Divergence of the Chapman-Enskog expansion

The Chapman-Enskog expansion for a fluid in uniform shear flow is investigated with use of a Bhatnagar-Gross-Krook model for the nonlinear Boltzmann equation. It is shown that an expansion of the pressure tensor in powers of the uniformity parameter (the shear rate) about the origin does not converge for hard spheres. However, a convergent expansion about the point at infinity can be used to establish that this Chapman-Enskog expansion is asymptotic. (Author)