Surface tension of liquids and capillary phenomena
Lessons 34–35 · 2 lessons · P. Habibullayev, A. Boydedayev, A. Bahromov, K. Suyarov, J. Usarov, M. Yuldasheva. Physics Grade 9, revised and expanded 3rd edition. G‘afur G‘ulom Publishing House, Tashkent, 2019
34
Properties of liquids
Textbook: pp. 94–96
GoalKnow the properties of liquids; the surface tension force F = σl, the surface tension coefficient σ and the surface energy W = σS, and use them.
A liquid keeps its volume but not its shape: it is fluid and takes the shape of its vessel. A molecule inside a liquid is acted on by forces from all sides that balance; a molecule at the surface is acted on only from below and from the sides, so it is pulled into the liquid. This is why the surface is stretched and a surface tension force F = σ·l acts along the line bounding the surface; σ is the surface tension coefficient, σ = F/l, unit N/m (at 20 °C water 0.073 N/m, soap solution 0.04, alcohol 0.022 N/m). The surface tension force tries to make the surface as small as possible, so a free drop and a raindrop are spherical. The extra potential energy of surface molecules is the surface energy W = σS, so σ can also be measured in J/m². When a drop breaks off a dropper, its weight mg equals the surface tension force: mg = σ·l (l = πd).
Worked examples
A thin wire ring 3 cm in diameter is being lifted off a water surface. The surface film clings to the ring along two lines (inside and outside), so F = 2σπd = 2·0.073·3.14·0.03 ≈ 1.4·10⁻² N. This force is needed in addition to the ring’s weight to pull it free.
If the water surface grows by 20 cm², the surface energy increases by ΔW = σΔS = 0.073·20·10⁻⁴ = 1.46·10⁻⁴ J ≈ 1.5·10⁻⁴ J.
Class activity
Observation (with an adult): place a small paper cut-out or a light metal washer carefully on water, then touch the water near it with a stick dipped in soap solution. What happens when the surface tension changes? Experiments with a needle are done with an adult; never handle sharp objects alone. A plasticine ball can be used instead.
Practice
1
Why is the surface of a liquid under tension?
Surface molecules are pulled into the liquid, so the surface tends to shrink.
2
Estimate the mass of a water drop breaking off a dropper of inner diameter 1.5 mm (σ = 0.073 N/m, g = 10 m/s², π ≈ 3.14).
m = σπd/g = 0.073·3.14·0.0015/10 ≈ 3.4·10⁻⁵ kg
3
Name two units of σ and explain how they are related.
N/m and J/m²: 1 J = 1 N·m, so J/m² = N/m.
4
Why is a raindrop, and a water drop in a spacecraft, spherical?
Surface tension tries to minimise the surface, and a sphere has the smallest surface for a given volume.