椭球颗粒随机紧密堆积实验研究
Experiments for Randomly Close Packing of Ellipsoids

针对随机堆积问题在数理领域和实际生产中意义重大且目前尚无一般性的理论模型的问题,采用一种基于高分辨率工业X射线断层扫描(CT)无损检测的实验方法较精确地测定了椭球颗粒随机紧密堆积体系的3个重要参数,即堆积分数、取向序和配位数分布,结果表明,椭球纵横比为0？？5左右时,堆积分数达到的最大值为74％,与现有的模拟结果一致,而在一定纵横比范围内,配位数的分布呈偏态分布,取向角与取向轴呈现出高对称性,但离散性较强,该结果与球体随机紧密堆积的差异较大。在不考虑摩擦刚体所需平均配位数为刚体自由度的2倍、有限堆积物的配位数分布满足古典的几何分布的2个假设下,提出了一种椭球的堆积理论,其能解释堆积参数的变化趋势。结论和实验手段对探讨非球体填充理论和计算堆积体孔隙率有一定的参考价值。
Random packing has important significance in both mathematical field and practical application. For a randomly close packing of ellipsoidal particle system, three important parameters, namely stacking fraction, orientational order and coordination number distribution, are accurately measured by an experimental method based on high resolution industrial CT nondestructive testing. The experimental results show that: When the aspect ratio of ellipsoid is 0.5 or 2.0, packing fraction reaches the maximum; The maximum packing fraction is 0.745 ±0？？037; Within the scope of the aspect ratio of the test sample, the distribution of coordination number obeys skewed distribution; The orientation angle has high symmetry on the orientation axis. These results are quite different from those of the sphere randomly close packing. An ellipsoid packing theory is proposed under two assumptions to explain the variation trend of the packing parameters. The theoretical simulation results coincide with the experimental ones. The conclusion and the experimental means are of some reference value for researching theory of non？？sphere filling and calculation of bulk porosity