Issue |
Europhys. Lett.
Volume 43, Number 5, September I 1998
|
|
---|---|---|
Page(s) | 497 - 502 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i1998-00388-9 | |
Published online | 01 September 2002 |
Extension of Haff's cooling law in granular flows
1
Departamento de Física Aplicada I, Universidad Complutense de Madrid, 28040 Madrid, Spain
2
Instituut voor Theoretische Fysica, Universiteit Utrecht, Postbus 80006, 3508 TA Utrecht, The Netherlands
Received:
27
April
1998
Accepted:
8
July
1998
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 (known as Haff's law), where τ
is the average number of collisions suffered by a particle within
time t, and
measures the degree of inelasticity,
with α the coefficient of normal restitution.
This decay law is extended for large times to
in d dimensions, far into the nonlinear clustering
regime. The theoretical predictions are
quantitatively confirmed by computer simulations, and hold for
small to moderate inelasticities with
.
PACS: 05.20.-y – Statistical mechanics / 05.20.Dd – Kinetic theory / 81.05.Rm – Porous materials; granular materials
© EDP Sciences, 1998
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