Capillary-driven liquid transport in a multistage micropillar array

Liquid transport in porous media is governed by capillary pressure and permeability, which are influenced by pore size regionally. Additionally, there exists a trade-off between achieving high capillary pressure and maintaining high permeability. In this work, porous structures consisting of micropillar arrays of gradient pore sizes are designed to balance such a regional trade-off to enable enhanced capillary-driven liquid transport. A dimensionless analytical model describing the wicking dynamics is developed to optimize the pore distribution. The model determines the optimal pore configuration characterized by a negative structural gradient, which minimizes the global wicking time for a given length of the porous media. The optimization result shows that the liquid wicking time can be reduced by up to 25% in the gradient structure compared to a uniform structure of the same length. Experimental validation of the optimized configuration is performed by measuring the wicking dynamics of different liquids in the porous structures. The results show that two-stage and three-stage gradient structures reduce the wicking time by 13.4% and 18.1%, respectively, which agrees well with theoretical predictions. Furthermore, we demonstrate a pillar spacing of 200 μm with the optimal capillary performance parameter K/reff of 4.6 μm at a given side length–spacing ratio of 1.27. The proposed model provides a practical tool for designing and optimizing porous structures at the pore scale to achieve maximum capillary flow rates.