Diffusion of impurities in a moderately dense confined granular gas

Abstract

Mass transport of impurities immersed in a confined quasi-two-dimensional moderately dense granular gas of inelastic hard spheres is studied. The effect of the confinement on granular particles is modeled through a collisional model (the so-called $\Delta$-model) that includes an effective mechanism to transfer the kinetic energy injected by vibration in the vertical direction to the horizontal degrees of freedom of grains. The impurity can differ in mass, diameter, inelasticity, or the energy injection at collisions, compared to the gas particles. The Enskog--Lorentz kinetic equation for the impurities is solved via the Chapman--Enskog method to first order in spatial gradients for states close to the homogeneous steady state. As usual, the three diffusion transport coefficients for tracer particles in a mixture are given in terms of the solutions of a set of coupled linear integral equations which are solved by considering the lowest Sonine approximation. The theoretical predictions for the tracer diffusion coefficient (relating the mass flux with the gradient of the number density of tracer particles) are compared with both direct simulation Monte Carlo and molecular dynamics simulations. The agreement is in general good, except for strong inelasticity and/or large contrast of energy injection at tracer-gas collisions compared to gas-gas collisions. Finally, as an application of our results, the segregation problem induced by both a thermal gradient and gravity is exhaustively analyzed.

arXiv comment26 pages, 12 figures, to be published in Physics of Fluids

References in corpus (46)

• Clustering, Order, and Collapse in a Driven Granular Monolayer
• The Reverse Brazil Nut Problem: Competition between Percolation and Condensation
• Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
• Kinetic Temperatures for a Granular Mixture
• Hydrodynamics for a granular binary mixture at low density
• Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
• Transient structures in a Granular Gas
• Non-equilibrium two-phase coexistence in a confined granular layer
• Energy partition and segregation for an intruder in a vibrated granular system under gravity
• The dynamics of thin vibrated granular layers
• Hydrodynamics and transport coefficients for Granular Gases
• Segregation in a fluidized binary granular mixture: Competition between buoyancy and geometric forces
• Segregation induced by inelasticity in a vibrofluidized granular mixture
• Diffusion of impurities in a granular gas
• Brazil-nut effect versus reverse Brazil-nut effect in a moderately dense granular fluid
• Segregation in granular binary mixtures: Thermal diffusion
• Hydrodynamic modes in a confined granular fluid
• Intermediate regimes in granular Brownian motion: Superdiffusion and subdiffusion
• Mass and heat fluxes for a binary granular mixture at low-density
• Thermal diffusion segregation in granular binary mixtures described by the Enskog equation
• Mass transport of impurities in a moderately dense granular gas
• Segregation by thermal diffusion of an intruder in a moderately dense granular fluid
• Hydrodynamic profiles for an impurity in a open vibrated granular gas
• Velocity distribution function and effective constant restitution coefficient for granular gas of viscoelastic particles
• Hydrodynamics for a model of a confined quasi-two-dimensional granular gas
• Enskog kinetic theory for a model of a confined quasi-two-dimensional granular fluid
• Quasi-crystalline order in vibrated granular matter
• The homogeneous steady state of a confined granular gas
• Stability analysis of the homogeneous hydrodynamics of a model for a confined granular gas
• Kinetic Theory and Hydrodynamics of Dense, Reacting Fluids far from Equilibrium
• Segregation of an intruder in a heated granular dense gas
• Shear viscosity of a model for confined granular media
• Understanding the instability of a vibrated granular monolayer
• Enhancing (quasi-)long-range order in a two-dimensional driven crystal
• Effective two-dimensional model for granular matter with phase separation
• Homogeneous hydrodynamics of a collisional model of confined granular gases
• Interplay between an absorbing phase transition and synchronization in a driven granular system
• Energy nonequipartition in a collisional model of a confined quasi-two-dimensional granular mixture
• Diffusion transport coefficients for granular binary mixtures at low density. Thermal diffusion segregation
• Kinetic theory of a confined quasi-one-dimensional gas of hard disks
• Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture
• Dynamics of an inelastic tagged particle under strong confinement
• Attractor non-equilibrium stationary states in perturbed long-range interacting systems
• Tracer diffusion coefficients in a moderately dense granular suspension. Stability analysis and thermal diffusion segregation
• Confined granular gases under the influence of vibrating walls
• Stability of the homogeneous steady state for a model of a confined quasi-two-dimensional granular fluid

Cited by in corpus (4)

• Non-equilibrium coexistence between a fluid and a hotter or colder crystal of granular hard disks
• 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
• Kinetic Theory of Chiral Active Disks: Odd Transport and Torque Density