The effect of meniscus on the permeability of micro-post arrays

This study aims to investigate the effect of meniscus curvature on the permeability of the micro-post arrays, which are widely used for applications of microfluidics. An analytical model that accounts for the meniscus curvature is developed. The model considers two common array types: quadratic and hexagonal arrays. The permeability of micro-post arrays is estimated using the capillary rate of rise experiment and numerical simulation. The results obtained from the analytical model match the experimental and numerical results within the error of 5% over the range of parameters commonly found in microfluidic applications (0.06 < d* < 0.6 and H* > 0.2), where d* and H* are the post-diameter and the post-height, respectively, which are normalized by the pitch. Based on the analytic results, the effects of the post-diameter, post-height and the contact angle on the permeability of post-arrays are investigated. It is shown that the previous permeability models based on the flat meniscus assumption overestimate the experimental value by 26% for the quadratic array and 24% for the hexagonal array when cos theta = 1, d* = 0.5 and H* = 1. The effect of the meniscus curvature is shown to become more pronounced as the contact angle or the post-height decreases.