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Rise velocity of a spherical cap bubble


University of Minnesota, Aerospace Engineering and Mechanics, 110 Union St. SE, Minneapolis, MN 55455, USA

(Received 23 October 2002 and in revised form 26 February 2003)


The theory of viscous potential flow is applied to the problem of finding the rise velocity of a spherical cap bubble (see Davies & Taylor 1950; Batchelor 1967). The rise velocity is given by


where is the radius of the cap, and are the density and kinematic viscosity of the liquid, is surface tension, and is the deviation of the free surface from perfect sphericity near the stagnation point . The bubble nose is more pointed when and blunted when . A more pointed bubble increases the rise velocity; the blunter bubble rises slower. The Davies & Taylor (1950) result arises when and vanish; if alone is zero,


showing that viscosity slows the rise velocity. This equation gives rise to a hyperbolic drag law


which agrees with data on the rise velocity of spherical cap bubbles given by Bhaga & Weber (1981).