Linear general rate model of chromatography for core-shell particles: Analytical solutions and moment analysis

Due to their proven performance and improved availability, core-shell particles are increasingly applied for chromatographic separations. This paper presents semi-analytical solutions and a moment analysis of a detailed mathematical model for fixed-beds packed with core-shell particles. The model considers axial dispersion, interfacial mass transfer, intraparticle diffusion, linear adsorption, and the injection of rectangular pulses. The Laplace transformation is used as a basic tool to derive semi-analytical solutions. In addition the first three statistical temporal moments are derived from solutions in the Laplace domain. The numerical Laplace inversion is applied for back transformation of the solution in the actual time domain. In order to demonstrate their potential, different scenarios are considered to quantify the effects of the relative core size, axial dispersion, film mass transfer resistance and intraparticle diffusion resistance in the porous layer on the elution profiles. An important new result is the derivation of a plate height equation for fully porous and core-shell particles respecting the Danckwerts boundary conditions.