Multiple-open-tubular column enabling transverse diffusion. Part 3: Simulation of solute dispersion along a real three dimensional-printed column with quadratic channels

Abstract

Multiple-open-tubular columns enabling transverse diffusion (MOTTD) consist of straight and parallel flow-through channels separated by a mesoporous stationary phase. In Part 1, a stochastic model of band broadening along MOTTD columns accounting for longitudinal diffusion, trans-channel velocity bias, and mass transfer resistance in the stationary phase was derived to demonstrate the intrinsic advantage of MOTTD columns over classical particulate columns. In Part 2, the model was refined for the critical contribution of the channel-to-channel polydispersity and applied to address the best trade-off between analysis speed and performance. In this Part 3, a MOTTD column with a square array of quadratic channels is fabricated by 3D-printing (combining polymer stereolithography with photolithography using photomasks) to deliver unprecedently small apparent channel diameters of 117.6 ± 5.0 μm. The colors in the microscopy photographs of the actual 3D-printed channels are binarized to delimitate the mobile phase volume from the stationary phase volume. The same numerical simulations as those in Part 2 are then performed for two MOTTD columns (external porosity ϵe=31.7%, same apparent channel diameter 117.6 μm): one containing 16 virtual perfect quadratic channels and the other 16 real 3D-printed channels. The reduced velocities (or Peclet numbers) are varied over a wide range from 0.2 to 5000 and the zone retention factors were fixed at k1=1.04, 5, and 25.The results demonstrate that smoothing the edges of the targeted quadratic channels by the 3D-printed technique is advantageous in terms of solute dispersion. It outperforms the negative effect of the channel-to-channel polydispersity which is mitigated by transverse diffusion of the analyte in the stationary phase. For Peclet numbers larger than 50, the HETP of the 3D-printed MOTTD column is found 7%, 15%, and 16% smaller than that of the MOTTD column consisting of a square array of perfect quadratic channels. This confirms the known effect of channel geometry on solute dispersion in microfluidic systems. Flow channels in fabricated MOTTD columns are preferred to be circular so that the distribution of transverse diffusion lengths across the open channels remains as tight as possible. Finally, the general theory of nonuniform columns of Giddings reveals that the polydispersity of the cross-sectional area (RSD 8.4%) along a single 3D-printed channel has no negative impact on solute dispersion in MOTTD columns. Overall, MOTTD columns could become a serious alternative technology to conventional particulate columns. This implies a novel fabrication process that delivers circular channel diameters smaller than 10 μm, cross-sectional area polydispersity no larger than 25%, external porosities in a range from 15% (high speed separations) to 75% (high performance separations), and conventional mesoporous silica as the stationary phase. It adresses new synthesis routes based on either organic fibers or tubular micelle templating agents in suspension with silica gel solutions.