Surface Tension Calculator: Capillary Rise, Bubble Pressure and Soap Film Force
Solve surface tension problems: soap film pull, excess pressure in drops and bubbles, capillary rise, coalescing drops and joined bubbles, with the steps shown.
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How this calculator works
Choose the problem, enter the surface tension S (water is about 0.072 N/m) and the sizes. For a soap film on a wire it gives the pull 2Sl and the hanging mass that balances it. For a drop or bubble it gives the excess pressure 2S/R (one surface) or 4S/R (a soap bubble, two surfaces), and the pressure inside an air bubble at depth.
For capillary rise it gives the height 2S cos(theta) divided by rho g r, shows the second tube from h r = constant, and the capillary length that tells you how narrow the tube must be. A contact angle above 90 degrees gives a depression.
For coalescing drops it finds the energy released when n drops join into one (4 pi S r squared times n minus n to the two thirds). It also gives the work to blow a soap bubble, the pressure in two concentric bubbles, and the radius of the common film between two joined bubbles, with the direction air flows.
Formulas used
- F = 2 S \ell
- \Delta p = \frac{2S}{R}\ \ (\text{drop}),\qquad \Delta p = \frac{4S}{R}\ \ (\text{soap bubble})
- h = \frac{2S\cos\theta}{\rho g r}
- E = 4\pi S r^2\left(n - n^{2/3}\right)
- R_c = \frac{rR}{R - r}
Worked example
With the default numbers in the calculator above:
- Pull of the film on the wire: 28.8 mN
- Hanging mass for equilibrium: 2.94 g
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: Surface tension S (water at 20 C is 0.0728) 0.5 N/m; Gravity 10 m/s2; Length of the movable wire (film case) 20 cm.
- Pull of the film on the wire: 200 mN
- Hanging mass for equilibrium: 20.00 g
Common questions
Why is a soap bubble 4S/R and a drop 2S/R?
A soap bubble has two surfaces, one inside and one outside, so surface tension pulls twice as hard. A drop, or an air bubble in a liquid, has only one.
Why does the liquid rise higher in a narrower tube?
The upward pull acts around the rim, which is proportional to the radius, but the weight of the column goes as the radius squared. So the height goes as one over the radius.
Which way does air flow between two bubbles?
From the smaller bubble to the larger one, because the smaller bubble has the higher pressure.
What value of S should I use?
Water at 20 C is 0.0728 N/m. It falls as the temperature rises and is much lower for soapy water, about 0.03.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any university physics text (surface tension and capillarity); White, Fluid Mechanics (surface tension and capillary effects).
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