Structure factors in granular experiments with homogeneous fluidization

Velocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi-2d fluidized granular experiment, with packing fractions $\phi\in[10%,40%]$. The fluidization is realized by vertically vibrating a rough plate, on top of which particles perform a Brownian-like horizontal motion in addition to inelastic collisions. On one hand, the density structure factor is equal to that of elastic hard spheres, except in the limit of large length-scales, as it occurs in the presence of an effective interaction. On the other hand, the velocity field shows a more complex structure which is a genuine expression of a non-equilibrium steady state and which can be compared to a recent fluctuating hydrodynamic theory with non-equilibrium noise. The temporal decay of velocity modes autocorrelations is compatible with linear hydrodynamic equations with rates dictated by viscous momentum diffusion, corrected by a typical interaction time with the thermostat. Equal-time velocity structure factors display a peculiar shape with a plateau at large length-scales and another one at small scales, marking two different temperatures: the "bath" temperature $T_b$, depending on shaking parameters, and the "granular" temperature $T_g<T_b$, which is affected by collisions. The two ranges of scales are separated by a correlation length which grows with $\phi$, after proper rescaling with the mean free path.