Capillary Rise

Physics: Jurin's law: h = 2γ·cosθ/(ρgr), where γ = 0.073 N/m (water-air), θ is contact angle, ρ is density, g = 9.81 m/s². For water in glass (θ ≈ 0°): r = 0.1 mm → h ≈ 15 cm; r = 1 mm → h ≈ 1.5 cm. The capillary length κ⁻¹ = √(γ/ρg) ≈ 2.7 mm sets the scale where surface tension equals gravity. Trees exploit capillary adhesion in xylem vessels (r ~ 25 μm); water strider legs use capillary forces to walk on water (contact angle ~160°).