Composite states of wetting

TL;DR

This paper analyzes and derives analytical expressions for liquid-vapor contact angles in various wetting states on complex substrates with multiple scales, highlighting intermediate states and proposing a composition rule for contact angles.

Contribution

It introduces a composition rule for contact angles on multi-scale substrates and explores intermediate wetting states beyond classical models.

Findings

Derived analytical expressions for contact angles in different wetting states.

Identified the relevance of intermediate wetting states.

Developed a composition rule for contact angles in multi-scale geometries.

Abstract

The analytical expressions of liquid-vapor macroscopic contact angles are analyzed for various simple geometries and arrangements of the substrate, in particular when the latter exhibits two or more scales. It concerns the Wenzel state of wetting when the substrate is completely wet, the Cassie-Baxter state when the liquid hangs over the substrate, but also intermediate states of wetting which are shown to be relevant and in competition with the two other ones. Under a separation of scales hypothesis, a composition rule of contact angles is developed whose interest is illustrated in a close packing setup of rasperry-like particles.