to be significant in important problems in granular mixtures such as
thermal diffusion segregation. Then, an independent source of energy
nonequipartition due to the existence of a divergence of the flow velocity is
studied. This effect (which was already analyzed in several pioneering works on
dense hard-sphere molecular mixtures) affects to the bulk viscosity
coefficient. Analytical (approximate) results are compared against Monte Carlo
and molecular dynamics simulations, showing the reliability of kinetic theory
for describing granular flows.
