Simulation of the performance of pillar array columns using the pore-throat ratio as efficiency descriptor

Traditional packed beds in chromatography suffer from increased band broadening due to the random nature of packing, leading non-ideal fluid flow and channeling. To address these challenges, pillar array columns have been developed, offering improved performance over random packing thanks to their homogenous fluid profiles. The study aims to i) evaluate fluid dynamics and chromatographic performance across different PAC morphologies, ii) establish the influence of column morphology on performance, and iii) assess the correlation between chromatographic performance and hydrodynamic parameters. Approximately 200 PAC morphologies with different pillar shapes, pillar sizes, rotations and radial stretching were simulated using the finite element method (FEM). The pore-throat ratio was introduced as a predictor for separation efficiency, showing a strong positive correlation between this ratio and the minimum reduced plate height $h_{min}$. It is suggested that a more homogenous fluid profile, indicated by a pore-throat ratio approaching 1, is associated with higher column efficiency and permeability, allowing for larger optimal velocities and reduced separation time. For PACs, the $h_{min}$ is close to 0.25 as the pore throat ratio approaches 1. The simplicity of calculating the pore-throat ratio from the column structure without the need for chromatographic experiments or modeling makes it a practical tool for predicting column performance.