Hard to find bubble rise paper/bubble shape determination

In summary, the conversation was about finding a paper on gas-bubble shape in axisymmetric flow of fluid, specifically one that treats bubble shape evolution as a variational problem and minimizes free energy to find an equation for the bubble. Several articles and references were mentioned, including one by Frolov that suggests Landau and Lifgarbagez may have tackled this problem in their Fluid Mechanics book. The conversation also touched on the difficulty of finding this paper, as it was published in 1963 and the journal began publication in 1965. Finally, some potential helpful articles were suggested, including Miksis, Vanden-Broeck, and Keller's 1981 paper and Duineveld's 1995 paper, as well as
  • #1
11bolts
3
0
Hi all. I'm looking for a paper that I've seen referenced in a couple of articles I've been reading. The paper is

O. M. Kiselev, Determination of gas-bubble shape in axisymmetric flow of fluid, Zh. Prikl. Mekhan. Tekh. Fiz., No. 3 (1963).

The English name of the journal is Journal of Applied Mechanics and Technical Physics. The biggest obstacle to me getting this paper is the fact that the journal didn't begin publication until 1965!

More generally, does anyone know of any papers treating bubble shape evolution as a variational problem? All of the papers I've found make assumptions about bubble shape and then worry about the fluid dynamics.

I read one paper by Frolov that suggests that Landau and Lifgarbagez tackle this problem in their Fluid Mechanics book, but I can't seem to find the page for this.

Thanks.
 
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  • #3
Thanks for the references. I guess what I'm really looking for is a seminal paper in this field in which the free energy is minimized and an equation for the bubble is found, and solved approximately. I've already produced what I think is the correct equation. It has the correct behavior in the absence of a density gradient (i.e. assuming constant radius leads to Young-Laplace), but the perturbative solution for a small density gradient is not forthcoming.

It seems like this is the kind of calculation that someone would have done 50-100 years ago, but I just can't find it. I was hopeful that the 1963 paper I mentioned would be what I'm looking for, but as I say it's nowhere to be found.
 
  • #4
  • #5
Thanks. I've come across several interesting articles published in the Cambridge Journal of Fluid Dynamics, including these two. Unfortunately my school only has a subscription for 1997-present, so I haven't been able to view them. I'm currently figuring out how I can access them.
 

1. What is hard to find bubble rise paper?

Hard to find bubble rise paper is a type of paper that is used in experiments to observe the rise of bubbles. It is specially designed with a grid pattern that allows for precise measurement and determination of the shape of bubbles.

2. How does hard to find bubble rise paper work?

Hard to find bubble rise paper works by capturing the bubbles as they rise and creating a visual record of their shape. The grid pattern on the paper helps to accurately measure the size and shape of the bubbles, providing valuable data for experiments.

3. What is the purpose of using hard to find bubble rise paper in experiments?

The purpose of using hard to find bubble rise paper is to accurately determine the shape and size of bubbles in experiments. This information can be used to study the behavior of different substances and their effects on bubble formation and rise.

4. How is bubble shape determined using hard to find bubble rise paper?

Bubble shape is determined by carefully observing and measuring the bubbles on the hard to find bubble rise paper. The grid pattern on the paper allows for precise measurements of the size and shape of the bubbles, which can then be analyzed and compared to other data.

5. Is hard to find bubble rise paper necessary for all experiments involving bubbles?

No, hard to find bubble rise paper is not necessary for all experiments involving bubbles. It is typically used in more advanced experiments that require precise measurements of bubble size and shape. Other methods, such as high-speed cameras, can also be used to study bubble behavior in experiments.

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