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 (θA and
θB) 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 (θW) is
calculated and displayed above the water droplet graphic; arrows on this plot show
where θW 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
θW = 0°, complete wetting occurs.
The Cassie model is used to determine the apparent contact
angle for a heterogeneous surface θC:
cos θC =
fA cos θA +
fB cos θB,
where fA and fB are the fractions
of components A and B on the surface, and
fB = 1 − fA;
θA and θB are the flat contact angles
for A and B.
The Wenzel apparent (or measured) contact angle θW and
roughness ratio r is
cos θW =
r cos θC,
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
V = (π/3) R3
(2 − 3 cos θW +
cos3θW).
Solving for R (mm) and eliminating extraneous solutions gives
R = 31/3 V1/3 ⁄
(2π − 3π cos θW +
π cos3θW)1/3.
The measured droplet height h (mm) is
h = R −
R sin(π/2 − θW).
Complete wetting occurs when θW = 0°, and no wetting
occurs when θW = 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) in collaboration with Washington
State University. Address any questions or comments to LearnChemE@gmail.com.