Fluctuations, correlations, and Casimir-like forces in the homogeneous cooling state of a granular gas

Abstract

The fluctuating hydrodynamics by Brey et al. [Phys. Rev. E 83, 041303 (2011)] is analytically solved to get the long-time limit of the fluctuations of the number density, velocity field, and energy density around the homogeneous cooling state of a granular gas, under physical conditions where it keeps stable. Explicit expressions are given for the nonwhite contributions in the elastic limit. For small dissipation, the latter is shown to be much smaller than the inelastic contributions, in general. The fluctuation-induced Casimir-like forces on the walls of the system are calculated assuming a fluctuating pressure tensor resulting from perturbing its Navier–Stokes expression. This way, the Casimir-like forces emerge as the correlation between the longitudinal velocity and the energy density. Interestingly, the fluctuation-induced forces push/pull the system toward the square or rectangular geometry where they vanish, in good agreement with the event-driven numerical simulations.