An assessment of the mathematical models for estimating the coordination number of the packing of multisized particles

Coordination number (CN) is an important microscopic parameter in describing the packing of particles. There are a few mathematical models proposed in the literature to calculate the CN of a particle mixture. However, they have not been comprehensively assessed as the experimental data are limited. In this paper, the applicability of three models, respectively proposed by Dodds, Ouchiyama & Tanaka, and Suzuki & Oshima, is assessed against the results recently generated by means of discrete element method. The results indicate that the model of Ouchiyama & Tanaka differ from the simulated CNs significantly, thus not recommended. The other two models produce similar results, but the Dodds model is probably more reasonable. In particular, these two models are able to estimate the variation trend of the average CN for various particle size distributions but their predictability reduces with the increase of particle size difference. The Dodds model becomes numerically unsolvable when the small-to-large size ratio is smaller than 0.154. Therefore, modification of the existing models or development of a new model is required in future studies for better prediction of the CN of the packings of multisized particles. [Display omitted] •The mathematical models proposed for estimating coordination number of particle mixtures are reviewed.•The applicability of three models respectively proposed by Dodds, Ouchiyama & Tanaka, and Suzuki & Oshima, is examined.•The Dodds model is the best when particle size range is small, but the Suzuki and Oshima model is more general.•The need for modifying the existing models or developing a new model is discussed.