Prediction and optimization of liquid propagation in micropillar arrays

Prediction and optimization of liquid propagation rates in micropillar arrays are important for various lab-on-a-chip, biomedical, and thermal management applications. In this work, a semianalytical model based on the balance between capillary pressure and viscous resistance was developed to predict liquid propagation rates in micropillar arrays with height-to-period ratios greater than 1 and diameter-to-period ratios less than 0.57. These geometries represent the most useful regimes for practical applications requiring large propagation rates. The capillary pressure was obtained using an energy approach where the meniscus shape was predicted using Surface Evolver simulations and experimentally verified by interference microscopy. The combined viscous resistance of the pillars and the substrate was determined using Brinkman's equation with a numerically obtained permeability and corroborated with finite element simulations. The model shows excellent agreement with one-dimensional propagation experiments of deionized water in silicon micropillar arrays, highlighting the importance of accurately capturing the details of the meniscus shape and the viscous losses. Furthermore, an effective propagation coefficient was obtained through dimensionless analysis that is functionally dependent only on the micropillar geometry. The work offers design guidelines to obtain optimal liquid propagation rates on micropillar surfaces.