Steady-state velocity distributions of an oscillated granular gas

We use a three-dimensional molecular dynamics simulation to study the single particle distribution function of a dilute granular gas driven by a vertically oscillating plate at high accelerations (15g–90g). We find that the density and the temperature fields are essentially time-invariant above a height of about 40 particle diameters, where typically 20% of the grains are contained. These grains form the nonequilibrium steady-state granular gas with a Knudsen number unity or greater. In the steady-state region, the probability distribution function of the horizontal velocity c_x (scaled by the local horizontal temperature) is found to be nearly independent of height, even though the hydrodynamic fields vary with height. We find that the high energy tails of the distribution function are described by a stretched exponential ∼exp(-Bc_x^α), where α depends on the restitution coefficient e and falls in the range 1.2<α<1.6. However, α does not vary significantly for a wide range of friction coefficient values. We find that the distribution function of a frictionless inelastic hard sphere model can be made similar to that of a frictional model by adjusting e. However, there is no single value of e that mimics the frictional model over a range of heights.