Khaled, my first guess is that bubble dynamics has little link with topology. Suppose that we study oscillating bubble of air in water. Then we have dynamics during which bubble always remains topologically equivalent to its spheric state.

But if you observe a division of one bubble into two, then it is a topological phenomenon. If you study dynamics of soap bubbles, this might be the case of relevant topological application. You can see photos here: http://www.ufunk.net/en/photos/giant-soap-bubbles/

Dear Yuri,

   Thanks for your contribution. In nano- and micro-scales we can assume that the bubble remains spherical in shape, but when these bubbles have macro-scales, it is easily affected by gravitational and buoyancy forces which affect on its shape making  visible deformations. you can find many articles talks about non-spherical bubbles.

   I found these articles which used topology in bubble dynamics field:

Best Regards

Khaled

http://www.math.ias.edu/~lazar/shapes.pdf

http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1243851

http://graner.net/francois/publis/jurine_structure_growth.pdf

http://users.aber.ac.uk/sxc/WORK/growth_function_pre.pdf

All mathematical analysis is under topology. So buble  dynamics is also under topology. 

yes minimal surfaces and package of spheress