Velocity statistics of a uniformly heated granular fluid

We report results from an experimental investigation of a uniformly heated granular fluid. We vertically vibrate an ensemble of spheres (diameter $D$) confined by two horizontal glass plates. The top and bottom plates are separated by $1.6D$ which ensures a quasi-two dimensional configuration. We show that the use a rough, instead of flat, bottom plate has the considerable advantage of a more effective transfer of momentum from the vertical mode of the cell's vibration onto the motion of individual spheres in the horizontal plane. This allows a greater range of cell's filling fraction, $\phi$, to be explored. We study the single particle velocity distributions, $f(c)$, as a function of $\phi$ and vibration parameters; frequency and amplitude. In agreement with previous studies, we find a consistent overpopulation in the distribution's high energy tails, of the form $\log f \sim -c^{3/2}$. Moreover, we calculate the deviations from a Mawellian, $\Delta(c)=f(c)/f_{MB}(c)-1$, where $f_{MB}\sim\exp(-c^2)$. We find $\Delta(c)$ to be well described by a 4th-order polynomial which, however, is not the Sonine polynomial commonly used in the solution of the Enskog-Boltzmann equation for inelastic hard spheres driven by a stochastic thermostat.