Energy required to raise a liquid in a capillary tube

When a capillary tube is dipped vertically into a liquid which wets the walls of the tube, there is rise of the liquid inside the tube. Due to the rise, the liquid, gains in potential energy. The question, therefore arises as to where does it get this increase in its potential energy from. The explanation is, however, simple.

We have three surface of separation to consider when a capillary tube is immersed in a liquid viz., (i) an air-liquid surface (ii) an air-glass surface and (iii) a glass-liquid surface each having its own surface tension, difference from the others, and equal to its free surface energy per unit area.

Now, as the plane liquid surface in the tube acquires a curvature, (i.e. become concave), the air-liquid surface increases and, as the liquid rises in the tube, the glass-liquid surface increases, the air-glass surface decreasing by an equal amount. Thus, the surface energy of the air-liquid and the
glass-liquid surface increases while that of the air-glass surface decreases by the same amount. In other words, the energy required to raise the liquid in the capillary tube is obtained from the surface energy of the air-glass surface.

On the other hand, a liquid, which does not wet the walls of the tube, get depressed inside it, below its level outside the tube. In this case, obviously the glass-liquid surface decreases, whereas the air-glass surface increases by an equal amount, resulting in a net increase in the surface energy of the whole system. This energy is derived form the depression of the liquid inside the tube, whose gravitational potential energy is thus decreased by an equal amount.