Surface tension effects on the behaviour of a rising bubble driven by buoyancy force

In the inviscid and incompressible fluid flow regime, surface tension effects on the behaviour of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by a volume of fluid (VOF) method. The ratio of the gas density to the liquid density is 0.001, which is close to the case of an air bubble rising in water. It is found by numerical experiment that there exist four critical Weber numbers We1, We2, We3 and We4, which distinguish five different kinds of bubble behaviours. It is also found that when 1 ≤ We We2, the bubble will not reach a steady shape, and in this case it will not rise with a constant speed. The mechanism of the above phenomena has been analysed theoretically and numerically.