Capillary height via surface tension and contact angle¶

The Jurin’s law determines the height to which the liquid rises in capillaries. It states that the maximum height of a liquid in a capillary tube is inversely proportional to the tube’s diameter.

Notation:

\(g\) (g) is acceleration_due_to_gravity.

Conditions:

The surface of the meniscus is spherical.
Height \(h\) of the raised (lowered) liquid is much larger than the radius \(r\) of the capillary.

Links:

Wikipedia.

height¶: height of the liquid column.

Symbol:: h
Latex:: \(h\)
Dimension:: length

surface_tension¶: surface_tension of the liquid.

Symbol:: gamma
Latex:: \(\gamma\)
Dimension:: force/length

angle¶: Contact angle between of the liquid and the tube wall.

Symbol:: phi
Latex:: \(\varphi\)
Dimension:: angle

density¶: density of the liquid.

Symbol:: rho
Latex:: \(\rho\)
Dimension:: mass/volume

radius¶: radius of the capillary.

Symbol:: r
Latex:: \(r\)
Dimension:: length

law¶

h = 2 * gamma * cos(phi) / (rho * r * g)

Latex:: \[h = \frac{2 \gamma \cos{\left(\varphi \right)}}{\rho r g}\]