This simulation calculates the measured contact angle for a rough, heterogeneous surface using the Wenzel and Cassie laws. The contact surface is a mixture of materials A and B. Change the fraction of component A and the surface contact angles of each material (θ_A and θ_B) with sliders. Another slider changes the surface roughness; for a completely smooth surface, the surface roughness ratio used in the Wenzel equation is 1. The measured contact angle (θ_W) is calculated and displayed above the water droplet graphic; arrows on this plot show where θ_W is measured. Surfaces with water contact angles > 90° have low wettability and are considered hydrophobic, whereas < 90° means the surface has high wettability and is considered hydrophilic. When θ_W = 0°, complete wetting occurs.

The Cassie model is used to determine the apparent contact angle for a heterogeneous surface θ_C:

where f_A and f_B are the fractions of components A and B on the surface, and f_B = 1 − f_A; θ_A and θ_B are the flat contact angles for A and B.

The Wenzel apparent (or measured) contact angle θ_W and roughness ratio r is

where r is the actual area divided by the apparent area; for a completely smooth surface, r = 1, while for a rough surface, r > 1.

The droplet represents a spherical cap; its volume V (μL) based on the volume of a sphere of radius R is

Solving for R (mm) and eliminating extraneous solutions gives

The measured droplet height h (mm) is

Complete wetting occurs when θ_W = 0°, and no wetting occurs when θ_W = 180°.

Reference
[1] Wikipedia. "Wetting." (Oct 26, 2015) en.wikipedia.org/wiki/Wetting.

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Rachael L. Baumann. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988). Address any questions or comments to LearnChemE@gmail.com.