  The objective of this study is to assess the impact of a dense-phase
treatment on the hydrodynamic description of granular, binary mixtures relative
to a previous dilute-phase treatment. Two theories were considered for this
purpose. The first, proposed by Garz\'o and Dufty (GD) [Phys. Fluids {\bf 14},
146 (2002)], is based on the Boltzmann equation which does not incorporate
finite-volume effects, thereby limiting its use to dilute flows. The second,
proposed by Garz\'o, Hrenya and Dufty (GHD) [Phys. Rev. E {\bf 76}, 31303 and
031304 (2007)], is derived from the Enskog equation which does account for
finite-volume effects; accordingly this theory can be applied to moderately
dense systems as well. To demonstrate the significance of the dense-phase
treatment relative to its dilute counterpart, the ratio of dense (GHD) to
dilute (GD) predictions of all relevant transport coefficients and equations of
state are plotted over a range of physical parameters (volume fraction,
coefficients of restitution, material density ratio, diameter ratio, and
mixture composition). These plots reveal the deviation between the two
treatments, which can become quite large ($>$100%) even at moderate values of
the physical parameters. Such information will be useful when choosing which
theory is most applicable to a given situation, since the dilute theory offers
relative simplicity and the dense theory offers improved accuracy. It is also
important to note that several corrections to original GHD expressions are
presented here in the form of a complete, self-contained set of relevant
equations.
