Numerical studies of bubble necking in viscous liquids.

The pinch-off of a gas bubble from a tiny nozzle immersed vertically in another quiescent viscous fluid due to buoyancy is numerically investigated. The dynamics of bubble growth and pinch-off are described by the full Navier-Stokes equations for both gas and liquid phases. The equations are solved with a finite-volume method based on the SIMPLE scheme, coupled with a front tracking method to locate the interface between the two phases. The effects of liquid viscosity, surface tension, and gas density on the bubble pinch-off dynamics, which are always coupled in experiments, are investigated separately through simulations. The numerical results are compared with experimental observations on the bubble pinch-off for validation purposes. The simulation results show that the radius of the necking region decreases in a power law mode with time as r approximately tau;{alpha} , where tau is the time to pinch-off and the exponent alpha varies in the range 0.5-1.0 depending strongly upon the liquid properties such as viscosity and surface tension. In addition, the surface tension can significantly affect the bubble pinch-off exponent alpha when the surface tension coefficient is smaller than 0.030 N/m with a Bond number higher than 0.72. It is also found that both higher viscosity of the liquid phase and higher surface tension may result in a delayed pinch-off process and a larger bubble. The effect of gas phase density on the pinch-off is also investigated. As reported in the literature, the gas density variation has minimal effect on the necking process because the density ratio of the gas phase to the liquid phase is small.