近日，北京大学李水乡团队实现了用二元球分解法预测摩擦多分散球的堆积密度。2026年10月29日出版的《颗粒学报》杂志发表了这项 最新成果。

颗粒堆积体系的堆积密度预测对科学研究与工业生产均具有重要意义。自然界与工业场景中的颗粒普遍存在粒间摩擦。

研究组将原本基于线性叠加态、针对无摩擦颗粒提出的双球分解法，拓展至具有任意摩擦系数的含摩擦颗粒体系，建立一套适用于含摩擦多分散球颗粒堆积密度预测的通用方法。该方法首先在随机密堆积（RCP）与随机松堆积（RLP）两种状态下，将多分散球颗粒分解为若干具有相同等效堆积直径的双球子体系；再基于线性叠加态，得到随机密堆积、随机松堆积状态下的堆积密度。

研究发现：对于单分散、双分散以及多分散球颗粒，归一化堆积密度随摩擦系数的变化服从一条普适曲线。因此，曲线上任意摩擦系数对应的堆积密度，均可通过该曲线上随机密堆积与随机松堆积的堆积密度插值得到。数值算例表明，对于多种多分散球颗粒组分、摩擦系数在 0~10 范围内的工况，该方法的平均预测误差约为 0.7%，验证了该方法用于估算含摩擦多分散球颗粒堆积密度的准确性与有效性。

附：英文原文

Title: Predicting the packing density of frictional polydisperse spheres via the binary-sphere decomposition method

Author: anonymous

Issue&Volume: 2026/10/29

Abstract: Packing density () prediction for particle packings is of great significance for both scientific research and industrial production. Particles in nature and industry usually have interparticle frictions. In this work, we extend the binary-sphere decomposition method, originally proposed for frictionless particles based on the linear superposition state, to frictional particles with arbitrary friction coefficients , establishing a general method for predicting of frictional polydisperse spheres. The method first decomposes the polydisperse spheres into several binary sphere subsystems with the same equivalent packing diameter under both random close packing (RCP) and random loose packing (RLP) states. The at RCP and RLP are then obtained based on the linear superposition state. We find that the normalized versus follows a universal curve for monodisperse, binary, and polydisperse spheres. Thus, the at any can be predicted by the interpolation between the of RCP and RLP on the curve. Numerical examples demonstrate that the method achieves an average prediction error of approximately 0.7% for various polydisperse sphere compositions and ranging from 0 to 10, confirming its accuracy and effectiveness for estimating of frictional polydisperse spheres.

DOI: 10.1016/j.partic.2026.10.031

Source: https://www.sciencedirect.com/science/article/abs/pii/S1674200126003937