Surface Energy and Surface Tension

A molecule deep inside the bulk of a liquid is surrounded, in every direction, by other liquid molecules within the short range over which intermolecular attractive forces act (this range is called the molecular range, typically of the order of a few times $10^{-9}\ \text{m}$). Because it is surrounded symmetrically on all sides, the net attractive force on such a molecule, averaged over time, is zero.

A molecule sitting exactly at the liquid's free surface (the boundary with air, or with a vapour, above it), however, is not surrounded symmetrically: within its molecular range, it has liquid molecules pulling it inward and sideways from below and from the sides, but comparatively very few molecules (of the much less dense air or vapour) pulling it outward from above. The net effect of all these attractive forces on a surface molecule is therefore a resultant force directed inward, into the bulk of the liquid, perpendicular to the surface.

Because of this net inward pull on every molecule at the surface, the liquid's surface behaves, macroscopically, almost exactly like a stretched elastic membrane under tension, always trying to minimise its own surface area (which is why, in the absence of other forces, a small quantity of liquid tends to form a sphere -- the shape with the least surface area for a given volume). Two closely related quantities are used to describe this behaviour precisely:

Surface tension, denoted $T$, is defined as the tangential force acting per unit length along an imaginary line drawn on the liquid's free surface, this force always acting perpendicular to the line and tangential to the surface itself, tending to pull the surface together on either side of the line:

where $F$ is the total tangential force acting along a length $l$ of the imaginary line. The SI unit of surface tension is therefore newton per metre ($\text{N/m}$).

Surface energy is defined as the potential energy stored per unit area of the liquid's free surface, as a direct consequence of the work that had to be done, against the net inward molecular pull described above, to bring molecules from the bulk of the liquid up to its surface in order to create that area of surface in the first place. Since creating a liquid surface of area $A$ (against a surface tension $T$, at constant temperature) requires an amount of work $W = T \times A$, the surface energy per unit area is: …