A numerical study of the assumptions underlying the calculation of the stationary zone mass transfer coefficient in the general plate height model of chromatography in two-dimensional pillar arrays.

The present study investigates the validity of one of the key assumptions underlying the general plate height model of chromatography, i.e., the presumed independency of the individual band broadening contributions. More precisely, it is investigated under which conditions the mass transfer inside the stationary zone (e.g., porous pillars) is independent from the axial transport of species outside this zone, and how strongly any such dependency would affect the validity of the general plate height model of chromatography. For this purpose, detailed calculations of the species concentration distribution inside and outside the porous pillars of a computer-mimic of a porous pillar array column have been made. These simulations revealed a clear interplay between the mass transfer inside and outside the pillars, manifesting itself as an asymmetry of the species concentration distribution inside the pillars. The latter is in disagreement with the basic assumption used to calculate the value of the C(s)-term of the general plate height model. The asymmetry-effect is largest at low reduced velocities, high retention factors and high intra-pillar diffusion coefficients. Fortunately, these are conditions where the C(s)-term is relatively small, which might explain why the general plate height model of chromatography (and based on the symmetry assumption) can represent the band broadening in a porous pillar array within an accuracy on the order of some 1-2%.