Hydrodynamics of Close-Packed Levitating Granular Clusters
Abstract
Continuum modelling of flow of macroscopic grains is a challenging task, even within the greatly simplified model of rapid granular flow. The Navier-Stokes granular hydrodynamics (NSGH) [1], developed for the rapid flow, is expected to be valid quantitatively only for moderate granular densities and for nearly elastic particle collisions. In this work [2] we probe the boundaries of hydrodynamics by considering a dense granular system. We focus on the phenomenon of a close-packed levitating granular cluster observed in monodisperse granular materials fluidized by vertical vibrations. The close-packed floating cluster is an extreme form of the granular density inversion that results from energy losses in the particle collisions. The model we adopted is that of inelastically colliding hard disks driven from below by a ``thermal" plate in two dimensions. We limit ourselves to nearly elastic collisions, so that the standard NSGH breaks down because of large densities, not large inelasticity. Molecular dynamics simulations show, in a wide range of parameters, a close-packed cluster supported by a low-density region. We find that the steady-state density profile, including the close-packed cluster part, is well described by a variant of NSGH suggested by Grossman et al. [3]. A tentative explanation of the success of NSGH beyond the freezing point is provided by the absence of shear motions in the system. Indeed, in this case the apparent divergence of the viscosity beyond the freezing point becomes irrelevant.
3 NSGH P.K. Haff, J. Fluid Mech. 134, 401 (1983); J.T. Jenkins and M.W. Richman, Phys. Fluids 28, 3485 (1985); Arch. Rat. Mech. Anal. 87, 355 (1985); Phys. Fluids 28, 3485 (1986). paper B. Meerson, T. Pöschel and Y. Bromberg, Phys. Rev. Lett. 91, 024301 (2003). Grossmann E.L. Grossman, T. Zhou, and E. Ben-Naim, Phys. Rev. E 55, 4200 (1997). thebibliography- Publication:
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APS March Meeting Abstracts
- Pub Date:
- March 2004
- Bibcode:
- 2004APS..MAR.P3005M