Extension of Haff's cooling law in granular flows

Details Extension of Haff's cooling law in granular flows Extension of Haff's cooling law in granular flows

1998-07-15

arxiv.org/abs/cond-mat/9807224v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, 4 PostScript figures. To be published in Europhysics Letters

Scientific paper

10.1209/epl/i1998-00388-9

The total energy E(t) in a fluid of inelastic particles is dissipated through inelastic collisions. When such systems are prepared in a homogeneous initial state and evolve undriven, E(t) decays initially as t^{-2} \aprox exp[ - 2\epsilon \tau] (known as Haff's law), where \tau is the average number of collisions suffered by a particle within time t, and \epsilon=1-\alpha^2 measures the degree of inelasticity, with \alpha the coefficient of normal restitution. This decay law is extended for large times to E(t) \aprox \tau^{-d/2} in d-dimensions, far into the nonlinear clustering regime. The theoretical predictions are quantitatively confirmed by computer simulations, and holds for small to moderate inelasticities with 0.6< \alpha< 1.

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