Thermal segregation beyond Navier-Stokes

A dilute suspension of impurities in a low-density gas is described by the Boltzmann and Boltzman-Lorentz kinetic theories. Scaling forms for the species distribution functions allow the determination of the space dependence of the hydrodynamic fields without restriction to small thermal gradients or Navier-Stokes hydrodynamics. The thermal diffusion factor characterizing segregation is identified in terms of collision integrals as a function of the mechanical properties of the particles and the temperature gradient. An evaluation of the collision integrals using Sonine polynomial approximations is discussed. The conditions for segregation both along and opposite to the temperature gradient are obtained and contrasted with the leading order Navier-Stokes approximation.