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# Capillary action

Capillary action or capillarity is the ability of a narrow tube to draw a liquid upwards against the force of gravity. It occurs when the adhesive intermolecular forces between the liquid and a solid are stronger than the cohesive intermolecular forces within the liquid. The effect causes a concave meniscus to form where the liquid is in contact with a vertical surface. The same effect is what causes porous materials to soak up liquids.

A common apparatus used to demonstrate capillary action is the capillary tube. When the lower end of a vertical glass tube is placed in a liquid such as water, a concave meniscus forms. Surface tension pulls the liquid column up until there is a sufficient weight of liquid for gravitational forces to overcome the intermolecular forces. The weight of the liquid column is proportional to the square of the tube's diameter, but the contact area between the liquid and the tube is proportional only to the diameter of the tube, so a narrow tube will draw a liquid column higher than a wide tube. For example, a glass tube 0.1 mm in diameter will lift a 30 cm column of water.

With some pairs of materials, such as mercury and glass, the interatomic forces within the liquid exceed those between the solid and the liquid, so a convex meniscus forms and capillary action works in reverse.

A plant makes use of capillary action to draw liquid water into its system, although larger plants require transpiration to move a sufficient quantity of water to where it is required.

Formula The height h in metres of a liquid column is given by:

$h={{2T\cos{\theta}}\over{\rho g r}}$
where
T = interfacial surface tension (N/m)
θ = contact angle
ρ = density of liquid (kg/m3)
g = acceleration due to gravity (m/s²)

For a water-filled glass tube in air at sea level,

T = 0.0728 N/m at 20°C
θ = 20°
ρ = 1000 kg/m3
g = 9.80665 m/s²

and so the height of the liquid column is given by

$h\approx {{1.4 \times 10^{-5}}\over r}$.

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