Wetting behavior of patterned micro-pillar array predicted by an equivalent surface tension model

Abstract

Micro-pillar array is widely applied to manipulate the wettability of surfaces. Cases where liquid has infiltrated such pillar arrays completely are drawing increased attention in miniaturized systems. An equivalent surface tension model is proposed to characterize the driving force of liquid evolution in patterned micro-pillar arrays after the Young-Laplace equation and surface energy analysis are applied on both the pillar unit and bulk liquid levels. The effects of local menisci induced from the wetting of pillars are bounded and treated as “equivalent liquid-vapor surface tension”, through which the bulk liquid profile is then obtained based on the principle of minimal surface energy. The model is found to be computationally efficient and can be easily obtained through numerical methods. A typical sample case is presented to demonstrate its advantages and simplicity. The bulk profile that considers the effects of pillar array is compared with the result without pillars. The influencing effects, including apparent tilt angle, pillar spacing, and pillar shape, are addressed.