Spherical-Cap Bubbles

fixed, and they break up or they coalesce. No unified treatment of their motion is within our grasp, and our understanding relies largely on experiment and intuition. Occasionally a semiempirical or fundamental theory valid for certain flow regimes has been successful. However, in spite of these difficulties efforts to understand bubble motions persist because of their importance in natural phenomena (e.g. Blanchard 1963). Moreover, engineering applications are ubiquitous and they range from steel making to lift pumps. Mechanical processes such as material transport, agitation, and stirring are induced by bubble motion. Moreover, absorption, desorpti on, vaporization, condensation, mass and heat transfer, and chemical reactions at the vapor­ liquid interface may be harnessed to benefit process technologies. Owing to this wide range of applications in different branches of engineering, the extensive literature is widely dispersed1 with reviews given e.g. by Siemes (1954), Haberman & Morton (1956), Calderbank (1967), Levich & Krylov (1969), and Harper (1972).