A century of granular packing models

This article provides a review of particle packing models. A summary roadmap shows their disciplinary genesis and the multidisciplinary interactions that have shaped them over a 100-year period. Described by field, their development has led to models that can be simple or piecewise, linear or non-linear, involving two or three geometric interactions, and possibly the packing process and a critical cavity size ratio. To facilitate comparisons, around twenty of them are rewritten in terms of specific volume. Their agreement with certain packing mechanisms and their extension to multi-sized mixtures are discussed. Finally, five of these non-linear packing models are applied to binary mixtures of aggregates. The analysis shows that they perform well, both in terms of estimating minimum specific volumes and the combinations needed to achieve the optimum. Two of them stand out slightly from the rest. The comparison is then extended to ternary combinations of aggregates or spheres.