  Transport coefficients associated with the mass flux of impurities immersed
in a moderately dense granular gas of hard disks or spheres described by the
inelastic Enskog equation are obtained by means of the Chapman-Enskog
expansion. The transport coefficients are determined as the solutions of a set
of coupled linear integral equations recently derived for polydisperse granular
mixtures [V. Garz\'o, J. W. Dufty and C. M. Hrenya, Phys. Rev. E {\bf 76},
031304 (2007)]. With the objective of obtaining theoretical expressions for the
transport coefficients that are sufficiently accurate for highly inelastic
collisions, we solve the above integral equations by using the second Sonine
approximation. As a complementary route, we numerically solve by means of the
direct simulation Monte Carlo method (DSMC) the inelastic Enskog equation to
get the kinetic diffusion coefficient $D_0$ for two and three dimensions. We
have observed in all our simulations that the disagreement, for arbitrarily
large inelasticity, in the values of both solutions (DSMC and second Sonine
approximation) is less than 4%. Moreover, we show that the second Sonine
approximation to $D_0$ yields a dramatic improvement (up to 50%) over the first
Sonine approximation for impurity particles lighter than the surrounding gas
and in the range of large inelasticity. The results reported in this paper are
of direct application in important problems in granular flows, such as
segregation driven by gravity and a thermal gradient. We analyze here the
segregation criteria that result from our theoretical expressions of the
transport coefficients.
