A stochastic model of transcolumn eddy dispersion along packed beds was derived. It was based on the calculation of the mean travel time of a single analyte molecule from one radial position to another. The exchange mechanism between two radial positions was governed by the transverse dispersion of the analyte across the column. The radial velocity distribution was obtained by flow simulations in a focused-ion-beam scanning electron microscopy (FIB-SEM) based 3D reconstruction from a 2.1 mm × 50 mm column packed with 2 μm BEH-C₁₈ particles. Accordingly, the packed bed was divided into three coaxial and uniform zones: (1) a 1.4 particle diameter wide, ordered, and loose packing at the column wall (velocity $u_w$), (2) an intermediate 130 μm wide, random, and dense packing (velocity u_i), and (3) the bulk packing in the center of the column (velocity u_c).

First, the validity of this proposed stochastic model was tested by adjusting the predicted to the observed reduced van Deemter plots of a 2.1 mm × 50 mm column packed with 2 μm BEH-C₁₈ fully porous particles (FPPs). An excellent agreement was found for u_i = 0.93u_c, a result fully consistent with the FIB-SEM observation (u_i = 0.95u_c). Next, the model was used to measure u_i = 0.94u_c for 2.1 mm × 100 mm column packed with 1.6 μm Cortecs-C₁₈ superficially porous particles (SPPs). The relative velocity bias across columns packed with SPPs is then barely smaller than that observed in columns packed with FPPs (+6% versus + 7%). $u_w=1.8u_i$ is measured for a 75 μm × 1 m capillary column packed with 2 μm BEH-C₁₈ particles. Despite this large wall-to-center velocity bias (+80%), the presence of the thin and ordered wall packing layer has no negative impact on the kinetic performance of capillary columns. Finally, the stochastic model of long-range eddy dispersion explains why analytical (2.1–4.6 mm i.d.) and capillary (<400 μm i.d.) columns can all be packed efficiently (1 <h_min< 2) with particles of size larger than 2 μm. In contrast, the model predicts that 0.4–1.2 mm i.d. columns and 2.1 mm i.d. columns cannot be packed well (h_min>3) with sub-2 μm particles and with 1 μm particles, respectively.

推导了沿着填充床的跨柱涡流扩散的随机模型。它基于单个分析物分子从一个径向位置到另一个径向位置的平均行进时间的计算。两个径向位置之间的交换机制由分析物在色谱柱上的横向分散控制。径向速度分布是通过在基于聚焦离子束扫描电子显微镜（FIB-SEM）的3D重建中从装有2μmBEH-C ₁₈颗粒的2.1 mm×50 mm色谱柱上进行流动模拟获得的。因此，填料床被分为三个同轴且均匀的区域：（1）色谱柱壁处的粒径为1.4的宽，有序和松散的填料（速度）。${ü}_w$），（2）中间的130μm宽，无规且致密的填料（速度u _i），以及（3）散装填料在柱子的中心（速度u _c）。

首先，通过将填充有2μmBEH-C ₁₈全多孔颗粒（FPPs）的2.1 mm×50 mm色谱柱的预测值减小到所观察到的简化的Van Deemter图，来检验该提议的随机模型的有效性。发现u _i  = 0.93 u _c极好一致性，结果与FIB-SEM观察结果完全一致（u _i  = 0.95 u _c）。接下来，该模型用于测量装有1.6μmCortecs-C _18的2.1 mm×100 mm色谱柱的u _i  = 0.94 u _c表面多孔颗粒（SPPs）。然后，在装有SPP的色谱柱上的相对速度偏差几乎比在装有FPP的色谱柱上观察到的相对速度偏差小（+ 6％对+ 7％）。${ü}_w=1.8{ü}_{\mathrm{一世}}$对于装有2μmBEH-C ₁₈颗粒的75μm×1 m毛细管色谱柱，需要进行柱头色谱分析。尽管存在较大的壁对中心速度偏差（+ 80％），但薄而有序的壁填充层的存在对毛细管色谱柱的动力学性能没有负面影响。最后，长距离涡旋分散的随机模型解释了为什么分析柱（2.1–4.6 mm内径）和毛细管（<400μm内径）都可以有效地填充（1 < h _min <2）且粒径大于2微米 相反，该模型预测，内径小于2 µm的颗粒和内径小于1μm的颗粒无法分别填充0.4–1.2 mm内径柱和2.1 mm内径柱（h _min > 3）。