Surface Tension & Capillary Action

h = 2γ cos θ / (ρgr) — liquid rises against gravity in narrow tubes

Capillary rise arises from the balance of surface tension pulling liquid up the tube walls and gravity pulling it down. For water in glass (θ ≈ 20°, γ ≈ 72 mN/m), a 1 mm radius tube gives ~14 mm rise. Mercury (θ ≈ 140°) shows capillary depression. The meniscus curvature creates a pressure difference ΔP = 2γ/R (Young-Laplace equation).