Capillarity is a physical phenomenon in which liquids flow without the help of
gravity. Liquids even rise to a height against gravity, through narrow
tubes.
Capillary action is due to the phenomenon of Surface tension of liquid as well
as adhesive forces between liquid molecules and molecules of the narrow tube.
Surface tension is due to cohesive attraction among liquid molecules.
Derivation:
When a thin (open or closed at the top) tube is inserted into a liquid in a
container, the liquid inside the tube rises to a height h above the liquid
surface outside. Let the diameter of the tube be D. The density of
liquid be ρ. The surface tension of the liquid be S.
Weight of liquid column acting downwards = m g
W = ρ (πD²/4) h g --(1)
The surface on the top liquid inside the capillary tube has a trough (cup) like
shape. Assume the angle of contact with the walls be Ф. Surface
tension is the contact force per unit length along the circumference of top
surface. This force pulls the liquid vertically upwards.
Force upwards = S * πD * CosФ ----- (2)
=>
h = 4 S CosФ / (ρ D g)
