99 9 Cluster - Growth in Freely Cooling Granular Media

When dissipative particles are left alone, their fluctuation energy decays due to collisional interactions, clusters build up and grow with time until the system size is reached. When the effective dissipation is strong enough, this may lead to the " inelastic collapse " , i.e. the divergence of the collision frequency of some particles. The cluster growth is an interesting physical phenomenon, whereas the inelastic collapse is an intrinsic effect of the inelastic hard sphere (IHS) model used to study the cluster growth – involving only a negligible number of particles in the system. Here, we extend the IHS model by introducing an elastic contact energy and the related contact duration t c. This avoids the inelastic collapse and allows to examine the long-time behavior of the system. For a quantitative description of the cluster growth, we propose a burning–like algorithm in continuous space, that readily identifies all particles that belong to the same cluster. The criterion for this is here chosen to be only the particle distance. With this method we identify three regimes of behavior. First, for short times a homogeneous cooling state (HCS) exists, where a mean-field theory works nicely, and the clusters are tiny and grow very slowly. Second, at a certain time which depends on the system's properties, cluster growth starts and the clusters increase in size and mass until, in the third regime, the system size is reached and most of the particles are collected in one huge cluster. Granular media consist of discrete particles and their interaction is governed by two major concepts: excluded volume and dissipation. Adhesive and frictional forces are neglected in this study for the sake of simplicity. Since the particles are solid, each particle occupies a certain amount of space, and no other particle may enter this volume. If another particle approaches, the pair eventually collides. During collisions, energy is lost from those degrees of freedom (linear motion) which are important for the behavior of the material. Heat or sound is radiated and plastic deformation takes place so that energy is irreversibly gone. Already such a simple, classical system shows an enormous number of interesting phenomena like, e.g., shock-waves, size-segregation, surface-waves, or the clustering in freely cooling systems. The latter will be examined more closely here. Since granular particles dissipate energy, the multi-particle system is usually not in equilibrium. This leads to various complex, non-linear phenomena, as mentioned above. …