A multi-stage normalization model for predicting the porosity of the multi-sized mixtures

A multi-stage normalization (MSN) model is established to predict the porosity of the multi-sized mixture. Based on the random filling theory, the proposed model repeats binary packing and ternary packing to continuously normalize the particle size groups of the multi-sized mixture, and finally obtains the target porosity. The predictions by the MSN model are compared with the experimental data and the predictions from other models. The results show that the MSN model's predictions are highly consistent with experimental data and correspond with the predictions given by the linear packing model, which demonstrates the validation of the MSN model. The MSN model can offer better predictions than the binary packing model, ternary packing model and empirical model due to a complete consideration of the particle size distribution. And the applicability of the model is further confirmed by investigating the porosity of mixtures with unimodal and bimodal Gaussian size distributions.