Granular Gaseous Flows: A Kinetic Theory Approach to Granular Gaseous Flows

1. Kinetic theory of inelastic hard spheres.- Introduction.- Enskog kinetic equation for granular gases at moderate densities . Macroscopic balance equations.- Chapman-Enskog expansion.- Enskog kinetic equation for granular mixtures. Low-density regime.- Kinetic models for simple and multicomponent granular gases.- 2. Homogeneous cooling states (HCS).- One-particle distribution function: scaling solution.- Sonine polynomial expansion: fourth cumulant of the distribution function.- Granular mixtures: energy nonequipartition.- Fourth cumulant of the distribution function of each species.- Driven granular mixtures.- 3. Navier-Stokes transport coefficients for simple granular gases.- Navier-Stokes hydrodynamics equations.- First-order Chapman-Enskog solution. Integral equations defining the transport coefficients.- Sonine polynomial approximations.- Shear and bulk viscosities coefficients.- Thermal conductivity coefficient and the Dufour-like transport coefficient.- Modified Sonine approximation.- Stability of the linearized hydrodynamic equations. Dispersion relations.- 4. Navier-Stokes transport coefficients for multicomponent granular gases.- Navier-Stokes hydrodynamics equations for granular mixtures.- Sonine polynomial approximations.- Transport coefficients. Comparison with computer simulations.- Onsager's reciprocal relations.- Linearized hydrodynamic equations and stabiltiy.- Einstein relation.- Thermal diffusion segregation.- 5. Non-Newtonian steady states for granular gases.- Simple shear flow. Rheological properties.- Energy nonequipartition under shear flow.- Nonlinear Couette flows. Grad's moment method and kinetic models.- Transport near steady shear flow states.- Stability. 6. Inelastic Maxwell models for granular gases.- Introduction.- Collisional moments.- Navier-Stokes hydrodynamic description.- Uniform shear flow (USF).- Small spatial perturbations around the USF.- Intruder in a granular sheared mixture: a new non-equilibrium phase transition.- 7. Transport coefficients for granular gas-solid flows.- Introduction.- Enskog kinetic equation for monodisperse gas-solid flows.- Navier-Stokes transport coefficients. Stability.- Non-Newtonian hydrodynamics for a dilute granular suspension under USF.- Boltzmann kinetic equation for multicomponent gas-solid flows.- Stability.-Onsager's reciprocal relations.