Multiple-open-tubular column enabling transverse diffusion. Part 1: Band broadening model for accurate mass transfer predictions

Abstract

We derive a model of band broadening in multiple-open-tubular columns enabling transverse diffusion (MOTTD). In MOTTD columns, the flow channels are straight, parallel, cylindrical tubes arranged in a hexagonal compact array. A mesoporous material or stationary phase (130 Å bridged-ethyl hybrid (BEH) silica support) is filling the volume between the flow channels. The model is based on Giddings’ random-walk theory of non-equilibrium chromatography. It is calibrated for the unknown configuration factor, qs, related to the specific geometry of the stationary phase in MOTTD columns. qs values are found based on the best fit of the model to simulated dispersion data obtained by the lattice-Boltzmann method for modelling fluid flow and a random-walk particle-tracking technique to address advective–diffusive transport of the analytes. For the model calibration, simulations are performed for different ratios, ρ, of the average inner diameter of the flow channels to their closest center-to-center distance under retained and non-retained conditions.The model is successfully validated (average relative errors below 10%) under both retained and non-retained conditions. For the same column format (4.6 mm i.d. × 150 mm), external porosity, zone retention factor, and relative standard deviation of the distribution of the inner diameters of the flow channels, the derived model reveals the intrinsic advantage of MOTTD columns (center-to-center distance between flow channels of 5 µm and ρ = 0.62) over a conventional column packed with 5 µm 130 Å BEH silica particles and the same multiple porous-layer open-tubular column (MPLOT) disabling transverse dispersion. MOTTD columns are weakly affected by the polydispersity of the inner diameter of the flow channels. Provided MOTTD columns could be prepared at a small feature size of 5 µm or less, they are expected to deliver a significant improvement in column technology relative to current particulate and silica monolithic columns.