Steady state velocity distributions of an oscillated granular gas

Abstract

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 35 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 distribution function of horizontal velocities (scaled by the local horizontal temperature) is found to be nearly independent of height, even though the hydrodynamic fields vary with height. The high energy tails of the distribution functions are described by a stretched exponential $\sim \exp (-\mathcal{B}{c}_x^{\alpha })$, where $\alpha$ depends on the normal coefficient of restitution $e$ ($1.2<\alpha <1.6$), but $\alpha$ does not vary for a wide range of the friction parameter. We find that the distribution function of a {\it 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.

arXiv commentsubmitted to Phys. Rev. E; to appear after a few more small changes

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• Role of friction in pattern formation in oscillated granular layers
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• Sonine approximation for collisional moments of granular gases of inelastic rough spheres
• Orientational correlation and velocity distributions in uniform shear flow of a dilute granular gas
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• Simulations of dense granular gases without gravity with impact-velocity-dependent restitution coefficient
• Energy distribution and effective temperatures in a driven dissipative model
• Equilibrium statistics of an inelastically bouncing ball, subject to gravity and a random force
• Velocity Distribution in a Viscous Granular Gas
• Tuning the distance to the equipartition by controlling the collision rate in a driven granular gas experiment