Moussa Ali, Huygens Bram, Venditti Claudia, Adrover Alessandra, Desmet Gert
Department of Chemical Engineering, Vrije Universiteit Brussel, Brussels, Belgium.
Dipartimento di Ingegneria Chimica Materiali Ambiente, Sapienza Università di Roma, Italy.
J Chromatogr A. 2024 Jan 25;1715:464607. doi: 10.1016/j.chroma.2023.464607. Epub 2023 Dec 24.
We have investigated the possibility to establish a theoretical plate height expression for the band broadening in the most widely used micro-pillar array column format, i.e., a cylindrical pillar array wherein the pillar walls and the channel bottom are coated with a thin layer of meso‑porous material. Assuming isotropic diffusion in the shell-layer, it was found that the vertical diffusive transport along the porous shell-layer covering the pillar walls significantly suppresses the band broadening originating from the vertical migration velocity gradients. As the vertical transport in the shell-layer increases linearly with the retention equilibrium constant K, this leads to an anomalous dependency on the retention factor. Indeed, instead of increasing with k'' and following the classic (1+ak''+bk'')/(1 + k'')-dependency governing a classic Taylor-Aris system, the variation of the mobile zone mass transfer resistance term h in a 3D pillar array with bottom-wall retention goes through a maximum (resp. factor 1.5 (k''=4) and 2 (k''=16) difference between observed and classic Taylor-Aris behaviour). This effect increases with increasing pillar heights and increasing reduced velocities. Because of this complex k''-dependency, it proves very cumbersome to establish a general plate height equation covering all conditions. Instead, a plate height expression was established that is limited up to k''=4, but remains accurate for higher k''-values for cases where the ratio of pillar height over inter-pillar distance remains below 5. It can however be anticipated the proposed analytical model is only valid in a rather limited range around the presently considered external porosity of ε=0.5.
我们研究了为最广泛使用的微柱阵列柱格式中的谱带展宽建立理论塔板高度表达式的可能性，即一种圆柱形柱阵列，其中柱壁和通道底部涂覆有一层介孔材料薄层。假设在壳层中各向同性扩散，发现沿覆盖柱壁的多孔壳层的垂直扩散传输显著抑制了源于垂直迁移速度梯度的谱带展宽。由于壳层中的垂直传输随保留平衡常数K线性增加，这导致了对保留因子的异常依赖性。实际上，对于具有底壁保留的三维柱阵列，流动相区传质阻力项h的变化不是随k''增加并遵循控制经典泰勒-阿里斯系统的经典(1+ak''+bk'')/(1 + k'')依赖性，而是经历一个最大值（分别为观测值与经典泰勒-阿里斯行为之间相差1.5倍(k''=4)和2倍(k''=16)）。这种效应随着柱高度的增加和折合速度的增加而增大。由于这种复杂的k''依赖性，建立一个涵盖所有条件的通用塔板高度方程非常麻烦。相反，建立了一个塔板高度表达式，该表达式在k''=4以内有效，但对于柱高度与柱间距之比低于5的情况，在k''值较高时仍保持准确。然而，可以预期所提出的分析模型仅在当前考虑的外部孔隙率ε=0.5的相当有限的范围内有效。
