Viscosity effects on the behavior of a rising bubble

Abstract

In the incompressible fluid flow regime, without taking consideration of surface tension effects, the viscosity effects on the behavior of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by the Volume Of Fluid (VOF) method. The ratio of the gas density to the liquid density is taken as 0.001, and the gas viscosity to the liquid viscosity is 0.01, which is close to the case of an air bubble rising in water. It is found by numerical experiments that there exist two critical Reynolds numbers Re 1 and Re 2, which are in between 30 and 50 and in between 10 and 20, respectively. As Re > Re 1 the bubble will have the transition to toroidal form, and the toroidal bubble will break down into two toroidal bubbles. In this case viscosity will damp the development of the liquid jet and delay the formation of the toroidal bubble. As Re< Re 1 the transition will not happen. As Re 2 < Re < Re 1, the bubble will split from its rim into a toroidal bubble and a spherical cap-like bubble, and as Re< Re 2 the splitting will not occur and the bubble can finally reach a stationary shape. With the decrease of the Reynolds number, the stationary shape changes from spherical-cap bubble with skirt to dimpled peach-like bubble. Before the bubble reaches its stationary shape the vortex structure in the flow field varies with time. The vortex structure corresponding to bubble stationary shape varies with the Reynolds number. It is also found that there exists another critical Reynolds number Re * which is in between Re 1 and Re 2, and as Re < Re *, after the bubble rises in an accelerating manner for a moment, it will rise with an almost constant speed, and the speed increases with increasing Reynolds number. As Re > Re *, it will not rise with a constant speed. The mechanism of the above phenomena has been analyzed theoretically and numerically.