Capillary Length and Surface Tension

Capillary rise, meniscus shape, and the competition between surface tension and gravity

Fluid Properties







Results

Capillary length λ_c
Capillary rise h
Bond number Bo
Laplace pressure ΔP

Key Relations

λ_c = √(γ/ρg)
h = 2γcos(θ)/(ρgr)
Bo = R²/λ_c² = ρgR²/γ
ΔP = 2γ/R

Physics

The capillary length λ_c sets the scale at which surface tension and gravity are comparable. For water: λ_c ≈ 2.7 mm. Objects smaller than λ_c can float on water surface tension. Capillary rise (Jurin's Law) balances surface tension lifting force 2πrγcos(θ) against weight πr²hρg. Negative curvature (θ > 90°) gives capillary depression (mercury in glass).