  Hydrodynamic equations for a binary mixture of inelastic hard spheres are
derived from the Boltzmann kinetic theory. A normal solution is obtained via
the Chapman-Enskog method for states near the local homogeneous cooling state.
The mass, heat, and momentum fluxes are determined to first order in the
spatial gradients of the hydrodynamic fields, and the associated transport
coefficients are identified. In the same way as for binary mixtures with
elastic collisions, these coefficients are determined from a set of coupled
linear integral equations. Practical evaluation is possible using a Sonine
polynomial approximation, and is illustrated here by explicit calculation of
the relevant transport coefficients: the mutual diffusion, the pressure
diffusion, the thermal diffusion, the shear viscosity, the Dufour coefficient,
the thermal conductivity, and the pressure energy coefficient. All these
coefficients are given in terms of the restitution coefficients and the ratios
of mass, concentration, and particle sizes. Interesting and new effects arise
from the fact that the reference states for the two components have different
partial temperatures, leading to additional dependencies of the transport
coefficients on the concentration. The results hold for arbitrary degree of
inelasticity and are not limited to specific values of the parameters of the
mixture. Applications of this theory will be discussed in subsequent papers.
