Department of Chemistry, Philipps-Universität Marburg, Germany.
J Chromatogr A. 2010 Jul 9;1217(28):4713-22. doi: 10.1016/j.chroma.2010.05.019.
We quantified the microstructural disorder of packed beds and correlated it with the resulting eddy dispersion. For this purpose we designed a set of bulk (unconfined) monodisperse random sphere packings with a systematic, protocol-dependent degree of microstructural heterogeneity, covering a porosity range from the random-close to the random-loose packing limit (ε = 0.366-0.46). With the precise knowledge of particle positions, size, and shape we conducted a Voronoiï tessellation of all packings and correlated the statistical moments of the Voronoiï volume distributions (standard deviation and skewness) with the porosity and the protocol-dependent microstructural disorder. The deviation of the Voronoiï volume distributions from the delta function of a crystalline packing describes the origin of short-range disorder of the investigated random packings. Eddy dispersion was simulated over a wide range of reduced velocities (0.5 ≤ ν ≤ 750) and analyzed with the comprehensive Giddings equation. Transient dispersion was found to correlate with the spatial scales of heterogeneity in the packings. The analysis of short-range disorder based on the Voronoiï volume distributions revealed a strong correlation with the short-range interchannel contribution to eddy dispersion, whereas transchannel dispersion was relatively little affected. The presented approach defines a strictly scientific route to the key morphology-transport relationships of current and future chromatographic supports, including their morphological reconstruction, statistical analysis, and the correlation with relevant transport phenomena. It also guides us in our understanding, comparison, and optimization of the diverse packing algorithms and protocols used in simulations and experimental studies.
我们量化了填充床的微观结构无序性，并将其与所得的涡流弥散相关联。为此，我们设计了一组具有系统的、协议相关的微观结构异质性程度的散装（无约束）单分散随机球体填充，涵盖了从随机紧密到随机松散填充极限的孔隙率范围（ε=0.366-0.46）。通过对颗粒位置、大小和形状的精确了解，我们对所有填充进行了 Voronoi 细分，并将 Voronoi 体积分布的统计矩（标准偏差和偏度）与孔隙率和协议相关的微观结构无序性相关联。Voronoi 体积分布相对于晶体填充的 delta 函数的偏差描述了所研究的随机填充的短程无序的起源。涡流弥散在很宽的减小速度范围内（0.5≤ν≤750）进行了模拟，并使用综合 Giddings 方程进行了分析。发现瞬态弥散与填充中不均匀性的空间尺度相关。基于 Voronoi 体积分布的短程无序分析与涡流弥散的短程通道间贡献之间存在很强的相关性，而通道间弥散则相对较少受到影响。所提出的方法为当前和未来色谱支撑物的关键形态-传输关系定义了一条严格的科学途径，包括其形态重建、统计分析以及与相关传输现象的相关性。它还指导我们理解、比较和优化模拟和实验研究中使用的各种填充算法和协议。
