Young's Equation — Contact Angles and Wetting

Equilibrium of solid–liquid–vapor surface tensions at the contact line

Surface Tensions







Results

Contact angle θ
cos θ

Young's Equation

cos θ = (γ_SV − γ_SL) / γ_LV

Young (1805) derived this from the horizontal force balance of three surface tensions meeting at the contact line. θ < 90°: hydrophilic (partial wetting). θ > 90°: hydrophobic. θ → 0°: complete wetting (spreading). θ → 180°: complete non-wetting.

Physics

The contact angle is determined purely by surface energy ratios, independent of gravity (for small drops). The spreading coefficient S = γ_SV − γ_SL − γ_LV determines whether a drop will spontaneously spread (S > 0) or bead up (S < 0). Real surfaces show contact angle hysteresis.