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Extension of Haff's cooling law in granular flows

R. Brito·M. H. Ernst
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Abstract

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[ - 2ετ] (known as Haff's law), where τis the average number of collisions suffered by a particle within time t, and ε=1-α^2 measures the degree of inelasticity, with αthe coefficient of normal restitution. This decay law is extended for large times to E(t) \aprox τ^{-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< α< 1.

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R. Brito, M. H. Ernst. 1998-07-15. Extension of Haff's cooling law in granular flows. https://doi.org/10.1209/epl%2Fi1998-00388-9

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