  A steady self-diffusion process in a gas of hard spheres at equilibrium is
analyzed. The system exhibits a constant gradient of labeled particles. Neither
the concentration of these particles nor its gradient are assumed to be small.
It is shown that the Boltzmann-Enskog kinetic equation has an exact solution
describing the state. The hydrodynamic transport equation for the density of
labeled particles is derived, with an explicit expression for the involved
self-diffusion transport coefficient. Also an approximated expression for the
one-particle distribution function is obtained. The system does not exhibit any
kind of rheological effects. The theoretical predictions are compared with
numerical simulations using the direct simulation Monte Carlo method and a
quite good agreement is found.
