Semi-analytic correlation for predicting permeability of micro-square-pillar array

In this study, we consider the permeability of hexagonal arrays of micro-square pillars. A semi-analytic model for predicting the permeability of micro-square pillar arrays is developed. In addition, a numerical analysis is performed with taking into account the effect of meniscus curvature. The analytic and numerical results are in good agreement, within an error of 3%. Based on our analytic and numerical results, the effects of the contact angle (0 < θ < 90°), nondimensional pillar diagonal length (0.1 < d* < 0.5), and nondimensional pillar height (0.5 < H* < 2.5) are investigated. The meniscus curvature is shown to reduce the permeability significantly, particularly when the contact angle is small or the pillar height is low. The permeability of the square pillar array is shown to be larger than that of a circular pillar array.