Hydrodynamics for a granular binary mixture at low density

The Boltzmann equation for inelastic Maxwell models is used to analyze nonlinear transport in a granular binary mixture in the steady simple shear flow. Two different transport processes are studied. First, the rheological properties (shear and normal stresses) are obtained by solving exactly the velocity moment equations. Second, the diffusion tensor of impurities immersed in a sheared inelastic Maxwell gas is explicitly determined from a perturbation solution through first ...

Two different kinetic theories [J. Solsvik and E. Manger (SM-theory), Phys. Fluids \textbf{33}, 043321 (2021) and V. Garz\'o, J. W. Dufty, and C. M. Hrenya (GDH-theory), Phys. Rev. E \textbf{76}, 031303 (2007)] are considered to determine the shear viscosity $\eta$ for a moderately dense granular binary mixture of smooth hard spheres. The mixture is subjected to a simple shear flow and heated by the action of an external driving force (Gaussian thermostat) that exactly compen...

The rheology of a dilute binary mixture of inertial suspension under simple shear flow is analyzed in the context of the Boltzmann kinetic equation. The effect of the surrounding viscous gas on the solid particles is accounted for by means of a deterministic viscous drag force plus a stochastic Langevin-like term defined in terms of the environmental temperature $T_\text{env}$. Grad's moment method is employed to determine the temperature ratio and the pressure tensor in term...

The Navier--Stokes order hydrodynamic equations for a low-density driven granular mixture obtained previously [Khalil and Garz\'o, Phys. Rev. E \textbf{88}, 052201 (2013)] from the Chapman--Enskog solution to the Boltzmann equation are considered further. The four transport coefficients associated with the heat flux are obtained in terms of the mass ratio, the size ratio, composition, coefficients of restitution, and the driven parameters of the model. Their quantitative vari...

The Navier-Stokes transport coefficients of a granular gas are obtained from the Chapman-Enskog solution to the Boltzmann equation. The granular gas is heated by the action of an external driving force (thermostat) which does work to compensate for the collisional loss of energy. Two types of thermostats are considered: (a) a deterministic force proportional to the particle velocity (Gaussian thermostat), and (b) a random external force (stochastic thermostat). As happens in ...

We study the transport properties of an impurity in a sheared granular gas, in the framework of the Boltzmann equation for inelastic Maxwell models. We investigate here the impact of a nonequilibrium phase transition found in such systems, where the tracer species carries a finite fraction of the total kinetic energy (ordered phase). To this end, the diffusion coefficients are first obtained for a granular binary mixture in spatially inhomogeneous states close to the simple s...

The Boltzmann kinetic theory for a model of a confined quasi-two dimensional granular mixture derived previously [Garz\'o, Brito and Soto, Phys. Fluids \textbf{33}, 023310 (2021)] is considered further to analyze two different problems. First, a linear stability analysis of the hydrodynamic equations with respect to the homogeneous steady state (HSS) is carried out to identify the conditions for stability as functions of the wave vector, the coefficients of restitution, and t...

In the present work, we calculate the transport coefficients for a relativistic binary mixture of diluted gases of hard-sphere particles. The gas mixture under consideration is studied within the relativistic Boltzmann equation in the presence of a gravitational field described by the isotropic Schwarzschild metric. We obtain the linear constitutive equations for the thermodynamic fluxes. The driving forces for the fluxes of particles and heat will appear with terms proportio...

An isolated mixture of smooth, inelastic hard spheres supports a homogeneous cooling state with different kinetic temperatures for each species. This phenomenon is explored here by molecular dynamics simulation of a two component fluid, with comparison to predictions of the Enskog kinetic theory. The ratio of kinetic temperatures is studied for two values of the restitution coefficient, $\alpha =0.95$ and 0.80, as a function of mass ratio, size ratio, composition, and density...

The hydrodynamic conservation equations and constitutive relations for a binary granular mixture composed of smooth, nearly elastic, hard spheres with non-equipartition energies and different mean velocities are derived. This research is aimed to build three-dimensional kinetic theory to characterize the behaviors of two species of particles suffering different forces. The standard Enskog method is employed assuming a Maxwell velocity distribution for each species of particle...