  The formation of velocity vortices and density clusters is an intriguing
phenomenon of freely cooling granular flows. In this work, the critical length
scale $L_c$ for the onset of instability is determined via stability analysis
of the linearized Navier-Stokes hydrodynamic equations of $d$-dimensional
granular binary mixtures at moderate densities. In contrast to previous
attempts, the analysis is not restricted to nearly elastic systems since it
takes into account the nonlinear dependence of the transport coefficients and
the cooling rate on the collisional dissipation. As expected from previous
results obtained in the very dilute regime, linear stability shows $d-1$
transversal (shear) modes and a longitudinal ("heat") mode to be unstable with
respect to long enough wavelength excitations. The theoretical predictions also
show that the origin of the instability is driven by the transversal component
of the velocity field that becomes \emph{unstable} when the system length
$L>L_c$. An explicit expression of $L_c$ is obtained in terms of the masses and
diameters of the mixture, the composition, the volume fraction and the
coefficients of restitution. Previous results derived in the limit of both
mechanically equivalent particles and low-density mixtures are consistently
recovered. Finally, a comparison with previous theoretical works which neglect
the influence of dissipation on the transport coefficients shows quantitative
discrepancies for strong dissipation.
