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 (${\alpha }_{ij}\ge 0.7$) and moderate solid volume fractions ($\varphi \le 0.2$). 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.

5 pages, 3 figures; to be published in Phys. Rev. E as a Rapid Communication

References in corpus (5)

• Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
• Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
• Energy decay in three-dimensional freely cooling granular gas
• Energy Loss at Propagating Jamming Fronts in Granular Gas Clusters
• Segregation of an intruder in a heated granular dense gas

Cited by in corpus (18)

• Kinetic theory of shear thickening for a moderately dense gas-solid suspension: from discontinuous thickening to continuous thickening
• Enskog kinetic theory for multicomponent granular suspensions
• Enskog kinetic theory for a model of a confined quasi-two-dimensional granular fluid
• Homogeneous states in driven granular mixtures: Enskog kinetic theory versus molecular dynamics simulations
• Enskog kinetic theory of rheology for a moderately dense inertial suspension
• Transport coefficients of solid particles immersed in a viscous gas
• Impact of roughness on the instability of a free-cooling granular gas
• Energy nonequipartition in a collisional model of a confined quasi-two-dimensional granular mixture
• Transport coefficients for granular suspensions at moderate densities
• Stability of freely cooling granular mixtures at moderate densities
• Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture
• Heat flux of driven granular mixtures at low density. Stability analysis of the homogeneous steady state
• Tracer diffusion coefficients in a moderately dense granular suspension. Stability analysis and thermal diffusion segregation
• Assessment of kinetic theories for moderately dense granular binary mixtures: Shear viscosity coefficient
• Enskog kinetic theory of binary granular suspensions: heat flux and stability analysis of the homogeneous steady state
• Transport properties in a model of confined granular mixtures at moderate densities
• Diffusion of intruders in a granular gas thermostatted by a bath of elastic hard spheres
• Instabilities in granular gas-solid flows