# What happens to surface tension upon increasing surface area

Pretty self explanatory title. But I just read in a book that the surface tension remains same even if the surface area is increased. What could be a possible explanation for that?

• Note that this is in the absence (or alternatively with a saturating bulk density) of surfactants, else there'll be a dependence. Jan 4, 2017 at 8:21

The surface tension is a consequence of the interfacial energy. If you consider some area of the liquid surface $A$ then there is an interfacial energy proportional to the area:

$$E = kA$$

for some constant $k$ that is dependent on the forces between the atoms/molecules in the liquid. If we increase the area of the liquid surface we increase its energy, and that means we have to do work on it. If we do work we must have been exerting a force on the boundaries of the surface, and the force per unit length of the boundary is what we call the surface tension.

The interfacial energy is a consequence of the atomic/molecular interactions in the liquid so the interfacial energy per unit area is a constant and not dependent on the total area. That means the surface tension is also dependent only on the interactions within the liquid and not on the total area.

In liquids, when the surface area is increased, molecules are allowed to move from the bulk phase to the interface. As a result, the number of molecules per unit area (i.e. the distance between the molecules at the interface) remains the same. Therefore, the surface tension does not change.

In solids, I am not sure about the change in the surface tension. I read in an article that the surface tension of a solid still remains the same and the solid molecules can travel to the interface. However, since it is difficult for them to travel, you need to apply a much larger force to bring the molecules to the interface and increase the surface area of a solid.

Just imagine that you want to stretch a copper wire. Isn't it easier to do so when the wire is hot? This is because

1. The mobility of the molecules is better at high temperatures so that they can go to the interface more easily, and

2. The surface tension of the solid is lower at higher temperatures so that the traveling molecules can be accommodated in the interface more easily.