Water Contact Angle for Heterogeneous Surface

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
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
Snapshots
Details
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
°.
Reference
[1] Wikipedia. "Wetting." (Oct 26, 2015) en.wikipedia.org/wiki/Wetting.
Permanent Citation