Capillary Rise
Capillary Rise
Surface tension pulls a wetting liquid up a narrow tube — the effect behind wicking, soil moisture and ink pens.
The capillary rise is h = 2γ/(ρ·g·r). where γ is the surface tension, ρ the density, g gravity and r the tube radius.
Inputs
gamma := 0.072 N/m=0.07 kg/s^2
rho := 1000 kg/m^3=1000 kg/m^3
g := 9.81 m/s^2=9.81 m/s^2
r := 0.0005 m=0.5 mm
Balance surface tension against the weight of the column.
h := 2·gamma/(rho·g·r)=29.36 mm
Results
The rise is inversely proportional to radius, so very fine tubes lift liquid much higher. A non-wetting liquid (like mercury) is depressed instead.
Assumptions & limitations
- Fully wetting liquid (zero contact angle).
- Clean, circular tube.
- Static equilibrium.