Scale dependence of omniphobic mesh surfaces

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 details of the surface topography. For low surface tension liquids such as methanol (γ_lv=22.7 mN/m) and octane (γ_lv=21.6 mN/m), a solid-liquid-air composite interface on a 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 the length scale (radius of the cylindrical features R varying from 18 to 114 μm) 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 the apparent contact angle and robustness of the metastable composite interface. Most revealing is the scaling of the robustness with the dimensionless parameter l_cap=R (where l_cap = (γ_lv/pg)^1/2 is the capillary length), 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.