Lotus-Leaf Cassie–Baxter Wetting Simulator

Wetting State

Droplet rests on pillar tops — air trapped below

Surface Design

Intrinsic contact angle θ_Y 110°

Pillar solid fraction f_s 0.12

Pillar aspect ratio (h/spacing) 1.4

Live Readouts

Apparent angle θ*

0°

Roughness r

1.00

Predicted stable state

—

Other-state angle

—

How it works

The lotus leaf's self-cleaning "lotus effect" comes from a micro/nano-pillar texture combined with a waxy hydrophobic coating. A flat drop of the same wax would already sit at the material's intrinsic (Young) contact angle θ_Y. Roughness amplifies that response into two very different regimes:

Wenzel (fully wetted):
  cos θ*_W = r · cos θ_Y

Cassie–Baxter (air trapped, "fakir" drop):
  cos θ*_CB = f_s (cos θ_Y + 1) − 1

Here r is the roughness factor — the actual surface area of the textured solid divided by its flat projected area (r = 1 + 2π·r_pillar·h_pillar / spacing², computed live from the pillar geometry). f_s is the fraction of the projected area actually touched by solid pillar tops; the rest sits over trapped air, which behaves as if θ = 180°.

θ_Y slider — the flat-surface chemistry (wax ≈ 110°, PTFE ≈ 108°, glass ≈ 30–40°).
f_s slider — how sparse the pillar tops are; smaller f_s means more trapped air and a higher Cassie angle.
Aspect ratio slider — taller/thinner pillars raise the wetted side-wall area and roughness factor r, which is what the Wenzel state actually responds to.
Cassie ⟷ Wenzel toggle — the two are both mechanically possible states for the same texture; nature (and coatings engineers) work hard to keep leaves in the low-adhesion Cassie state, because pressing on a drop, or condensation filling the gaps, can irreversibly collapse it into the sticky Wenzel state.

Droplet volume is held constant as the state or angle changes — the visible shape is an exact spherical-cap solid of revolution computed from θ* and the fixed volume, so a bigger apparent angle makes the same drop ball up taller instead of spreading wider.

Water droplet Wax pillar array

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