Is superhydrophobicity robust with respect to disorder?

TL;DR

This paper theoretically investigates how surface disorder affects superhydrophobicity, demonstrating that disorder generally reduces contact angles but can be optimized to maintain superhydrophobic properties.

Contribution

It introduces a theoretical framework for analyzing the impact of disorder on wetting states and derives explicit contact angle formulas for various geometries.

Findings

Disorder tends to lower contact angles compared to periodic surfaces.

Certain types of disorder can minimize the loss of superhydrophobicity.

Superhydrophobicity can be made robust despite surface disorder.

Abstract

We consider theoretically the Cassie-Baxter and Wenzel states describing the wetting contact angles for rough substrates. More precisely, we consider different types of periodic geometries such as square protrusions and disks in 2D, grooves and nanoparticles in 3D and derive explicitly the contact angle formulas. We also show how to introduce the concept of surface disorder within the problem and, inspired by biomimetism, study its effect on superhydrophobicity. Our results, quite generally, prove that introducing disorder, at fixed given roughness, will lower the contact angle: a disordered substrate will have a lower contact angle than a corresponding periodic substrate. We also show that there are some choices of disorder for which the loss of superhydrophobicity can be made small, making superhydrophobicity robust.