CLUSTER MODEL FOR COMPACTION OF VIBRATED GRANULAR-MATERIALS

In this paper we present a one-dimensional model describing properties of compaction observed in recent experiments with vibrated granular m aterials. In this model, a granular material undergoing vertical vibra tions is considered as a system of randomly packed clusters. Each clus ter in the system is supposed to be hexagonally packed to the maximum possible density, and porosity of material arises from random packing of the clusters. Vibrations cause fragmentation of clusters through se paration of individual particles from a cluster, and reassociation of the individual particles with surrounding clusters. This model success fully describes experimental results on the dynamics of granular compa ction, reversible and irreversible behavior, dependence of the steady- state density on the magnitude of external vibrations, and predicts th e crystallization of the material for a small magnitude of vibrations. It also connects microscopic properties of granular media with the ex perimental data on density fluctuations, such as temporal behavior, am plitude, and spectral properties of the fluctuations. In combination w ith experiment, this model can be instrumental in extracting constants of the mechanism and rate of cluster fragmentation, clusters arrangem ent in the media, and voids distribution. The importance and effective ness of the cluster approach are discussed as the key points of the mo del.