Mass transport of impurities in a moderately dense granular gas

Abstract

Transport coefficients associated with the mass flux of impurities immersed in a moderately dense granular gas of hard disks or spheres described by the inelastic Enskog equation are obtained by means of the Chapman-Enskog expansion. The transport coefficients are determined as the solutions of a set of coupled linear integral equations recently derived for polydisperse granular mixtures [V. Garzó, J. W. Dufty and C. M. Hrenya, Phys. Rev. E {\bf 76}, 031304 (2007)]. With the objective of obtaining theoretical expressions for the transport coefficients that are sufficiently accurate for highly inelastic collisions, we solve the above integral equations by using the second Sonine approximation. As a complementary route, we numerically solve by means of the direct simulation Monte Carlo method (DSMC) the inelastic Enskog equation to get the kinetic diffusion coefficient $D_0$ for two and three dimensions. We have observed in all our simulations that the disagreement, for arbitrarily large inelasticity, in the values of both solutions (DSMC and second Sonine approximation) is less than 4%. Moreover, we show that the second Sonine approximation to $D_0$ yields a dramatic improvement (up to 50%) over the first Sonine approximation for impurity particles lighter than the surrounding gas and in the range of large inelasticity. The results reported in this paper are of direct application in important problems in granular flows, such as segregation driven by gravity and a thermal gradient. We analyze here the segregation criteria that result from our theoretical expressions of the transport coefficients.

10 figures. to be published in Phys. Rev. E

References in corpus (15)

• Mechanisms in the size segregation of a binary granular mixture
• Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
• Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
• Inherent Rheology of a Granular Fluid in Uniform Shear Flow
• Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
• Energy partition and segregation for an intruder in a vibrated granular system under gravity
• Modified Sonine approximation for the Navier-Stokes transport coefficients of a granular gas
• Breakdown of the Sonine expansion for the velocity distribution of Granular Gases
• Segregation in granular binary mixtures: Thermal diffusion
• Brazil-nut effect versus reverse Brazil-nut effect in a moderately dense granular fluid
• Mass and heat fluxes for a binary granular mixture at low-density
• Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases
• Dynamics of a hard sphere granular impurity
• Effect of inelasticity on the phase transitions of a thin vibrated granular layer
• Modified Sonine approximation for granular binary mixtures

Cited by in corpus (22)

• Thermal diffusion segregation in granular binary mixtures described by the Enskog equation
• Grad's moment method for a granular fluid at moderate densities. Navier-Stokes transport coefficients
• Segregation by thermal diffusion of an intruder in a moderately dense granular fluid
• Enskog kinetic theory for multicomponent granular suspensions
• Instabilities in moderately dense granular binary mixtures
• Steady base states for Navier-Stokes granular hydrodynamics with boundary heating and shear
• Segregation of an intruder in a heated granular dense gas
• Diffusion transport coefficients for granular binary mixtures at low density. Thermal diffusion segregation
• Thermal Segregation Beyond Navier-Stokes
• Diffusion of intruders in granular suspensions: Enskog theory and random walk interpretation
• Steady base states for non-Newtonian granular hydrodynamics
• Stability of freely cooling granular mixtures at moderate densities
• Segregation by thermal diffusion in granular shear flows
• Heat flux of driven granular mixtures at low density. Stability analysis of the homogeneous steady state
• Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture
• Tracer diffusion coefficients in a moderately dense granular suspension. Stability analysis and thermal diffusion segregation
• Thermal segregation of intruders in the Fourier state of a granular gas
• Diffusion of impurities in a moderately dense confined granular gas
• Computer simulations of an impurity in a granular gas under planar Couette flow
• Mobility and diffusion of intruders in granular suspensions. Einstein relation
• Mean square displacement of intruders in freely cooling multicomponent granular mixtures
• Hydrodynamic equations for a granular mixture from kinetic theory - fundamental considerations