Numerical Elucidation of Flow and Dispersion in Ordered Packed Beds: Nonspherical Polygons and the Effect of Particle Overlap on Chromatographic Performance

Abstract

Spherical particles are widely considered as the benchmark stationary phase for preparative and analytical chromatography. Although this has proven true for randomly packed beds in the past, we challenge this paradigm for ordered packings, the fabrication of which are now feasible through additive manufacturing (3D printing). Using computational fluid dynamics (Lattice Boltzmann Method) this work shows that non-spherical particles can both reduce mobile-phase band broadening and increase permeability compared with spheres in ordered packed beds. In practice, ordered packed beds can only remain physically stable if the particles are fused to form a contiguous matrix, thus creating a positional overlap at the points of fusion between what would otherwise be discrete particles. Overlap is shown to decrease performance of ordered packed beds in all observed cases, thus we recommend it should be kept to the minimum extent necessary to ensure physical stability. Finally, we introduce a metric to estimate column performance, the mean deviated velocity, a quantitative description of the spread of the velocity field in the column. This metric appears to be a good indicator of mobile-phase dispersion in ordered packed bed media, including overlapped beds and is a useful tool for screening new stationary phase morphologies without having to perform computationally expensive simulations. Recent computational studies have demonstrated that ordered sphere packings can improve chromatographic performance compared with random packing 1,2. This is caused by the homogenous distribution of path lengths along which the mobile phase is transported through ordered media. These theoretical studies are now gaining practical relevance because ordered stationary phases can be fabricated using additive manufacturing technologies or three-dimensional printing 3-5. 3D printing offers a high level of control over the morphology of fabricated micro-structures, thus facilitating the translation of ordered packings from the virtual environment to practical implementation in real chromatographic systems 6-8. Spherical beads have been shown to have better chromatographic performance when compared to irregular particles in randomly packed beds 9. This was a result of more homogenous porosity distribution in packings of spherical particles, which increased the heterogeneity of the random flow channels and reduced eddy dispersion. Comparatively, ordered beds of spherical particles are homogeneous by design and inherently reduce eddy dispersion effects 1,2,10,11. Because ordered packings do not require the homogeneity that spherical particles provide in random packings, we question the superiority of spherical particles in the context of ordered packed beds.

Scalable3D‐printed lattices for pressure control in fluid applications

“…Illustrating the differences in bulk properties between pipe scales, fitted models for each of the configurations showed statistically significant differences between pipe sizes at p < 0.05 (Section 8 of Data S1). For other types of additively manufactured porous media, the hydraulic diameter has been identified as a critical parameter for system scaling 37 . In line with these previous findings, the differences in pressure behavior observed between overall system scales are most prominent when there is a significant change in hydraulic diameter.…”

“…For other types of additively manufactured porous media, the hydraulic diameter has been identified as a critical parameter for system scaling. 37 In line with these previous findings, the differences in pressure behavior observed between overall system scales are most prominent when there is a significant change in hydraulic diameter. These results suggest that an overall system diameter of 10 l c or greater is best suited to reduce the effects of deviations in hydraulic diameter and achieve representative outcomes of a larger system when using a small-scale system.…”

“…In the context of fluid dynamics, hydraulic diameter is another critical dimension 30,37 . Defined as 4 ε / a v , it can also be scaled by the unit cell dimension to produce a self‐similar profile, shown in Figure 3C.…”

“…Taken in conjunction with experimental process knowledge, the resul- 29,35,36 In the context of fluid dynamics, hydraulic diameter is another critical dimension. 30,37 Defined as 4ε/a v , it can also be scaled by the unit cell dimension to produce a self-similar profile, shown in between surface features and the imaging modality. 39 However, the increased porosity and decreased specific surface area are consistent with generalized beam thinning, a result of processing phenomena that lead to part shrinkage or overcuring, yielding deviations from designed dimensions.…”

A Review of Portable High-Performance Liquid Chromatography: the Future of the Field?

“…In recent years, the opportunity to drastically improve the performance of chromatographic separations beyond what is currently possible has been realised. The advance of 3D printing technologies present a newfound ability to fabricate precisely ordered stationary phases of varying shapes which have the potential to increase the efficiency of chromatographic columns [80,81]. The developments in this research are impressive and may, in the future, improve the analytical sector significantly.…”