How Does the Cassie-Baxter Model Explain the Lotus Effect?

[Klaus von Faust]

1.The lotus effect refers to self-cleaning properties that are a result of ultrahydrophobicity as exhibited by the leaves of "lotus flower". Dirt particles are picked up by water droplets due to the micro- and nanoscopic architecture on the surface, which minimizes the droplet's adhesion to that surface. If the apparent contact area of a droplet with such a surface is A, and the real contact area because of the microscopic whiskers is xA with x = 0.003, what is the contact angle? Assume that without “whiskers”, the contact angle would be α0 = 110 ◦ .2. F = σa
U = Sσ

3. I tried to use the fact that the volume is being constant, and I assumed that the drop has the shape of a spherical cap, so I expressed it's volume in terms of contact angle.
A/xA=pi*R^2/pi*r^2
V=const
V=pi/3*R^3*(2+cos(a))(1-cos(a))^2=pi/3*r^3*(2+cos(b))(1-cos(b))^2
But the equation I have obtained which is not solvable. Can you help me and show another approach?

 

[Chestermiller]

I can't understand what you are modeling. Can you please provide a schematic diagram?

 

[Klaus von Faust]

I can't understand what you are modeling. Can you please provide a schematic diagram?

I solved it myself, I don't know how to draw on this forum properly, but I searched and read about wetting and about 3 models of wetting, Young's model, Wenzel's model and Cassie-Baxter model. This case particularly is a Cassie-Baxter model, so after deriving the Cassie-Baxter equation I got the right result.

https://en.m.wikipedia.org/wiki/File:Cassie-Baxter.png