A unified non-dominant equation model for density prediction of multi-component spherical particle mixtures

Abstract

The conventional packing models generally rely on the dominant particle component assumption, where the structure of the particle mixture is dictated by the dominant particle skeleton. However, this assumption is not effective when applied to particle mixtures with multiple significant components, leading to a noticeable discrepancy between model predictions and experimental results. In this study, we draw from solution thermodynamics to introduce two new concepts, “ideal specific volume” and “excess specific volume,” for modeling packing density. Based on this new approach, we derived an equation which is capable of accurately describing the nonlinear packing behavior of these mixtures, named the Unified Non-Dominant Equation Model (UNDEM). This model does not depend on the dominant particle component assumption and employs a unified continuous function to represent changes in packing density. The UNDEM requires no additional parameters and exhibits broad applicability, particularly showing high accuracy in predicting the packing densities of multi-component particle mixtures. Its reliability has been validated against experimental data, showing that the UNDEM is generally more accurate than existing models and can accurately describe most experimental results.