2024/01/08 by Vicente Garzó, Garzó, Vicente, Ricardo Brito +3 · 1 citation
Engineering · Materials Science · Mathematics · #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Material Dynamics and Properties #Particle Dynamics in Fluid Flows #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2401.03822
openalex publication_date 2024/01/08 · openalex created_date 2024/01/13 · openalex updated_date 2026/07/28
The Boltzmann kinetic theory for a model of a confined quasi-two dimensional granular mixture derived previously [Garzó, Brito and Soto, Phys. Fluids 33, 023310 (2021)] is considered further to analyze two different problems. First, a linear stability analysis of the hydrodynamic equations with respect to the homogeneous steady state (HSS) is carried out to identify the conditions for stability as functions of the wave vector, the coefficients of restitution, and the parameters of the mixture. The analysis, which is based on the results obtained by solving the Boltzmann equation by means of the Chapman--Enskog method to first order in spatial gradients, takes into account the (nonlinear) dependence of the transport coefficients and the cooling rate on the coefficients of restitution and applies in principle to arbitrary values of the concentration, and the mass and diameter ratios. In contrast to the results obtained in the conventional inelastic hard sphere (IHS) model, the results show that all the hydrodynamic modes are stable so that, the HSS is linearly stable with respect to long enough wavelength excitations. As a second application, segregation induced by both a thermal gradient and gravity is studied. A segregation criterion based on the dependence of the thermal diffusion factor Λ on the parameter space of the mixture is derived. Comparison with previous results derived from the IHS model is carried out.