Inelastic gas: An experimental study of vibro-fluidized dilute granular media
We conduct an experimental study of a two dimensional vibro-fluidized dilute granular medium. The system is composed of spherical beads confined to move in a vertical plane and excited by intense vertical vibrations. We perform full-field tracking of positions and orientations of the spheres by high speed photography. In steady-state, the motion of the grains resembles that of a molecular gas, thus the name granular gas.
We study the distribution of linear velocities in the granular gas. The investigation shows that the distributions are non-gaussian, best fitted by the function P(v) ∼ exp(−β| v|/σ)1.5), and insensitive to number density, driving parameters and particle inelasticity. The distribution is a one parameter distribution, parameterized by the mean square velocity; which defines a granular temperature. T = 1⁄2 ⟨v 2⟩.
We study binary mixtures of the granular media. We find that, in general, the granular temperature is not equal for the two types of spheres. However, the temperature ratio is constant in the bulk. The ratio depends strongly on the mass ratio of the spheres, but not on their inelasticity. The ratio is also insensitive to compositional parameters of the mixture such as number fraction and number density.
We also investigate the statistics of the power flux into a subsystem of the granular gas. The power shows large fluctuations, including frequent large negative fluctuations. The relative probabilities of positive and negative fluctuations in the power flux are in close accord with the Fluctuation Theorem of Gallavotti and Cohen (Gallavotti & Cohen, 1995b). We also compare the effective temperature that emerges from this analysis to the kinetic granular temperature.
Finally, we study the rotational dynamics of the granular gas. We find that the granular temperature is not equipartitioned between translational and rotational degrees of freedom. We also demonstrate that the ratio of rotational to translational energy is independent of the vibration intensity and concentration of particles, if we isolate the component of rotational energy that is fed only by inter-particle collisions.