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

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 (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 .