  We derive the form of the viscous corrections to the phase-space distribution
function due to the bulk viscous pressure and shear stress tensor using the
iterative Chapman-Enskog method. We then calculate the transport coefficients
necessary for the second-order hydrodynamic evolution of the bulk viscous
pressure and the shear stress tensor. We demonstrate that the transport
coefficients obtained using the Chapman-Enskog method are different than those
obtained previously using the 14-moment approximation for a finite particle
mass. Specializing to the case of boost-invariant and transversally homogeneous
longitudinal expansion, we show that the transport coefficients obtained using
the Chapman-Enskog method result in better agreement with the exact solution of
the Boltzmann equation in the relaxation-time approximation compared to results
obtained in the 14-moment approximation. Finally, we explicitly confirm that
the time evolution of the bulk viscous pressure is significantly affected by
its coupling to the shear stress tensor.
