The rise of a cylindrical bubble in an inviscid liquid

Abstract

An expansion in powers of t2 is obtained which gives the shape of an initially horizontal cylindrical bubble filled with a massless gas as it rises through an incompressible inviscid infinite fluid in a uniform vertical gravitational field. For larger times the series does not converge but we have found that a variation of the Padé approximant method gives good results for the locations of the top and bottom of the bubble, although not for times quite as large as might be desired. The results compare favourably with experiment.