Transport coefficients for driven granular mixtures at low-density

Abstract

The transport coefficients of a granular binary mixture driven by a stochastic bath with friction are determined from the inelastic Boltzmann kinetic equation. A normal solution is obtained via the Chapman-Enskog method for states near homogeneous steady states. The mass, momentum, and heat fluxes are determined to first order in the spatial gradients of the hydrodynamic fields, and the associated transport coefficients are identified. They are given in terms of the solutions of a set of coupled linear integral equations. As in the monocomponent case, since the collisional cooling cannot be compensated locally for by the heat produced by the external driving, the reference distributions (zeroth-order approximations) $f_i^{(0)}$ ($i=1,2$) for each species depend on time through their dependence on the pressure and the temperature. Explicit forms for the diffusion transport coefficients and the shear viscosity coefficient are obtained by assuming the steady state conditions and by considering the leading terms in a Sonine polynomial expansion. A comparison with previous results obtained for granular Brownian motion and by using a (local) stochastic thermostat is also carried out. The present work extends previous theoretical results derived for monocomponent dense gases [V. Garzó, M. G. Chamorro, and F. Vega Reyes, Phys. Rev. E \textbf{87}, 032201 (2013)] to granular mixtures at low density.

7 figures, to be published in Phys. Rev. E

References in corpus (14)

• Stationary state volume fluctuations in a granular medium
• Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
• Approach to jamming in an air-fluidized granular bed
• Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
• Granular Brownian motion
• 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
• Fluctuation-Dissipation relation in sub-diffusive systems: the case of granular single-file
• Universal reference state in a driven homogeneous granular gas
• Navier-Stokes transport coefficients of $d$-dimensional granular binary mixtures at low density
• Theory of thermostatted inhomogeneous granular fluids: a self-consistent density functional description
• Segregation of an intruder in a heated granular dense gas
• Long-range interactions in randomly driven granular fluids

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• Homogeneous states in driven granular mixtures: Enskog kinetic theory versus molecular dynamics simulations
• Kinetic theory of granular particles immersed in a molecular gas
• Energy nonequipartition in a collisional model of a confined quasi-two-dimensional granular mixture
• Transport coefficients for granular suspensions at moderate densities
• The BBGKY Hierarchy and Fokker-Planck Equation for Many-Body Dissipative Randomly Driven Systems
• Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture
• Influence of the first-order contributions to the partial temperatures on transport properties in polydisperse dense granular mixtures
• 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
• Generalized time evolution of the homogeneous cooling state of a granular gas with positive and negative coefficient of normal restitution
• Influence of a drag force on linear transport in low-density gases. Stability analysis
• Rheology of a dilute binary mixture of inertial suspension under simple shear flow
• Heat flux of a granular gas with homogeneous temperature
• Enskog kinetic theory of binary granular suspensions: heat flux and stability analysis of the homogeneous steady state
• Shear-rate dependent transport coefficients in granular suspensions
• Kinetic theory of polydisperse granular mixtures: influence of the partial temperatures on transport properties. A review