Stokely K, Diacou A, Franklin Scott V
Department of Physics and Astronomy, Rochester Institute of Technology, 84 Lomb Memorial Drive, Rochester, New York 14623, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 May;67(5 Pt 1):051302. doi: 10.1103/PhysRevE.67.051302. Epub 2003 May 7.
We investigate the two-dimensional packing of extremely prolate (aspect ratio alpha=L/D>10) granular materials, comparing experiments with Monte Carlo simulations. The average packing fraction of particles with aspect ratio alpha=12 is 0.68+/-0.03. We quantify the orientational correlation of particles and find a correlation length of two particle lengths. The functional form of the orientational correlation is the same in both experiments and simulations which three orders of magnitude in aspect ratio, all decaying over a distance of two particle lengths. It is possible to identify voids in the pile with sizes ranging over two orders of magnitude. The experimental void distribution function is a power law with exponent -beta=-2.43+/-0.08. Void distributions in simulated piles do not decay as a power law, but do show a broad tail. We extend the simulation to investigate the scaling at very large aspect ratios. A geometric argument predicts the pile number density to scale as alpha(-2). Simulations do indeed scale this way, but particle alignment complicates the picture, and the actual number densities are quite a bit larger than predicted.
我们研究了极长径比（长径比α = L/D > 10）的颗粒材料的二维堆积情况，并将实验结果与蒙特卡罗模拟进行了比较。长径比α = 12的颗粒的平均堆积分数为0.68±0.03。我们对颗粒的取向相关性进行了量化，发现相关长度为两个颗粒长度。在实验和模拟中，取向相关性的函数形式相同，长径比相差三个数量级，且均在两个颗粒长度的距离内衰减。有可能识别出堆积中尺寸范围跨越两个数量级的空隙。实验空隙分布函数是一个指数为-β = -2.43±0.08的幂律。模拟堆积中的空隙分布并非按幂律衰减，但确实显示出一个宽尾。我们扩展了模拟，以研究在非常大的长径比下的标度关系。一个几何论证预测堆积数密度按α^(-2)标度。模拟结果确实是这样标度的，但颗粒排列使情况变得复杂，实际数密度比预测值大得多。
