Grad's 14-moments model for dense gases of spheres subjected to inelastic collisions

A 14-moments model for a dense granular gas is developed in the context of Grad's theory. The gas consists of spheres subjected to inelastic collisions. This condition implies that the energy is not conserved, but a part of it is transformed into heat and this determines a dissipation of temperature. Furthermore, dense gases are characterized by two phenomena in inelastic collisions: the transfer and the transport of particle properties. The balance laws for mass, momentum, energy, stress tensor, heat flux and the fourth scalar moment are derived. The fluxes and the source terms are computed for each balance equation following the procedures elaborated by J. T. Jenkins and M. W. Richman [Arch. Rational Mech. Anal. 87, 355 - 377 (1985)]. The results are compared with the dilute elastic and inelastic gases. This new set of field equations can be useful in different applications.