Time-evolution of bubble formation in a viscous liquid

Time-evolutions of bubble vesiculation in viscous liquid are characterized by two stages, i.e., the bubble formation stage and the bubble coalescence stage. We have focused on the former stage of bubble vesiculation and investigated numerically bubble formation in decompressed viscous liquid. Bubble formation consists of nucleation and growth of bubbles due to the exsolution of volatile elements from liquid. In order to describe the bubble formation processes, we have developed a theoretical model, taking into account the bubble size distribution and the viscosity of liquid, on the base of the model proposed by Toramaru (J. Geophils. Res., 100, 1913-1931, 1995). Numerical solutions show that the feature of bubble nucleation is significantly varied according to the magnitude of the liquid viscosity. In low viscosity cases, the growth of bubbles is mainly controlled by the diffusive flux of volatile molecules to bubbles. The number density of bubbles is sensitive to the diffusivity of volatile element in liquid. On the other hand, bubbles hardly grow in the case of the extremely high viscosity. Therefore, bubbles continue to be formed in order to reduce the volatile oversaturation of liquid. In the case of the intermediate viscosity, bubbles grow to the large size slowly by the viscous resistance. After the nucleation of bubbles ceases, the Ostwald ripening occurs and leads to the dissolution of small bubbles. The number density of bubbles varies greatly with time. The time-evolutions of the bubble size distribution have been also caluclated. In the case of the low and extreme high viscosity, the bubble size distribution evolves as an unimodal size distribution. In the case of the moderate viscosity, the size distribution of bubbles shows the distribution with a wider dispersion. These characteristic time-evolutions of the number density and size distribution of bubbles would be useful in evaluating material quantities such as the diffusivity, the viscosity, and the surface tension of liquid from experimental results. Furthermore our results provide the number density and size distribution of bubbles just before bubble coalescence occurs.