Structure factors in granular experiments with homogeneous fluidization

TLDR

The fluidization is achieved by vertically vibrating a rough plate, causing particles to undergo Brownian‑like horizontal motion in addition to inelastic collisions. Velocity and density structure factors were measured across a hydrodynamic range of scales in a horizontal quasi‑2D fluidized granular experiment with packing fractions ϕ ∈ [10 %, 40 %]. The density structure factor matches that of elastic hard spheres except at large length scales, while the velocity field displays a complex non‑equilibrium steady‑state structure with two temperature regimes (bath and granular) and a correlation length that grows with packing fraction, all consistent with fluctuating hydrodynamic theory and linear hydrodynamic decay governed by viscous diffusion and thermostat interactions.

Abstract

Velocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi-2D fluidized granular experiment, with packing fractions ϕ ∈ [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 Tb, depending on shaking parameters, and the “granular” temperature Tg < Tb, which is affected by collisions. The two ranges of scales are separated by a correlation length which grows with ϕ, after proper rescaling with the mean free path.