Vicente Garzó (University of Extremadura, Spain)

Enskog kinetic theory for monodisperse granular gases

Under rapid flow conditions, it is well known that many features of granular media can be modeled by a fluid of smooth hard spheres with inelastic collisions. In the rapid flow regime, the sample of grains resembles a granular gas or fluid so that binary collisions prevail and kinetic theory tools can be a quite useful tool to analyze granular flows. This talk provides a concise introduction to the Enskog kinetic equation of granular gases at moderate densities. The Enskog equation is first heuristically derived for smooth monocomponent granular gases. Then, a connection with hydrodynamics is established where the corresponding macroscopic balance equations for the densities of mass, momentum and energy are exactly derived from the above kinetic equation with expressions for the momentum and heat fluxes and the cooling rate as functionals of the one-particle velocity distribution function. Given that the hydrodynamic equations do not constitute a closed set of equations, constitutive equations for the fluxes and the cooling rate are derived by solving the Enskog equation by means of the Chapman-Enskog method to first order in the spatial gradients. The corresponding Navier-Stokes transport coefficients are determined from the solution to a set of coupled linear integral equations analogous to those for elastic collisions. These integral equations are solved by using different approximate methods that yield explicit expressions for the transport coefficients in terms of the coefficient of restitution and the solid volume fraction. The theoretical results are confronted against computer simulations results performed by several research groups. The comparison shows in general good agreement even for conditions of strong collisional dissipation and moderate densities. The talk ends offering several interesting applications of the Enskog kinetic theory.