Surface tension and surface energy

Why liquid surfaces are special

Narrated video. Transcript:

A pond skater walks on water without sinking. A dry steel needle, laid gently on water, floats. Rain falls in round drops. The surface of a liquid seems to behave like a stretched skin.

Zoom in to the molecules. Neighbouring molecules attract each other. A molecule deep inside the liquid is pulled equally in all directions by the molecules around it, so the pulls cancel.

A molecule at the surface has liquid neighbours only below it and beside it, not above. It has fewer bonds than a molecule inside.

Each bond lowers a molecule’s energy, the way a ball sits lower in a dip. With only about half its bonds, a surface molecule has more energy than one inside.

So to make more surface, you must drag molecules up from the inside to the surface, and that takes work. The surface stores this extra energy. It is called surface energy.

Since extra surface costs energy, a liquid left to itself pulls its surface in to the smallest possible area. For a given volume, the shape with the least surface is a sphere.

That is why small raindrops and drops of mercury on a glass plate are nearly round, and why a soap film on a wire frame snaps back if you let it.

Dip a paintbrush in water and pull it out. The wet hairs cling together in a point: water films between the hairs shrink their surface by pulling the hairs together.

Measuring surface tension

Narrated video. Transcript:

Bend a wire into a U shape and lay a straight wire of length l across its arms, free to slide. Dip it in soap solution and lift it out. A thin soap film fills the frame.

Let go of the slider and the film pulls it in, shrinking. To hold the slider still you must pull outwards with a force F.

Now pull the slider out slowly by a distance d. You do work F times d. The film’s area increases. Note: a film has two surfaces, a front and a back, so the new surface area is 2 l d.

If S is the surface energy per unit area, the extra energy stored is S times 2 l d. Your work goes into this energy: F d equals S times 2 l d.

So S equals F divided by 2 l. S is called the surface tension: the force per unit length acting along the surface, at right angles to any line drawn in it. It is also the surface energy per unit area.

Its unit is newtons per metre, the same as joules per square metre. Unlike a stretched rubber sheet, a film pulls with the same force however far you stretch it: S does not depend on the area.

Water at 20 degrees has S of about 0.073 newtons per metre; mercury, about 0.47. Soap solution has a much lower S, around 0.03. The surface tension of a liquid falls as it gets hotter.

Worked example: a soap film, S equals 0.03 newtons per metre, holds a slider 5 centimetres long. The pull is 2 times 0.03 times 0.05: 3.0 times 10⁻³ newtons, the weight of about a third of a gram.

Pull it out a further 2 centimetres and you do 3.0 times 10⁻³ times 0.02, or 6 times 10⁻⁵ joules of work, all stored as surface energy in the new film.

Soaps and detergents lower the surface tension of water. That lets water spread out and soak into the fibres of dirty clothes much better.

Try it: a soap film on a frame

Interactive simulation. Things to try:

• Drag the amber slider wire, or use the slider. Watch the pull F as the film grows.
• F = 2SL: the 2 is there because the film has two surfaces.
• Press Let go (or Space) and the film snaps the slider back.
• Switch to water: its surface tension is about three times that of soap solution.

Film or rubber?

You slowly pull the sliding wire on a soap-film frame further and further out. How does the force needed to hold it change?

1. It grows steadily, like stretching a rubber band
2. It stays the same, because F = 2SL does not depend on the area of the film
3. It gets smaller, because the film gets thinner
4. It doubles each time the area doubles

Holding the slider

A wire slider 4 cm long rests on a soap film (S = 0.025 N/m) in a U-shaped frame. What force is needed to hold the slider still?

1. 1.0 × 10⁻³ N
2. 2.0 × 10⁻³ N
3. 4.0 × 10⁻³ N
4. 0.10 N

Summary

• Surface tension: S = F / l (force per unit length along the surface)
• Film on a frame (two surfaces): F = 2Sl
• Work to enlarge a film: W = S × ΔA = S × 2ld
• Units: N/m = J/m²

• Surface molecules have fewer neighbours, so they have extra energy. Making more surface takes work.
• Surface tension is both the force per unit length and the surface energy per unit area.
• Liquids pull in to the smallest surface area: small drops are spherical.
• S does not depend on the area of the surface. It falls as the temperature rises, and detergents lower it.