Multiple-open-tubular column enabling transverse diffusion. Part 2: Channel size distribution and structure optimization

Abstract

Multiple-open-tubular columns enabling transverse diffusion (MOTTD) are made of straight, parallel, and cylindrical flow channels separated by a mesoporous stationary phase. In Part 1, a model of band broadening along MOTTD columns accounting for longitudinal diffusion, the trans-channel velocity bias, and mass transfer resistance in the stationary phase was proposed and validated. In this Part 2, the model is completed by considering the impact of short-range inter-channel velocity biases on the MOTTD plate number. These velocity biases are caused by the wide distribution of the channel diameters. Different ratios, ρ, of the average inner diameter, 2<rc>, of the flow channels to their closest center-to-center distance d (d= 5 μm, ρ= 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9) with a relative standard deviation (RSD) increasing from 0 to 50% are considered. The zone retention factor k1 was increased from 1 to 25. The complete model of band broadening is validated after adjustment to dispersion data obtained by 1) the lattice-Boltzmann method for modeling fluid flow, 2) a random-walk particle-tracking (RWPT) technique to address advective–diffusive transport, and 3) by considering two distinct populations of flow channels (inner radii rc,1=<rc>(1−RSD) and rc,2=<rc>(1+RSD)) arranged at the nodes of a hexagonal compact array.The completed model of band broadening in MOTTD columns reveals that the RSD of the channel diameters has only a moderate impact on the optimum plate number of MOTTD columns: the relative increase of the minimum plate height do not exceed 30% even for the largest RSDs. However, when the mass transfer of the analyte is governed by its slow rate of transverse diffusion across the MOTTD column, the plate height can be increased by up to 100% at high average velocities. Regarding the best trade-off between analysis speed and column performance at a fixed pressure drop of 400 bar, irrespective of the zone retention factor and RSD of the distribution of the channel diameters, the fastest analyses are recommended for MOTTD columns having a small structural parameter ρ. In contrast, for the longest analysis times, the largest values of ρ are required to maximize the performance of MOTTD columns.