Multicapillary columns with diffusional bridging: the combined polydispersity and scatter problem

The present study expands upon the modelling of band broadening in multicapillary columns with diffusional bridging, which have been proposed as an alternative to more conventional column designs. The plate height of these columns, consisting of a bundle of cylindrical capillaries, is already known to be affected by the variance of the capillaries' diameters but may furthermore be affected by the spatial distribution of the capillaries across the cross-section. The combined effect of these 'polydispersity' and 'scatter' problems is modelled here by means of mathematical analysis and numerical computations, building upon the framework of Taylor-Aris dispersion and assuming the capillaries are randomly distributed across the cross-section. Both the steady-state and the transient regime of dispersion are evaluated. The acquired data allow to establish equations relating the plate height to the geometrical parameters of the column (including the external porosity and the number of capillaries) as well as the physicochemical parameters of the analyte (including the diffusion coefficient and the retention factor). The term originating from polydispersity, which has been the subject of previous studies, is found to be exceeded by the term originating from scatter, which has not yet received the same attention. The best approach to alleviate the effect of disorder is found to be maximising the external porosity of the multicapillary columns, by adding more capillaries within a given cross-section.