Analysis of microstructure–effective diffusivity relationships for the interparticle pore space in physically reconstructed packed beds

Abstract

We evaluate the effective diffusion coefficient in the interparticle pore space of eight physically reconstructed chromatographic packings of fully porous and core-shell particles, employing an analytical formula that involves the three-point microstructural parameter calculated from two-point and three-point correlation functions through an approach based on sampling templates. Diffusivities calculated by the approximate analytical formula are close to those obtained from pore-scale simulations in the reconstructions using a random-walk particle-tracking technique. Diffusivities are affected, apart from the interparticle porosity, by the actual bed microstructure and packing defects like particle oligomers, spalled shells, larger voids, and debris. Importantly, the data for the microstructural parameter and effective diffusion coefficient over the porosity range spanned by the individual packings (0.363–0.444) reveals non-monotonic behavior. Our analysis demonstrates that the three-point microstructural parameter reflects this morphological specificity of the packings and, as a result, Eq. (3) provides accurate estimates of the effective diffusion coefficients. The presented numerical approach can therefore be applied to evaluate diffusivities in packed beds with all their salient features just from the geometrical information embodied in the bed porosity and the three-point microstructural parameter.