On the Identification of Mobile and Stationary Zone Mass Transfer Resistances in Chromatography

A robust and elegant approach, based on the Two-Zone Moment Analysis (TZMA) method, is proposed to assess the contributions of the mobile and stationary zones, HCm and HCs, to the C term HC in the van Deemter equation for plate height. The TZMA method yields two formulations for HCm and HCs, both fully equivalent in terms of HC, yet offering different decompositions of the contributions from the mobile and stationary zones. The first formulation proposes an expression for the term HCs that has strong similarities, but also significant differences, from the well-known and widely used one proposed by Giddings. While it addresses the inherent limitation of Giddings’ approach—namely, the complete decoupling of transport phenomena in the moving and stationary zones—it introduces the drawback of a non-unique decomposition of HC. Despite this, it proves highly valuable in highlighting the limitations and flaws of Giddings’ method. In contrast, the second formulation not only properly accounts for the interaction between the moving and stationary zones, but provides a unique and consistent decomposition of HC into its components. Three different geometries are investigated in detail: the 2D triangular array of cylinders (pillar array columns), the 2D array of rectangular pillars (radially elongated pillar array columns) and the 3D face-centered cubic array of spheres. It is shown that Giddings’ approach significantly underestimates the HCs term, especially for porous-shell particles. Its accuracy is limited, being reliable only when intra-particle diffusivity (Ds) and the zone retention factor (k″) are very low, or when axially invariant systems are considered.