Abstract
One defining property of granular materials is their low number of constituents when compared to molecular systems. This implies that (statistical) fluctuations can have a dominant effect on the global dynamics of the system. In the following we create identical time-averaged macroscopic states with significantly different numbers of particles in order to directly study the role of fluctuations in granular systems. The dependency of the hydrodynamic conservation equations on the particles’ size is derived, which directly relates to different particle–number densities. We show that, provided that the particles’ dissipation is properly scaled, equivalent states can be obtained in the small particle size limit. Simulations of the granular Leidenfrost state confirm the validity of the scalings, and allow us to study the effects of fluctuations on collective oscillations. We observe that the amplitude of these oscillations decreases with the square root of the number of particles, while their frequency remains constant.
Highlights
Granular flows often show a remarkable similarity with those of molecular fluids [1, 2]
An additional fundamental difficulty stems from the enormous difference in the total number of constituents between granular and molecular systems; while in molecular media the microscopic relevant length-scale is orders of magnitude smaller than the macroscopic one, in granular media macroscopic fields may vary in distances of the order of a few particle diameters
We have studied the possibility of creating macroscopically equivalent granular systems in the same volume with significantly different numbers of particles N, by varying their size d
Summary
Granular flows often show a remarkable similarity with those of molecular fluids [1, 2]. An additional fundamental difficulty stems from the enormous difference in the total number of constituents between granular and molecular systems; while in molecular media the microscopic relevant length-scale is orders of magnitude smaller than the macroscopic one, in granular media macroscopic fields may vary in distances of the order of a few particle diameters. This possibly big influence of a few particles on macroscopic quantities implies the existence of inherently large fluctuations, which can drastically modify the global dynamics, especially near transitions [13,14,15]. Deepening our understanding of the role played by these fluctuations is of fundamental importance for the development of a successful continuum description of granular media
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