The best known method for determining surface tension is of capillary rise as shown in Figure 2.3.6. A liquid wets the wall of a capillary if the meniscus is concave up, like the case with water. If the liquid doesn’t wet the sides, the meniscus is concave down (like the case of mercury). For wettability, see the next topic, 2.3.7.
The surface tension acts on the entire circumference of the tube with a vertical component of , where is the contact angle between the liquid and the wall. At equilibrium, we have
\[(2\pi r ) (\gamma cos \theta ) = (\pi r ^{2} h)pg \tag{3.2}\]
or
\[\gamma = \frac{pgrh}{2} cos \theta \tag{3.3}\]
Where ρ is the density of the liquid, g is the acceleration of gravity and h is the height of the column. For liquids that wet the walls of the tube, θ is small and \(cos\theta\simeq1\), so
\[\gamma\simeq \frac{pgrh}{2} \tag{3.4}\]
This way the surface tension can be determined directly measuring the height of the capillary climb. The table provides values of for some metallic and inorganic liquids.
