  A collisional model of a confined quasi-two-dimensional granular mixture is
considered to analyze homogeneous steady states. The model includes an
effective mechanism to transfer the kinetic energy injected by vibration in the
vertical direction to the horizontal degrees of freedom of grains. The set of
Enskog kinetic equations for the velocity distribution functions of each
component is derived first to analyze the homogeneous state. As in the
one-component case, an exact scaling solution is found where the time
dependence of the distribution functions occurs entirely through the granular
temperature $T$. As expected, the kinetic partial temperatures $T_i$ of each
component are different and hence, energy equipartition is broken down. In the
steady state, explicit expressions for the temperature $T$ and the ratio of
partial kinetic temperatures $T_i/T_j$ are obtained by considering Maxwellian
distributions defined at the partial temperatures $T_i$. The (scaled) granular
temperature and the temperature ratios are given in terms of the coefficients
of restitution, the solid volume fraction, the (scaled) parameters of the
collisional model, and the ratios of mass, concentration, and diameters. In the
case of a binary mixture, the theoretical predictions are exhaustively compared
with both direct simulation Monte Carlo and molecular dynamics simulations with
a good agreement. The deviations are identified to be originated in the
non-Gaussianity of the velocity distributions and on microsegregation patterns,
which induce spatial correlations not captured in the Enskog theory.
