New insights in the velocity dependency of the external mass transfer coefficient in 2D and 3D porous media for liquid chromatography

Numerical calculations of the mobile zone mass transfer rate in a variety of ordered 2D and 3D structures are presented. These calculations are in line with earlier theoretical and experimental findings made in the field of chemical engineering and suggest that the Sherwood-number (Shm) appearing in the mobile phase mass transfer term of the general plate height expression of liquid chromatography is not correctly predicted by the Wilson–Geankoplis – or the Kataoka – or the penetration model expression that have been used up to now to in the field of LC, and that at least more research is needed before these expressions can be continued to be used with confidence. The aforementioned expressions were obtained by neglecting the effect of axial dispersion on the mass transfer process, and it seems that they therefore underestimate the true Shm-number by a factor of 2–5 around the minimum of the van Deemter-curve. New correlations describing the variation of the Shm-coefficient as a function of the reduced velocity for a number of other packing geometries (tetrahedral monolith, 2D pillar array) are proposed. These correlations are in agreement with earlier theoretical and experimental studies showing that at low velocities the local-driving force-based Shm-value is of the order of 10–20 in a packed bed column with an external porosity on the order of 35–40%.

► Numerical calculations of the Sherwood number in ordered beds have been made.
► Results suggest that validity of Wilson–Geankoplis expression may need revisal.
► Results are in agreement with earlier studies in the field of chemical engineering.
► New correlations improve fitting quality of the general rate expression.