Analytic correlation for the capillary pressure of micro-square-pillar arrays

In this study, the capillary pressure of hexagonal arrays of micro-square-pillars is investigated analytically. The effects of spacing between pillars (30 ≤ s ≤ 90 μm) and contact angle (10° ≤ θ ≤ 50°) on the capillary pressure are considered. In order to estimate the capillary pressure, the shape of liquid interface in the micro-square-pillar array is estimated numerically using a surface-energy-minimization algorithm. The capillary pressure is subsequently obtained as the change in interfacial energy per unit volume. The results indicate that the capillary pressure is directly proportional to the cosine of the contact angle, and monotonically decreases as the spacing between neighboring pillars. Based on the numerical results, a semi-analytic correlation for predicting the capillary pressure of hexagonal arrays of micro square pillars is proposed as a nondimensional form. The hexagonal arrays of square pillars are shown to have 13% higher capillary pressure compared with hexagonal arrays of circular pillars with same solid fraction and pitch.