A liquid interface behaves as though it tends to reduce its area. This effect is described by surface tension, denoted $\gamma$.

For a simple liquid interface in mechanical equilibrium, surface tension can be viewed in two complementary ways:

• as a tangential force per unit length acting along a line drawn in the interface;
• as the reversible work required to create additional interfacial area.

These descriptions give the same units:

$$\boxed{[\gamma]=\mathrm{N/m}=\mathrm{J/m^2}}.$$

Force-per-length viewpoint

Imagine a straight movable wire of length $L$ bounding one side of a liquid film with a single interface. Surface tension pulls the wire tangentially to the film with magnitude

$$\boxed{F=\gamma L}.$$

The force is perpendicular to the wire but lies in the local tangent plane of the interface.

A soap film has two liquid-air interfaces, one on each side. If both have the same surface tension, the total force on the movable wire is

$$\boxed{F=2\gamma L}.$$

The factor of two comes from two interfaces, not from a different definition of $\gamma$.

Energy viewpoint

If a single interface increases its area by a small amount $dA$, the reversible work required is

$$\boxed{dW=\gamma,dA}$$

when $\gamma$ is approximately constant.

For a soap film, increasing the geometric film area by $dA$ creates area on both faces, so

$$dW=2\gamma,dA.$$

This area-energy cost explains why an unconstrained droplet tends to become spherical: among shapes enclosing the same volume, a sphere has the smallest surface area.

Worked example: force on a soap-film slider

A rectangular soap-film frame has a movable wire of length

$$L=5.0,\mathrm{cm}=0.050,\mathrm m.$$

Take the surface tension to be

$$\gamma=0.030,\mathrm{N/m}.$$

Because the film has two surfaces, the inward force on the wire is

$$F=2\gamma L =2(0.030)(0.050) =3.0\times10^{-3},\mathrm N.$$

Thus

$$\boxed{F=3.0,\mathrm{mN}}.$$

If the wire is pulled outward slowly by $1.0,\mathrm{cm}$, the geometric film area increases by

$$\Delta A=L\Delta x=(0.050)(0.010)=5.0\times10^{-4},\mathrm{m^2}.$$

The two interfaces therefore require work

$$W=2\gamma\Delta A =2(0.030)(5.0\times10^{-4}) =3.0\times10^{-5},\mathrm J.$$

The same result follows from $W=F\Delta x$.

Molecular origin

Molecules deep inside a liquid are surrounded by neighboring molecules in all directions. Molecules near an interface have a different local environment, so creating more interface generally changes the intermolecular energy. Surface tension is the macroscopic mechanical consequence of that interfacial thermodynamics.

Its value depends on the substances forming the interface and can change with temperature, dissolved substances, or surfactants.

Surface tension is not a pressure

Surface tension has units of force per length, whereas pressure has units of force per area. A curved interface can convert the tangential action of surface tension into a pressure difference across the interface, but that curvature-pressure relation is an additional mechanical result.

Surface tension is therefore the local interfacial property; curvature determines how that property contributes to normal force balance.