A liquid droplet resting on a flat solid settles at the contact angle θ where the three interfacial tensions balance horizontally at the contact line — Young's equation:
γSV = γSL + γLV·cosθ
cosθ = (γSV − γSL) / γLV
γSL isn't directly measurable, so this simulator uses the Fowkes/Girifalco–Good approximation (good for the dispersive-dominated solid/liquid pairs shown here): γSL ≈ γS + γL − 2√(γS·γL), which reduces Young's equation to:
cosθ = 2√(γS/γL) − 1
PTFE's γs ≈ 18.5 mN/m is the lowest of any common solid — its C–F bonds (485 kJ/mol) leave almost no dispersive attraction for a droplet, so water (γl = 72.8) beads up near θ ≈ 108°, non-stick. Glass, at γs ≈ 70, is nearly wetted flat (θ → 0) because it is close to water's own surface tension.
Real surfaces are never atomically flat. The Wenzel equation amplifies whatever the flat surface already prefers, using a roughness factor r = true area / projected area (r ≥ 1):
cosθ* = r · cosθ
Roughening a hydrophobic polymer (θ > 90°) pushes θ* even higher — the basis of engineered superhydrophobic (lotus-leaf) coatings. Roughening a hydrophilic surface pulls θ* toward 0 instead.
The droplet itself is drawn as a true spherical cap: given θ and a fixed volume V, the sphere radius R solves V = (πR³/3)(2 − 3cosθ + cos³θ); the cap's base radius a = R·sinθ and height h = R(1 − cosθ) follow directly, so the rendered shape — not just the numbers — is the physically correct equilibrium droplet.
Work of adhesion (Young–Dupré): Wa = γL(1 + cosθ) — the energy per unit area to separate the droplet from the surface; it is what makes PTFE useful as a release coating (low Wa) and what makes epoxy useful as an adhesive (high Wa).