The pinch-off of a bubble

We report ultra-high-speed imaging of the pinch-off of a bubble, using frame-rates up to 1,000,000 frames/s, with an exposure time as short as 0.5 $\mu $s and spatial resolution as small as 5 $\mu $m. The bubbles are grown attached to a circular needle at a very slow rate, until they become unstable to buoyancy forces and pinch off from the needle. Our focus is on measuring the power-law describing the reduction in the neck-radius vs time, for a bubble in a low-viscosity liquid, such as water. Our measurements will be compared to theory which suggests the radius should decrease as time to the power $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $. Results will be presented for three different gases as well as different bubble sizes, generated by using different sized needles from 2 to 5 mm.