Why does the vapour bubble in an inkjet printhead collapse so fast? I am studying the inkjet printer in detail. I have come across thermal inkjet printing technology (bubble inkjet technology) and this short discussion below.
We create a water vapour bubble by heating a resistance, which displaces ink and forms a drop but after that.
Why does the bubble collapse in 10 to 20 microseconds?

Bubble Lifetime
The bubble lifetime can be determined from the reflectance measurements. If the bubble collapse is considered complete when the reflectance recovers to 0.75 of its initial value, then the typical lifetime for this printhead is about 11 μs, depending on the voltage applied to the heater. A higher voltage tends to length the bubble lifetime as seen in Figure 3b. The reflectance does not assume its initial value quickly until the heater cools to its steady state temperature.

(screenshot of original)
 A: Here is why.
The exploding vapor bubble launches up off the surface of the heater resistor at an initial speed of about 5 meters/second and reaches a maximum thickness (top to bottom) of between 25 to 100 microns, depending on which HP printhead design you are studying. That vapor bubble acts as a piston to push a droplet of ink out of the nearby nozzle.
(BTW as soon as the resistor surface has been covered by a thin layer of vapor, heat transfer between the hot resistor surface and the liquid is essentially shut off and the bubble expands ballistically.)
Because that bubble is expanding ballistically upwards, the inertia of the liquid next to it causes the bubble to overexpand. Its internal temperature falls due to the expansion and also due to heat loss to the cold ink immediately surrounding it. By the time its expansion stops, its internal temperature is ~ambient and its internal pressure has already fallen to subatmospheric, and the bubble begins a very rapid contraction as the vapor inside it quickly condenses back to liquid.
The shape of the bubble as it expands and collapses is that of a cushion or pillow with an almost flat top and rounded sides. It has a scale length of order ~1/2(heater length) and for HP's earliest inkjet heaters this varied from 30 to 55 microns. This means that for almost all times during bubble collapse except for the very end stages (where the advancing liquid front is  ~1 micron off the heater surface) the effects of surface tension can be safely ignored in comparison to the magnitude of the inertial effects.
Also note that the momentum of the inrushing liquid creates a huge overpressure or water-hammer effect at the instant the bubble vanishes, and will swiftly pound holes in the protective layer atop the heater, causing it to fail. The walls enclosing the sides of the heater must be carefully shaped to urge the bubble collapse impingement point off the active surface of the heater to avoid this cavitation damage.
I spent 28 years in the business of designing and building thermal inkjet printheads for HP and have lots more information on inkjet device physics to share if you need it.
A: I can't compete with Niels' years of experience in the field, but I'll add a note explaining why the bubble collapse is so fast once the heating is turned off.
If you have ever inflated a party balloon then you will know that the tension in the rubber skin of the balloon exerts a pressure on the air inside. That's why if you let go of the balloon all the air rushes out.
In this case the heater creates a bubble of steam inside the water, and the steam/water interface has an elasticity like the rubber skin of a balloon. This interfacial elasticity is called surface tension, and usually given the symbol $\gamma$. Just like a balloon the surface tension compresses the steam inside, and the pressure is given by:
$$ P = \frac{2\gamma}{r} $$
where $r$ is the radius of the bubble. The surface tension of the steam/water interface is about $0.06$ N/m, so for a one micron radius bubble the pressure inside is about an atmosphere. That means as soon as the heating is switched off, and no more steam is being created the bubble is very quickly crushed out of existence by the one atmosphere pressure exerted on it by the surface tension.
In a balloon the balloon collapses because the air rushes out of the nozzle. In a bubble of steam the bubble collapses because the steam is cooled by the water around it and condenses back into water.
