  The transport coefficients of a dilute gas of inelastic hard spheres immersed
in a molecular gas are determined. We assume that the number density of the
granular gas is much smaller than that of the surrounding molecular gas, so
that the latter is not affected by the presence of solid particles. In this
situation, the molecular gas may be treated as a thermostat (or bath) of
elastic hard spheres at a fixed temperature. This system (granular gas
thermostated by a bath of elastic hard spheres) can be considered as a reliable
model for describing the dynamic properties of particle-laden suspensions. The
Boltzmann kinetic equation is the starting point of the present work. First
step is to characterise the reference state in the perturbation scheme, namely
the homogeneous state. Theoretical results for the granular temperature and
kurtosis obtained in the homogeneous steady state are compared against Monte
Carlo simulations showing a good agreement. Then, the Chapman-Enskog method is
employed to solve the Boltzmann equation to first order in spatial gradients.
As expected, the Navier-Stokes-Fourier transport coefficients of the granular
gas are given in terms of the solutions of a coupled set of linear integral
equations which are approximately solved by considering the leading terms in a
Sonine polynomial expansion. Our results show that the dependence of the
transport coefficients on the coefficient of restitution is quite different
from that found when the influence of the interstitial molecular gas is
neglected (dry granular gas). When the granular particles are much more heavier
than the gas particles (Brownian limit) the expressions of the transport
coefficients are consistent with those previously derived from the
Fokker-Planck equation. Finally, a linear stability analysis of the homogeneous
steady state is performed showing this state is always linearly stable.
