Hard to find bubble rise paper/bubble shape determination

[11bolts]

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.

 

[Andy Resnick]

Something like this?

http://www.google.com/url?sa=t&rct=...sg=AFQjCNHTc4mFModMlth2HwSLTd_N3MUqVg&cad=rja

http://www.google.com/url?sa=t&rct=...sg=AFQjCNHJ0bxVLNUIjD8ppjuZTZTI92y2yA&cad=rja

http://journals.cambridge.org/actio...56188CDAB.journals?fromPage=online&aid=386413

http://www.sciencedirect.com/science/article/pii/004578259290060W

 

[11bolts]

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.

 

[olivermsun]

I wonder if either of these would help (at least they have a good references list):

Michael Miksis, Jean-Marc Vanden-Broeck and Joseph B. Keller (1981). Axisymmetric bubble or drop in a uniform flow. Journal of Fluid Mechanics, 108 , pp 89-100 doi:10.1017/S0022112081002000

P. C. Duineveld (1995). The rise velocity and shape of bubbles in pure water at high Reynolds number. Journal of Fluid Mechanics, 292 , pp 325-332 doi:10.1017/S0022112095001546

Also Lamb's textbook.

 

[11bolts]

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.