For a bubble of radius r, the pressure from the film surface tension is given by the Laplace-Young law
where and are the inner and outer radii of the bubble, respectively, and is the surface tension of the fluid. Letting r be the average of and (actually, ) gives
Bragg Raft, Bubble Chamber, Drop, Sonoluminescence, Stokes Velocity
References
Almgren, F. J. and Taylor, J. E. "The Geometry of Soap Films and Soap Bubbles." Sci. Amer. 231, 82-93, July 1976.
Batchelor, G. K. and Davies, R. M. (Eds.) Surveys in Mechanics: A Collection of Surveys of the Present Position of Research in Some Branches of Mechanics, Written in Commemoration of the 70th Birthday of Geoffrey Ingram Taylor. Cambridge, England: Cambridge University Press, p. 162, 1956.
Brennen, C. E. Cavitation and Bubble Dynamics. Oxford, England: Oxford University Press, 1995. http://resolver.caltech.edu/CaltechBOOK:1995.001.
Boys, C. V. Soap-Bubbles and the Forces Which Mold Them. New York: Dover, 1959.
Courant, R. "Soap Film Experiments with Minimal Surfaces." Amer. Math. Monthly 47, 167-174, 1940.
Isenberg, C. The Science of Soap Films and Soap Bubbles. New York: Dover.
Lamb, H. Hydrodynamics, 6th ed. New York: Dover, 1945.
Lovett, D. Demonstrating Science with Soap Films. Philadelphia: Inst. Phys., 1994.
Plateau, J. "Sur les figures d'équilibre d'une masse liquide sans pésanteur." Mémoires de l'Académie Royale de Belgique, nouvelle série, 23, 1849.
Plateau, J. Statique expérimentale et theoretique des Liquides. Paris: 1873.
Weisstein, E. W. "Books about Bubbles." http://www.ericweisstein.com/encyclopedias/books/Bubbles.html.
