  We present the perturbative solution of the multicomponent Boltzmann kinetic
equation based on the set of observables including the hydrodynamic velocity
and temperature for each component. The solution is obtained by modifying the
formal density scaling scheme by Enskog, such that the density of each
component is scaled independently. As a result we obtain the species momentum
and energy balance equations with the source terms describing the transfer of
corresponding quantities between different components. In the zero order
approximation those are the Euler equations with the momentum and heat
diffusion included in the form of the classical Maxwell-Stefan diffusion terms.
The first order approximation results in equations of a Navier-Stokes type with
the partial viscosity and heat conductivity including only the correlations of
the particles of the same component. The first order corrections to the
Maxwell-Stefan terms as well as the contributions bilinear in gradients and
differences of observables are calculated. The first order momentum source term
is shown to include thermal diffusion. The nondiagonal (in component indexes)
components of viscosity and heat conductivity appear as second order
contributions.
