When scientists do experiments, they obviously pay attention to the initial conditions involved. But in experiments on how fluids break up from underwater nozzles, physicists from the University of Chicago have discovered that the initial conditions didn't matter. It's even appropriate to talk about amnesia of air bubbles. As they say, the equations which rule fluid dynamics also are the equations governing our lives. And they took images at 130,000 frames per second of air bubbles to prove their point. But read more...
Here is a quote of the University of Chicago news release about this research.
The research is helping scientists understand the mathematical explosions they encounter in the equations that govern the physics of fluids. "These are the equations of our lives," said Wendy Zhang, Assistant Professor in Physics at the University of Chicago. They govern everything from the bubbles of carbonated beverages to the venting of gas from deep oceanic fissures. They even apply to such large-scale processes such as exploding stars.
But what's so new in this research? The physicists have discovered "a new class of behavior in air bubbles rising from an underwater nozzle."
In order to better understand what these researchers have found, we now need to look at their last scientific paper, authored by Nathan Keim under the direction of Zhang and Sidney Nagel.
This paper was published by Physical Review Letters under the title "Breakup of Air Bubbles in Water: Memory and Breakdown of Cylindrical Symmetry" (Volume 97, Number 14, Article 144503, October 6, 2006). Here are two links to the abstract and to the full paper (PDF format, 4 pages, 254 KB).
Now, let's turn to some pictures. First, here is a representation of the symmetrical pinch-off of an burst of air from a level nozzle (Credit: University of Chicago).
And here are front and side views of a pinch-off in an air burst from a nozzle tilted by two degrees. The nozzle’s tilt is indicated in white in the bottom-left frame. In the front views at top, the neck broadens before breakup, resembling a crimped and bent double cone. Then, a pair of tiny satellite bubbles is produced. (Credit: University of Chicago)
And here is a good explanation of this work.
Using high-speed video, we have studied air bubbles detaching from an underwater nozzle. As a bubble distorts, it forms a thin neck which develops a singular shape as it pinches off. As in other singularities, the minimum neck radius scales with the time until breakup. However, because the air-water interfacial tension does not drive breakup, even small initial cylindrical asymmetries are preserved throughout the collapse. This novel, non-universal singularity retains a memory of the nozzle shape, size and tilt angle. In the last stages, the air appears to tear instead of pinch.
For even more details, you can read a lecture given by Wendy Zhang in Boulder on July 5, 2006, "Capturing Liquid Motion the Art & Science of Freezing Time" (PDF format, 47 pages, 3.62 MB).
Sources: University of Chicago news release, via EurekAlert!, October 5, 2006; and various websites
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