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The granular phase diagram (1997)
| Venue: | J. Stat. Phys |
| Citations: | 19 - 6 self |
BibTeX
@ARTICLE{Esipov97thegranular,
author = {Sergei E. Esipov and Thorsten Pöschel},
title = {The granular phase diagram},
journal = {J. Stat. Phys},
year = {1997},
pages = {1385}
}
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Abstract
The kinetic energy distribution function satisfying the Boltzmann equation is studied analytically and numerically for a system of inelastic hard spheres in the case of binary collisions. Analytically, this function is shown to have a similarity form in the simple cases of uniform or steady-state flows. This determines the region of validity of hydrodynamic description. The latter is used to construct the phase diagram of granular systems, and discriminate between clustering instability and inelastic collapse. The molecular dynamics results support analytical results, but also exhibit a novel fluctuational breakdown of mean-field descriptions. Key words: granular Dynamics Granular media such as sand provide an attractive opportunity to revisit a number of topics in classical physics, and contribute new angles. In this paper we describe the granular phase diagram which we hope will be helpful to a broad community given the raising interest in granular systems [1]. The researchers interested in diluted granular gases, such as in astrophysical applications [2], and researchers who study, say, compaction of sand [3] use different approaches. The phase diagram may represent a ground for communication. The phase of granular system depends on inelasticity of collisions, r, (restitution coefficient approximation, [4, 5, 6]), particle density, ρ, particle size, a, system size, ∗ J. Stat. Phys. (in press) L, and the observation time, t. The external influence of shaking, gravity, boundaries enters through the above parameters. Granular temperature, or any other characteristic of the rate of bulk-averaged motion doesn’t appear on the phase diagram since there is no characteristic energy scale for hard-core interaction assumed here. As we shall see below, a combination, ρLad−1, where d is the system dimension, is playing the key role. It represents the average number of particles inside an imaginary tube of length L and cross-section ad−1. Presently we think that the phase
Keyphrases
granular phase diagram phase diagram granular system mean-field description granular temperature new angle boltzmann equation binary collision kinetic energy distribution function particle density restitution coefficient approximation cross-section ad inelastic collapse classical physic average number granular dynamic granular medium key role novel fluctuational breakdown system size hydrodynamic description use different approach imaginary tube similarity form attractive opportunity particle size inelastic hard sphere molecular dynamic result diluted granular gas hard-core interaction system dimension broad community characteristic energy scale observation time key word bulk-averaged motion doesn astrophysical application analytical result external influence simple case steady-state flow
