What is capillary action? Derive an expression for the height to which a liquid rises in a capillary tube. How does this height depend on the radius of the tube and the angle of contact?

1. 1 · Define capillarity. The rise or fall of a liquid in a very narrow tube is capillary action. It is caused by surface tension.
2. 2 · Draw the figure. A capillary tube in water: concave meniscus, rise h, angle of contact θ, tube radius r and radius of curvature R.
3. 3 · Pressure below the meniscus. Just below the concave surface the pressure is 2T/R less than atmospheric, so liquid flows up.
4. 4 · Condition for equilibrium. The rise stops when hρg = 2T/R.
5. 5 · Use the geometry. R = r/cos θ, so h = 2T cos θ / (rρg).
6. 6 · Factors. The rise depends on T, θ, r and ρ. A finer tube gives a higher rise (h ∝ 1/r). If θ is more than 90°, cos θ is negative and the liquid falls, as mercury does in glass.
7. 7 · Real life. Oil climbs a lamp wick and ink soaks into blotting paper by capillary action.
8. 8 · Close in one line. Capillary rise grows with T and cos θ and falls as r, ρ or g grow.

Scoring tip: Write R = r/cos θ as a separate line, with a small figure of the meniscus. Examiners give a mark for this step.