When you think bubbles, you probably don’t think of nineteenth century aristocrats. But bubbles were one of the many things the 3rd Baron Rayleigh studied towards the end of the nineteenth century. He is in the picture at the top left.
Nowadays we have fancy high-speed cameras and so we can see bubbles bursting:
http://youtu.be/SpcXtmkk26Q
which is just amazing. Rayleigh did not have access to this sort of kit, although I am sure he would have loved to have a fast frame-rate camera like the one used to make this movie. But he already knew the answer to one basic question you can ask about bubbles bursting: How fast does the edge of the retreating soap film move?
He found that as the hole grows the speed at which the retreating edge moves is (approximately) constant. The argument for this is simplicity itself. It is just a conservation of energy argument, combined with the realisation that as the hole grows all the molecules that were in the soap film that has gone from the hole are piled up around the rim of the growing hole, and so the mass of this rim increases with the increasing area of the hole.
After the hole has grown to an an area A, then it must have a kinetic energy (1/2) mv², where m is the mass of the rim of the bubble that is moving at speed v. But this rim of the bubble is just composed of all the molecules that started off in the part of the soap film that has now gone, and so if the mass per unit area of the soap film is w, then m = wA.
Thus the kinetic energy = (1/2) w A v². This kinetic energy comes from the tension released by shrinking the area of the film. The energy released by reducing the area of a soap film by A is just tA, where t is the surface tension of the soap film.
Conservation of energy means that the kinetic energy of the rim of the bursting bubble equals the energy released by decreasing the area of the soap film A, so
(1/2) w A v² = tA
the A‘s cancel giving us the constant velocity
v = √ ( 2 t / w )
As the bubble grows it does so at constant speed. The surface tension of a soap film is maybe 0.01 J/m², and for a film 10 nanometres thick, w will be around 0.01 g / m². Putting these numbers in gives a speed of around 10 m/s. Enough to burst a bubble 1 cm across in 1 ms, or 0.001 s.
This is faster than we can see of course, which is why we need a superfast camera to see it. Rayleigh never saw a bursting bubble as we can now, but he still knew how fast it burst.
