That darn vortex ring

Despite a  plea to the internet community at large in a previous posted titled “Vortex rings – suggestions please” no one came forward with any explanation of my splitting vortex rings. As popular as our little blog is, it wasn’t popular enough to reach any fluidics experts that could help us. To be honest, I had written this whole problem off a while back and that post was my last attempt at getting an answer before filling it into a folder on my computer called “things to solve when time = ∞”, a folder that is growing to slowly fill a large portion of my hard drive space. At the end of the day, the split vortex rings are at best a quirk and appeared so rarely that they were hardly worth considering….

That last sentence is a lie – I have never thought weird data abborations “hardly worth considering”, in fact weird data tends to dwell in my mind and keep me up at night. Once such night while I was mentally cursing my inability to solve this problems for the 1000th time, it occurred to me that I hadn’t properly looked at the vortex rings I was creating. I’ve recorded their progression and played about with the conditions but, never actually seen the moment of formation. So I went back to the lab and recorded the drop addition using a 200x USB microscope. My hope was that there may be some property of the rings conferred from the addition of the liquid and its coalescence with the bulk water. Below is the resulting video.

Apart from being very clear (not bad for a £20 camera) the video doesn’t really show how the rings initially form, as I had hoped. When slowed down, we can see that the drop completely coalesces with the water in less than a single frame of the 25 fps video. In order to properly visualise the formation a better camera would be required. Thankfully I work for a department that has a few lying around… or in this case attached to other experiment that Dan and Tom very kindly disassembled so I could play with rings. With Dan and Tom’s help we relocated to another lab (with a better computer) and set up a high-speed camera to record the rings.

High-speed camera set up for filming vortex rings. The large halogen light is there to compensate for having an exposure time of just 200 microseconds

For those interested, the camera was an Baumer HX13 with a consumer SLR lens on the front. The camera is rated for speeds of up to 500 fps a limit mostly set by the speed of your hard drive. If you are shooting at around 500 fps you are generating 250 MB of data per second of footage all of which needs to go directly to RAM as the HDD can’t store data that fast (well not without some fiddling). So you can then only film until the RAM fills up, and the program promptly crashes, the first sign of which is Dan frowning. However, though some tweaking and custom coding Dan has managed to hack the camera to run at speeds of up to 17,000 fps (provided you didn’t mind capturing a 2×2 pixel video). So with some fiddling we got the camera running at around 1200 fps (48x faster that the USB camera) with which we could capture about 7s of footage. Below is the first run with the critical point slowed down.

Even at 1200 fps the coalescence of the drop is still occurring in less than 10 frames. That means the entire event occurs in less than 8 milliseconds, or about the time it takes a bullet to travel 2 metres. What you can just about see in these few frames is the drop merges with the water and then gets ‘pinched’ off leaving a small amount of liquid on the tip. As the water is strongly attracted to itself, you can see how the ‘pinching’ off results in a very quick movement of the water down in to the liquid creating a ‘dimple’ in the water.

In addition to this video I also wanted to capture the formation of split vortex rings which, as previously discussed, are rare events. However, re-reading through my notes I did spot something I hadn’t before, all the split rings were produced using a needle to generate the drops (as seen in the USB video) rather than the pipette tip (high-speed) video. So again, with Dan’s help we repeated the previous high-speed camera experiment this time using the needle.

On its own, the drops look very similar, the only clearly visible difference is the instability of the needle drop after it has been touched to the surface. While not visible this drop did form a split vortex ring just as we had observed before. A better way of examining this drop would be to compare it directly with the pipette drop, which thanks to the video editing power of Final Cut X I can do.

You may need to watch the video several times to see the differences between the two drops. They both form in a very similar manner and at a very similar rate. However, it is just about possible to discern that the pinching off of the drop from the needle occurs quite differently and appears to ‘elongate’ into a thinner and less stable thread of water.

How this creates split vortex rings I am still not sure of, there is obviously some movement of fluid within this drop addition process that is at least partially responsible. Given a little more time to think these results over I may be able to come up with a model that explains it. Although this is just one very small set of data, so what I really need to keep repeating this until a common cause starts appearing, and to do that I think I need an even FASTER camera – anyone got one that will work at 10,000 fps…?