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The hydrodynamic conservation equations and constitutive relations for a binary granular mixture composed of smooth, nearly elastic spheres with nonequipartition 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 stressstrain 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.

The free path of a vibro-fluidized two-dimensional (2D) inelastic granular gas confined in a rectangular box is investigated by 2D event-driven molecular simulation. By tracking particles in the simulation, we analyze the local free path. The probability distribution of the free path shows a high tail deviating from the exponential prediction. The anisotropy of the free path is found when we separate the free path to x and y components. The probability distribution of y component is exponential, while x component has a high tail. The probability distribution of angle between the relative velocity and the unit vector joined two particle centers deviates from the distribution of two random vectors, indicating the existence of the dynamic heterogeneities in our system. We explain these results by resorting to the kinetic theory with two-peak velocity distribution. The kinetic theory agrees well with the simulation result.

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