Fluctuating hydrodynamics and correlation lengths in a driven granular fluid

Abstract

Static and dynamical structure factors for shear and longitudinal modes of the velocity and density fields are computed for a granular system fluidized by a stochastic bath with friction. Analytical expressions are obtained through fluctuating hydrodynamics and are successfully compared with numerical simulations up to a volume fraction ∼ 50%. Hydrodynamic noise is the sum of external noise due to the bath and internal one due to collisions. Only the latter is assumed to satisfy the fluctuation-dissipation relation with the average granular temperature.Static velocity structure factors S ⊥ (k) and S (k) display a general non-constant behavior with two plateaux at large and small k, representing the granular temperature T g and the bath temperature T b > T g respectively. From this behavior, two different velocity correlation lengths are measured, both increasing as the packing fraction is raised. This growth of spatial order is in agreement with the behaviour of dynamical structure factors, the decay of which becomes slower and slower at increasing density.

Theoretical approaches to the steady-state statistical physics of interacting dissipative units

“…Here, we discuss the statistics of the granular gas in the more refined framework of kinetic theory and Boltzmann equation. A granular gas is a gas of inelastic particles that evolves through binary collisions [2,57,58,59,60,61,62,100,63]. Interestingly, the convergence to a stationary state under the combined effect of injection and dissipation of energy does not satisfy the usual H-theorem [64], but can be described by a generalized H-theorem [65].…”

Hydrodynamics of a Granular Gas in a Heterogeneous Environment

“…We can model this interaction by means of a fluctuating volume force [40], that we denote as F st (r) and fulfills the conditions [32,35,40,41] …”

“…being ξ 2 (r) the fluctuating force intensity [32,41] (that has dimensions of velocity squared times time), 1 the unit matrix in d dimensional space, δ ij is the Kronecker delta function and A indicates average of magnitude A over a sufficiently long time interval (long compared with the characteristic microscopic time scale). It has been shown in the case of the large mass limit and homogeous energy injection, that Equation (1) for a particle can be written as a Langevin equation corresponding to a granular brownian particle [42].…”

“…In the presence of a volume force, there is an additional step that accounts for the action of the fluctuating volume force. Implementation of this step, is described for instance in [32,63]. However, for this work, we consider a more general situation where the noise intensity ξ 2 (y) is space-dependent.…”

“…In previous theoretical works, granular gas fluidization has been studied only in the simplistic case of a homogeneous interstitial fluid [27][28][29][30][31][32]. And yet this theoretical homogeneous state is not quite a realistic situation [33].…”