Automated micropillar array design with Bayesian optimization and computational fluid dynamics

In recent years, machine learning has been increasingly applied across various scientific fields, including microfluidics. This study presents a fully automated workflow for the optimization of the geometry of periodic microfluidic systems for chromatography. In particular, Bayesian optimization is combined with Computational Fluid Dynamics to compute the permeability and axial liquid dispersion in perfectly ordered micropillar array beds designed for liquid chromatography, within a fully automated closed-loop iterative optimization toward the best-performing structure. To achieve a sufficiently rapid computation of the data points, the Two-Zone Moment Analysis, which reduces the computational effort for the axial dispersion to a steady-state computation on a single unit cell, was used. During the optimization, the performance of the pillar array geometries was evaluated by calculating their minimal chromatographic separation impedance E_min, which merges the demands for both a low dispersion and a high permeability. Restricting ourselves to the case where the external porosity is kept constant at ε=50%, it has been found that, compared to the most commonly used pillar array arrangement reported in the literature (lattice angle α=60^∘, circular pillars), E_min can be reduced by 25% by adjusting the lattice angle to 70^∘ for circular pillars and that E_min can even be reduced by 35% by also allowing for elliptical pillars and adjusting the lattice angle to 50^∘.