Modeling the Effects of Short-Range Randomness in Packed Sphere Beds

We have for the first time applied the recently developed Brenner formalism-based two-zone moment analysis (TZMA) method for chromatographic band broadening to a unit cell containing randomly packed fully porous spheres instead of containing only perfectly ordered packings, as in previous literature reports. In total, 4 random packings have been simulated. Each containing 100 fully porous spheres, they can be considered a good proxy for the short-range randomness appearing in randomly packed chromatography beds. Compared to the minimal plate height h_min in real packed columns, the h_min produced by these random packings is roughly only half (h_min ≅ 1 at k″ = 4). This must imply that the band broadening in state-of-the-art packed bed columns originates for about 50% from the polydispersity of the particles and from the long-range, column-wall-induced transversal packing density variations, two effects that are not included in the present study. The data further show that, if also the short-range randomness could be eliminated, plate heights would drop by another 30%, i.e., decrease to h_min = 0.7 at k″ = 4. Covering a broad range of Péclet-values (1 ≤ Pe ≤ 800) and zone retention factors k″ (0.5 ≤ k″ ≤ 16), a model for the mobile zone dispersion occurring at the short-range randomness scale could be proposed. The model only contains 4 fitting parameters and consists of a logarithmic term (linked to the randomness of the packing) and a local mass transfer term (linked to the dispersion occurring at the level of a single through-pore). Unlike other models used in the literature, the model contains an explicit dependency on the retention factor k″ such that the strong effect of the latter on the short-range eddy dispersion can be rightfully accounted for.