Young-Laplace: Wetting & Contact Angle

Surface energy balance determines whether droplets spread (hydrophilic) or bead (hydrophobic) — from Young's equation

Parameters

90°
72
5.0
Partial wetting (θ=90°)
Contact angle θ90.0°
Radius of curvature R
Base radius r
Height h
ΔP = 2γ/R (Laplace)
Contact angle hysteresisθ_adv−θ_rec
cos θ_Y = (γ_SV−γ_SL)/γ_LV
Wenzel roughness effect
Spreading coefficient S
Young's Equation (1805):
cos θ = (γSV − γSL) / γLV

Young-Laplace pressure: ΔP = γ(1/R₁ + 1/R₂) = 2γ/R for a sphere

Regimes:
• θ < 90°: hydrophilic (partial wetting)
• θ ≈ 0°: complete wetting (S > 0)
• θ > 90°: hydrophobic
• θ > 150°: superhydrophobic (lotus effect)

Spreading coefficient: S = γSV − γSL − γLV
S > 0 → spontaneous spreading

Cassie-Baxter: air pockets on rough surface → apparent θ increases. Wenzel: roughness amplifies wettability.