Instabilities in moderately dense granular binary mixtures

Abstract

A linear stability analysis of the Navier-Stokes (NS) granular hydrodynamic equations is performed to determine the critical length scale for the onset of vortices and clusters instabilities in granular dense binary mixtures. In contrast to previous attempts, our results (which are based on the solution to the inelastic Enskog equation to NS order) are not restricted to nearly elastic systems since they take into account the complete nonlinear dependence of the NS transport coefficients on the coefficients of restitution $\alpha_{ij}$. The theoretical predictions for the critical length scales are compared to molecular dynamics (MD) simulations in flows of strong dissipation ($\alpha_{ij}\geq 0.7$) and moderate solid volume fractions ($\phi\leq 0.2$). We find excellent agreement between MD and kinetic theory for the onset of velocity vortices, indicating the applicability of NS hydrodynamics to polydisperse flows even for strong inelasticity, finite density, and particle dissimilarity.