  Nematic ordering describes the phenomenon where anisotropic molecules tend to
locally align, like matches in a matchbox. This ordering can arise in solids
(as nematic elastomers), liquids (as liquid crystals), and in gases. In the
1940s, Onsager described how nematic ordering can arise in dilute colloidal
suspensions from the molecular point of view. However, the kinetic theory of
nonspherical molecules has not, thus far, accounted for phenomena relating to
the presence of nematic ordering.
  In this work we develop a kinetic theory for the behavior of rarified
calamitic (rodlike) gases in the presence of nematic ordering. Building on
previous work by Curtiss, we derive from kinetic theory the rate of work
hypothesis that forms the starting point for Leslie--Ericksen theory. We
incorporate ideas from the variational theory of nematic liquid crystals to
create a moment closure that preserves the coupling between the laws of linear
and angular momentum. The coupling between these laws is a key feature of our
theory, in contrast to the kinetic theory proposed by {Curtiss \& Dahler},
where the couple stress tensor is assumed to be zero. This coupling allows the
characterization of anisotropic phenomena arising from the nematic ordering.
Furthermore, the theory leads to an energy functional that is a compressible
variant of the classical Oseen--Frank energy (with a pressure-dependent Frank
constant) and to a compressible analogue of the Leslie--Ericksen equations. The
emergence of compressible aspects in the theory for nematic fluids enhances our
understanding of these complex systems.
