Diffusion models in chromatographic columns packed with fully and superficially porous particles

Most theoretical analyzes of molecular diffusion in chromatographic columns are based on more or less approximate models. Macroscopic sample diffusion along packed columns results from a complex combination of the local sample diffusivity in the external porosity of the bed (Dm) and in the porous particles (ΩDmΩDm). A further complication arise from the use of the new superficially porous (or core–shell) particles. The obstruction to axial diffusion caused by the presence of their impermeable core has to be quantified.Two original models of longitudinal diffusion in packed beds are derived for these ternary composite materials. They account for the actual 3D micro-structure of the packed column bed. The micro-structure results from the presence of (1) the impermeable spherical cores; (2) the porous shells surrounding these cores; and (3) the eluent within which the particles are randomly dispersed. The theoretical approach is based on the combination of the effective medium theory of Garnett for core–shell spherical inclusions and of the probabilistic theory of Torquato for randomly dispersed spheres in a continuous matrix. The impacts of the core to the shell diameter, ρρ, and of the porous shell to the bulk diffusivity, ΩΩ, on the longitudinal diffusion B coefficient of chromatographic columns packed with core–shell particles are analyzed from a theoretical point of view.