Vicente Garzó (University of Extremadura, Spain)

Transport properties in driven granular mixtures at low density. some application

A well established model for a granular gas is a system constituted by smooth hard spheres or disks with inelastic collisions. Since the energy monotonically decays in time, one needs to inject external energy into the system to keep it under rapid flow conditions. In real experiments, the external energy is provided to the granular gas from the boundaries or by the presence of the interstitial fluid surrounding them. When this external energy compensates for the energy dissipated by collisions, a nonequilibrium steady state is achieved. However, when the granular gas is locally driven, strong spatial gradients appear in the bulk domain and hence, the usual Navier--Stokes (NS) hydrodynamic equations do not apply. Thus, to avoid the difficulties associated with the theoretical description of far from equilibrium states, it is usual in computer simulations to drive the gas by means of external nonconservative forces or thermostats. An interesting and reliable model to fluidize a granular gas is by means of an external force composed by two terms: (i) a drag force proportional to the velocity of the solid particles and (ii) a stochastic force (Langevin-like model) where the particles are randomly accelerated between collisions. While the drag force mimics the friction of grains with the viscous surrounding fluid, the stochastic term models the transfer of energy from the interstitial fluid to the grains. In this talk, we will extend first the above model to the case of driven granular mixtures described by the Boltzmann kinetic equation. Then, some dynamic properties of the homogeneous steady state (HSS) will be theoretically obtained and compared against computer simulations. Once the HSS is well characterized, the Navier-Stokes transport coefficients will be determined by solving the Boltzmann equation by means of the Chapman-Enskog method. Finally, the stability of the HSS will be analyzed.