Surface Tension, Beads & Capillary Rise

Surface tension is a force per unit length, γ = F / L. Change it and watch a drop bead up, the Laplace pressure ΔP = 2γ/R climb, and water in a narrow tube climb to h = 2γcosθ / (ρgr).

Surface tension  γ = F / L
72.8 mN/m
0.0728 N/m · water at 20 °C
Laplace pressure  ΔP = 2γ/R
34.36 Pa
R = 4.24 mm · droplet
Bead height
2.12 mm
free cap: γ cannot raise it
Capillary length  a = sqrt(γ / ρg)
2.72 mm
taller beads get flattened
Surface tension γ72.8 mN/m
Contact angle θ60°
Drop volume V50 µL
Tube radius r0.50 mm
Liquid surfaces
Liquid density ρ = 1000 kg/m³ · g = 9.81 m/s²
Tip: push the contact angle past 90° and switch to the tube — cosθ turns negative and the column is pushed below the reservoir. That is the mercury case, and it is correct.