Wetting transition: Macroscopic roughness, static friction, and energy barrier

When a droplet is deposited on a rough solid substrate, the classic Cassie-Wenzel theory (CWT) is often used to describe the wetting states. However, CWT fails to explain experimental observations of high static friction on hydrophobic surfaces with a critical roll-off angle close to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msup> <a:mn>90</a:mn> <a:mo>∘</a:mo> </a:msup> </a:math> ; the static friction is associated with the minimum energy required for the transition between the Cassie state and the Wenzel state. Here, we propose an alternative theory for calculating the static friction force of a droplet on a rough solid surface, based on a complete energy landscape method. Our results for static friction are orders of magnitude larger than those predicted by CWT and have been validated through quantitative comparisons with experiments.