Kinetic theory of binary particles with unequal mean velocities and non-equipartition energies

The hydrodynamic conservation equations and constitutive relations for a binary granular mixture composed of smooth, nearly elastic 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 particles. The collision components of the stress tensor and the other parameters are calculated from the zeroth- and first-order approximation. Our results demonstrate that three factors, namely the differences between two granular masses, temperatures and mean velocities all play important roles in the stress-strain relation of the binary mixture, indicating that the assumption of energy equipartition and the same mean velocity may not be acceptable. The collision frequency and the solid viscosity increase monotonously with each granular temperature. The zeroth-order approximation to the energy dissipation varies greatly with the mean velocities of both species of spheres, reaching its peak value at the maximum of their relative velocity.