Example calculations for how to utilize Wenzel and Cassie-Baxter equations Connected to lecture 2 and exercise 3.

Cassie-Baxter: cos (θcassie)=f*(cosθ)-(1-f) Height of pillars, also 10 µm f = fraction of the liquid droplet touching solid and not air To calculate, look at one unit cell. Unit cell is a “representative sample of the surface” that samples all features with their correct relative amounts. By putting unit cells next to each-other, you can construct the surface. In this case, in the unit cell marker, 10µm * 10 µm touches the solid while 3 * 10 µm* 10µm touches the air. So f = 1/4. If θ = 110°, then cos θcassie=0.25*cosθ – 0.75 θ≈147 degrees 10µm unit cell 10µm Cassie formula can also be used, and was originally developed for, calculating the apparent contact angle of surfaces that have fraction f of θ1 and fraction (1-f) of θ2. Then the formula is: cos (θcassie)=f*(cosθ1)+(1-f)*(cosθ2) So actually the Cassie-Baxter formula used for superhydrophobic surfaces is arrived at by putting θ2 = 180deg since from surface energy point of view, the air contact angle is 180 degrees (adhesion of water to air is zero).

Wenzel formula: cos (θwenzel)=r*(cosθ) Height of pillars, also 10 µm r = roughness factor = real area of liquid/solid contact divided by the corresponding “projected” area of flat surface Similarly calculated from a unit cell The projected area is 4*10µm * 10 µm For the real area, we have: 3 * 10µm * 10 µm at the bottom 1 * 10µm * 10µm at the top 4 * 10 µm * 10µm at the sidewalls So f = 2 If θ = 110°, then cos θwenzel=2*cos110 θ≈133 degrees 10µm unit cell 10µm