What are new methods, specially analytic methods that deal with non-spherical bubble dynamics?
Dear Khaled,
The following text describes most methods dealing with non-spherical bubble dynamics.
Experiments of Rayleigh collapse have involved the use of a spark discharge (Kling & Hammitt 1972; Tomita & Shima 1986) or a laser (Lauterborn & Bolle 1975; Vogel, Lauterborn & Timm 1989) to vaporize a small volume of liquid, thus generating a cavitation bubble. Recently, high-speed photography has allowed detailed observations of cavitation bubble collapse near solid surfaces, including visualizations of the re-entrant jet formation and shock emission (Philipp & Lauterborn 1998; Lindau & Lauterborn 2003). Experimental investigations of shock-induced collapse also show the formation of a re-entrant jet in the direction of shock propagation and the emission of a shock wave upon collapse (Shima, Tomita & Takahashi 1984; Ohl & Ikink 2003; Sankin et al. 2005).
In addition, numerical simulations have therefore emerged as an alternative tool to complement the analysis and experiments. For more details, see the link indicated in the bottom of this answer.
Kling CL, Hammitt FG. A photographic study of spark-induced cavitation bubble collapse. Trans ASME D: J Basic Engng. 1972;94:825–833.
Tomita Y, Shima A. Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse. J Fluid Mech. 1986;169:535–564.
Lauterborn W, Bolle H. Experimental investigations of cavitation-bubble collapse in the neighbourhood of a solid boundary. J Fluid Mech. 1975;72:391–399.
Vogel A, Lauterborn W, Timm R. Acoustic transient generation by laser-produced cavitation bubbles near solid boundaries. J Acoust Soc Am. 1988;84:719–731.
Philipp A, Lauterborn W. Cavitation erosion by single laser-produced bubbles. J Fluid Mech. 1998;361:75–116.
Lindau O, Lauterborn W. Cinematographic observation of the collapse and rebound of a laser-produced cavitation bubble near a wall. J Fluid Mech. 2003;479:327–348.
Shima A, Tomita Y, Takahashi K. The collapse of a gas bubble near a solid wall by a shock wave and the induced impulsive pressure. Proc Inst Mech Engng. 1984;198C:81–86.
Ohl CD, Ikink R. Shock-wave-induced jetting of micron-size bubbles. Phys Rev Lett. 2003;90:1–4.
Sankin GN, Simmons WN, Zhu SL, Zhong P. Shock wave interaction with laser-generated single bubbles. Phys Rev Lett. 2005;95:034501.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2743482/
Hoping this will be helpful,
Rafik
There is a very interesting numerical method called Level-Set Method. Take a look at this method!
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