Capillarity

Capillarity - or capillary action - is the ability of a narrow tube to draw a liquid upwards against the force of gravity.

The height of liquid in a tube due to capillarity can be calculated

h = 2 σ cosθ / (ρ g r)                              (1)

where

h = height of liquid (ft, m)

σ = surface tension (lb/ft, N/m)

θ = contact angle ( θ = 0 for clean tube)

ρ = density of liquid (lb/ft³, kg/m³ )

g = acceleration of gravity (32.174 ft/s², 9.81 m/s²)

r = radius of tube (ft, m)

Surface Tension

Surface tension is typically measured in dynes /cm or N/m .

Capillarity, like surface tension, decreases with increasing temperature. The temperature variation, however, is small and insignificant in most problems.

Example - Water Capillarity Rise in Tube

The capillarity rise in a clean tube (θ = 0) with diameter 2 mm and water temperature 20 ^oC with density 1000 kg/m³ can be calculated as

h = 2 (0.0728 N/m) cos(0) / ((1000 kg/m³ ) (9.81 m/s²) (2 10^-3 m))

= 0.0074 m

= 7.4 mm

Capillarity Rise in Tubes

Capillarity rise in clean circular glass tubes for distilled water, fresh water and mercury at temperature 20 ^oC (68 ^oF) :