Design of textured surfaces for super-hydrophobicity

Abstract

Although the Cassie–Baxter and Wenzel equations predict contact angles for relative dimensions of micro-pillars on textured surfaces, the absolute pillar dimensions are determined by trial and error. Alternatively, geometries of natural super-hydrophobic surfaces are often imitated to design textured surfaces. Knowing the limitations of both the approaches, this work presents a constraint minimization model on the basis of Cassie–Baxter equation to determine the absolute dimensions of square micro-pillars on a textured surface so as to maximize the contact angle. The constraints are derived based on the limiting physical conditions at which spontaneous breakdown of super-hydrophobicity takes place. The single-droplet numerical simulations on textured surface gave the duration for which super-hydrophobicity is sustained. The model demonstrated that the round edged pillars, arising out of fabrication imperfections, reduce the height of the pillars without significantly compromising on the contact angle. The measurement of contact angle on the fabricated textured surfaces was found to be in agreement with the model predictions when the fabricated pillars had fairly uniform dimensions. The proposed approach is sufficiently general that its application can be extended to design other textured surfaces.