Contact angles on heterogeneous surfaces; a new look at Cassie's and Wenzel's laws

TL;DR

This paper introduces a new generalized approach to understanding contact angles of liquid drops on complex surfaces, extending classical laws to heterogeneous and rough substrates with gravity and line tension considerations.

Contribution

It develops a novel minimization technique to derive a generalized Young's equation and extends Cassie and Wenzel laws for heterogeneous surfaces, including a microscopic-level equation.

Findings

Derived a generalized Young's equation for contact angles.

Extended Cassie and Wenzel laws to heterogeneous surfaces.

Proposed a microscopic-level contact angle equation.

Abstract

We consider a three dimensional liquid drop sitting on a rough and chemically heterogeneous substrate. Using a novel minimization technique on the free energy of this system, a generalized Young's equation for the contact angle is found. In certain limits, the Cassie and Wenzel laws, and a new equivalent rule, applicable in general, are derived. We also propose an equation in the same spirit as these results but valid on a more `microscopic' level. Throughout we work under the presence of gravity and keep account of line tension terms.