5 research outputs found
A note on the violation of the Einstein relation in a driven moderately dense granular gas
The Einstein relation for a driven moderately dense granular gas in
-dimensions is analyzed in the context of the Enskog kinetic equation. The
Enskog equation neglects velocity correlations but retains spatial correlations
arising from volume exclusion effects. As expected, there is a breakdown of the
Einstein relation relating diffusion and
mobility , being the temperature of the impurity. The kinetic theory
results also show that the violation of the Einstein relation is only due to
the strong non-Maxwellian behavior of the reference state of the impurity
particles. The deviation of from unity becomes more significant as
the solid volume fraction and the inelasticity increase, especially when the
system is driven by the action of a Gaussian thermostat. This conclusion
qualitatively agrees with some recent simulations of dense gases [Puglisi {\em
et al.}, 2007 {\em J. Stat. Mech.} P08016], although the deviations observed in
computer simulations are more important than those obtained here from the
Enskog kinetic theory. Possible reasons for the quantitative discrepancies
between theory and simulations are discussed.Comment: 6 figure
Non-equilibrium phase transition in a sheared granular mixture
The dynamics of an impurity (or tracer particle) immersed in a dilute
granular gas under uniform shear flow is investigated. A non-equilibrium phase
transition is identified from an exact solution of the inelastic Boltzmann
equation for a granular binary mixture in the tracer limit, where the impurity
carries either a vanishing (disordered phase) or a finite (ordered phase)
fraction of the total kinetic energy of the system. In the disordered phase,
the granular temperature ratio (impurity "temperature" over that of the host
fluid) is finite, while it diverges in the ordered phase. To correctly capture
this extreme violation of energy equipartition, we show that the picture of an
impurity enslaved to the host fluid is insufficient
Transport coefficients for inelastic Maxwell mixtures
The Boltzmann equation for inelastic Maxwell models is used to determine the
Navier-Stokes transport coefficients of a granular binary mixture in
dimensions. The Chapman-Enskog method is applied to solve the Boltzmann
equation for states near the (local) homogeneous cooling state. The mass, heat,
and momentum fluxes are obtained to first order in the spatial gradients of the
hydrodynamic fields, and the corresponding transport coefficients are
identified. There are seven relevant transport coefficients: the mutual
diffusion, the pressure diffusion, the thermal diffusion, the shear viscosity,
the Dufour coefficient, the pressure energy coefficient, and the thermal
conductivity. All these coefficients are {\em exactly} obtained in terms of the
coefficients of restitution and the ratios of mass, concentration, and particle
sizes. The results are compared with known transport coefficients of inelastic
hard spheres obtained analytically in the leading Sonine approximation and by
means of Monte Carlo simulations. The comparison shows a reasonably good
agreement between both interaction models for not too strong dissipation,
especially in the case of the transport coefficients associated with the mass
flux.Comment: 9 figures, to be published in J. Stat. Phy