Department of Chemistry, Philipps-Universität Marburg, Hans Meerwein Strasse, 35032 Marburg, Germany.
J Chromatogr A. 2012 Sep 28;1257:98-115. doi: 10.1016/j.chroma.2012.08.024. Epub 2012 Aug 14.
We study the impact of microscopic order on transverse dispersion in the interstitial void space of bulk (unconfined) chromatographic beds by numerical simulations of incompressible fluid flow and mass transport of a passive tracer. Our study includes polydisperse random sphere packings (computer-generated with particle size distributions of modern core-shell and sub-2 μm particles), the macropore space morphology of a physically reconstructed silica monolith, and computer-generated regular pillar arrays. These bed morphologies are analyzed by their velocity probability density distributions, transient dispersion behavior, and the dependence of asymptotic transverse dispersion coefficients on the mobile phase velocity. In our work, the spherical particles, the monolith skeleton, and the cylindrical pillars are all treated as impermeable solid phase (nonporous) and the tracer is unretained, to focus on the impact of microscopic order on flow and (particularly transverse) hydrodynamic dispersion in the interstitial void space. The microscopic order of the pillar arrays causes their velocity probability density distributions to start and end abruptly, their transient dispersion coefficients to oscillate, and the asymptotic transverse dispersion coefficients to plateau out of initial power law behavior. The microscopically disordered beds, by contrast, follow power law behavior over the whole investigated velocity range, for which we present refined equations (i.e., Eq.(13) and the data in Table 2 for the polydisperse sphere packings; Eq.(17) for the silica monolith). The bulk bed morphologies and their intrinsic differences addressed in this work determine how efficient a bed can relax the transverse concentration gradients caused by wall effects, which exist in all confined separation media used in chromatographic practice. Whereas the effect of diffusion on transverse dispersion decreases and ultimately disappears at increasing velocity with the microscopically disordered chromatographic beds, it dominates in the pillar arrays. The pillar arrays therefore become the least forgiving bed morphology with macroscopic heterogeneities and the engendered longitudinal dispersion in chromatographic practice. Wall effects in pillar arrays and the monolith caused by their confinement impact band broadening, which is traditionally observed on a macroscopic scale, more seriously than in the packings.
我们通过对不可压缩流体流动和被动示踪剂传质的数值模拟，研究了微观有序性对整体（无约束）色谱床中体相空隙中横向弥散的影响。我们的研究包括多分散随机球体堆积（使用现代核壳和亚 2μm 颗粒的粒径分布通过计算机生成）、物理重建的二氧化硅整体柱的大孔空间形态以及计算机生成的规则柱状阵列。通过它们的速度概率密度分布、瞬态弥散行为以及渐近横向弥散系数对流动相速度的依赖性来分析这些床形态。在我们的工作中，球形颗粒、整体柱骨架和圆柱形柱子都被视为不可渗透的固相（无孔），示踪剂不被保留，以专注于微观有序性对体相空隙中流动和（特别是横向）水动力弥散的影响。柱状阵列的微观有序性导致它们的速度概率密度分布突然开始和结束，它们的瞬态弥散系数振荡，渐近横向弥散系数脱离初始幂律行为而趋于平稳。相比之下，微观无序的床在整个研究的速度范围内遵循幂律行为，对此我们提出了改进的方程（即，多分散球体堆积的方程(13)和表 2 中的数据；对于二氧化硅整体柱的方程(17)）。本文所研究的整体床形态及其内在差异决定了床在多大程度上能够有效缓解由壁效应引起的横向浓度梯度，而壁效应存在于色谱实践中使用的所有约束性分离介质中。随着微观无序的色谱床的速度增加，扩散对横向弥散的影响减小并最终消失，而在柱状阵列中则占据主导地位。因此，柱状阵列成为在色谱实践中具有宏观异质性和产生的纵向弥散的最不可原谅的床形态。柱状阵列和整体柱的约束引起的壁效应对带展宽的影响比在堆积物中更严重，传统上在宏观尺度上观察到的带展宽。
