  Mass transport of a driven granular binary mixture is analyzed from the
inelastic Boltzmann kinetic equation for inelastic Maxwell models (IMM). The
mixture is driven by a thermostat constituted by two terms: a stochastic force
and a drag force proportional to the particle velocity. The combined action of
both forces attempts to mimic the interaction of solid particles with the
interstitial surrounding gas. As with ordinary gases, the use of IMM allows us
to exactly evaluate the velocity moments of the Boltzmann collision operator
and so, it opens up the possibility of obtaining the exact forms of the
Navier--Stokes transport coefficients of the granular mixture. In this work,
the diffusion coefficients associated with the mass flux are explicitly
determined in terms of the parameters of the mixture. As a first step, the
steady homogeneous state reached by the system when the energy lost by
collisions is compensated for by the energy injected by the thermostat is
addressed. In this steady state, the ratio of kinetic temperatures are
determined and compared against molecular dynamics simulations for inelastic
hard spheres (IHS). The comparison shows an excellent agreement, even for
strong inelasticity and/or disparity in masses and diameters. As a second step,
the set of kinetic equations for the mixture is solved by means of the
Chapman-Enskog method for states near homogeneous steady states. In the
first-order approximation, the mass flux is obtained and the corresponding
diffusion transport coefficients identified. The results show that the
predictions for IMM obtained in this work coincide with those previously
derived for IHS in the first-Sonine approximation when the non-Gaussian
corrections to the zeroth-order approximation are neglected.
