# Capillary force

From Soft-Matter

The force by which water ascends in wood, sponge, blotting-paper, and other porous bodies. By the same action the flame of a lamp is fed with oil. The wick is a bundle of threads whose surfaces are nearly in contact, and the oil rises between them in the same way as if they were narrow tubes. Water is supposed to rise from reservoirs and springs below the surface of the ground to the roots or plants in the same way as it rises in fine tubes.

## Formula

The height *h* of a liquid column is given by:

- <math>h={2{ \gamma \cos{\theta}}\over{\rho g r}}</math>

where:

- <math>\scriptstyle \gamma </math> is the liquid-air surface tension(energy/area)
*θ*is the contact angle*ρ*is the density of liquid (mass/volume)*g*is acceleration due to gravity (length/time^{2})*r*is radius of tube (length).

For a water-filled glass tube in air at sea level, using SI units:

*<math>\scriptstyle \gamma </math>*is 0.0728 J/m² at 20 °celsius|C*θ*is 20° (0.35 radians|rad)*ρ*is 1000 kg/m^{3}*g*is 9.8 m/s²

therefore, the height of the water column is given by:

- <math>h\approx {{1.4 \times 10^{-5}\ \mbox{m}^2}\over r}</math>.

## Reference

1.http://chestofbooks.com/reference/Home-Cyclopedia-Of-General-Information/Capillary-Force.html