Cluster model for compaction of vibrated granular materials

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Abstract
In this paper we present a one-dimensional model describing properties of compaction observed in recent experiments with vibrated granular materials. In this model, a granular material undergoing vertical vibrations is considered as a system of randomly packed clusters. Each cluster 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 separation of individual particles from a cluster, and reassociation of the individual particles with surrounding clusters. This model successfully describes experimental results on the dynamics of granular compaction, reversible and irreversible behavior, dependence of the steady-state density on the magnitude of external vibrations, and predicts the crystallization of the material for a small magnitude of vibrations. It also connects microscopic properties of granular media with the experimental data on density fluctuations, such as temporal behavior, amplitude, and spectral properties of the fluctuations. In combination with experiment, this model can be instrumental in extracting constants of the mechanism and rate of cluster fragmentation, clusters arrangement in the media, and voids distribution. The importance and effectiveness of the cluster approach are discussed as the key points of the model.

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