Water Contact Angle for Heterogeneous Surface

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The measured contact angle is calculated for a rough, heterogeneous surface using the Wenzel and Cassie laws. The contact surface is a mixture of materials and . With sliders, you can change the fraction of component and the surface contact angles of each material ( and ). Also a slider can change the surface roughness; for a completely smooth surface, the surface roughness ratio used in the Wenzel equation is 1. The measured contact angle () is calculated and displayed above the water droplet graphic; arrows on this plot show where is measured. Surfaces with water contact angles ° have low wettability and are considered hydrophobic, whereas ° means the surface has high wettability and is considered hydrophilic. When °, complete wetting occurs.

Contributed by: Rachael L. Baumann and Nathan S. Nelson (November 2015)
Additional contributions by: John L. Falconer
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA



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


where and are the fractions of components and on the surface, and ; and are the flat contact angles for and .

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


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

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


Solving for (mm) and eliminating extraneous solutions gives


The measured droplet height (mm) is


Complete wetting occurs when °, and no wetting occurs when °.


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

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