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The Boltzmann kinetic theory for a model of a confined quasi-two dimensionalgranular mixture derived previously [Garz\'o, Brito and Soto, Phys. Fluids\textbf{33}, 023310 (2021)] is considered further to analyze two differentproblems. First, a linear stability analysis of the hydrodynamic equations withrespect to the homogeneous steady state (HSS) is carried out to identify theconditions for stability as functions of the wave vector, the coefficients ofrestitution, and the parameters of the mixture. The analysis, which is based onthe results obtained by solving the Boltzmann equation by means of theChapman--Enskog method to first order in spatial gradients, takes into accountthe (nonlinear) dependence of the transport coefficients and the cooling rateon the coefficients of restitution and applies in principle to arbitrary valuesof the concentration, and the mass and diameter ratios. In contrast to theresults obtained in the conventional inelastic hard sphere (IHS) model, theresults show that all the hydrodynamic modes are stable so that, the HSS islinearly \emph{stable} with respect to long enough wavelength excitations. As asecond application, segregation induced by both a thermal gradient and gravityis studied. A segregation criterion based on the dependence of the thermaldiffusion factor $\Lambda$ on the parameter space of the mixture is derived.Comparison with previous results derived from the IHS model is carried out.

Applications of the kinetic theory for a model of a confined quasi-two  dimensional granular mixture: Stability analysis and thermal diffusion  segregation