Scale Dependence of Omniphobic Mesh Surfaces

By Shreerang S. Chhatre, Wonjae Choi, Anish Tuteja, Kyoo-Chul (Kenneth) Park, Joseph M. Mabry,Gareth H. McKinley, Robert E. Cohen

We provide a simple design chart framework to predict the apparent contact angle on a textured surface in terms of the equilibrium contact angle on a chemically identical smooth surface and the details of the

surface topography. For low surface tension liquids like methanol (γ_lv = 22.7 mN/m) or octane (γ_lv = 21.6 mN/m), a solid-liquid-air composite interface on textured surface is inherently metastable. Thus on application of a sufficient pressure difference (e.g. an externally applied pressure or a sufficiently large Laplace pressure at small droplet size) the metastable composite interface transitions to a fully-wetted interface. A dimensionless robustness factor is used to quantify the breakthrough pressure difference necessary to disrupt a metastable composite interface and to predict a priori the existence of a robust composite interface. The impact of length scale (radius of the cylindrical features R varying from 18 to 114 microns) and the feature spacing ratio (D* =(R+D)/R varying from 2.2 to 5.1, where 2D is the spacing between the cylindrical features) on the robustness is illustrated by performing contact angle measurements on a set of dip-coated wire-mesh surfaces, which provide systematically quantifiable

cylindrical texture. The design chart for a given feature size R shows how the two independent design parameters, surface chemistry as revealed in the equilibrium contact angle and texture spacing embodied

in the dimensionless spacing ratio (D*), can be used to develop surfaces with desirably large values of apparent contact angle and robustness of the metastable composite interface. Most revealing is the

scaling of the robustness with the dimensionless parameter which indicates clearly why, in the consideration of self-similar surfaces, ‘smaller is better’ for producing omniphobic surfaces that resist wetting by liquids with low surface tension.