Modified Wenzel and Cassie equations for wetting on rough surfaces

TL;DR

This paper derives modified Wenzel and Cassie equations for wetting on rough surfaces using homogenization, aligning theoretical models with experimental observations by considering local energy minimizers.

Contribution

It introduces new formulas for apparent contact angles on rough surfaces that are rigorously derived and more consistent with experiments than classical models.

Findings

Modified equations match experimental contact angles.

Formulas derived via rigorous homogenization.

New models account for local energy minimization.

Abstract

We study a stationary wetting problem on rough and inhomogeneous solid surfaces. We derive a new formula for the apparent contact angle by asymptotic two-scale homogenization method. The formula reduces to a modified Wenzel equation for geometrically rough surfaces and a modified Cassie equation for chemically inhomogeneous surfaces. Unlike the classical Wenzel and Cassie equations, the modified equations correspond to local minimizers of the total interface energy in the solid-liquid-air system, so that they are consistent with experimental observations. The homogenization results are proved rigorously by a variational method.