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

Jesús David Jiménez Oliva; Pablo Rodriguez-Lopez; Nagi Khalil

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arXiv · 2311.14059

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

Jesús David Jiménez Oliva·Pablo Rodriguez-Lopez·Nagi Khalil

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Abstract

The fluctuating hydrodynamics by Brey et. al. 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 non-white 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 emerges as the correlation between the longitudinal velocity and the energy density. Interestingly, the fluctuation-induced forces push/pull the system towards the square or rectangular geometry when they vanish, in good agreement with the event-driven numerical simulations.

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Jesús David Jiménez Oliva, Pablo Rodriguez-Lopez, Nagi Khalil. 2023-11-23. Fluctuations, correlations, and Casimir-like forces in the homogeneous cooling state of a granular gas. https://arxiv.org/abs/2311.14059

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