Bubble Dynamics

Role of Dimensionality and Axisymmetry in Fluid Pinch-Off and Coalescence

J.C. Burton and P. Taborek

PRL 98, 224502 (2007)

URL: http://link.aps.org/abstract/PRL/v98/e224502

A very interesting paper. Figure 2 is amazing!

This pair of researchers from UC Irvine has investigated two phenomena that occure at fluid interfaces: pinch off and coalescence. As the authors point out, these are topological transitions which involve a conversion of interfacial energy into kinetic energy of fluid flow.

Pinch off is what happens when a droplet is pulled apart. At some point it breaks up into two or more pieces. Coalescence is the merging of two droplets into one. The authors have used high-speed, high-resolution video to study these two processes for both two-dimensional and three-dimensional alkane droplets.

What Burton and Taborek observed in 2D pinch off blows me away. Watch the video. When a 3D droplet is pulled apart, it transforms into two globules connected by a thin filament just before pinch off. At one of the filament-globule interfaces, the filament separates, leaving a flat surface and a cone whose opening angle is determined by the fluid properties of the droplet. For the 2D droplets in this paper, the filament starts to pinch off at both ends, so there are two large globules on the left and right connected to a small globule in the middle. As these filaments pinch off, they repeat the process on a smaller scale. The authors observe 5 generations of successive pinch offs, with each generation of droplets smaller than its parents by a factor of 3. The end result is that a single droplet has broken up into about 30 smaller droplets, the smallest of which are almost 1000 times smaller than the original droplet. If that's confusing, watch the video. It's amazing!

Burton and Taborek did not observe any striking differences in the coalescence of 2D and 3D droplets. As two spherical droplets start to merge, the radius of the connected region grows linearly in time. At longer times, the radius grows with the square root of time. The authors use the two scaling laws to determine the approximate size of the droplet at the crossover. The crossover length scale is 2 orders of magnitude larger than the natural length scale of the fluid system.

This is a very interesting paper, with beautiful images, clean data, and insightful explanations.