Non-Equilibrium Velocity Statistics in Vibrated Binary Granular Gases: Anisotropic Distributions and Inelastic Collision Effects

We explore the velocity distributions in a vibrated binary granular gas system, focusing on how these distributions are influenced by the coefficient of restitution (CoR) and the inelasticity of particle collisions. The system consists of a binary mixture of particles with equal number fractions and identical densities, resulting in a dilute overall particle volume fraction. Through molecular dynamics simulations, we examine the system's behavior for a range of CoR values below unity and track the evolution of velocity distributions as the system approaches a non-equilibrium steady state. Our findings reveal significant directional anisotropy, particularly along the vibration axis, with component-wise distributions showing distinct deviations from the classical Maxwell-Boltzmann distribution. Statistical analysis reveals enhanced high-velocity tails, positive kurtosis values, and rightward skewness, confirming the non-equilibrium nature of the steady state. These deviations become more pronounced as CoR decreases, with the system rapidly evolving toward a consistent pattern of central depletion and tail enhancement relative to equilibrium statistics. The observed behavior underscores the intricate dynamics inherent in inelastic collisions and highlights the significance of particle inelasticity in determining the system's velocity distributions. These results provide valuable insights into the complex interplay between energy injection and dissipation in vibrated granular systems, offering improved predictive frameworks for velocity distributions that account for directional anisotropy and non-Maxwellian behavior, with direct applications to industrial processes involving mixing, segregation, and transport of granular materials.