Dynamics of rising bubble population undergoing mass transfer and coalescence in highly viscous liquid

The two-phase flow dynamics involving mass transfer and coalescence is investigated. The model is specifically developed to describe the dynamics of bubble population dispersed in glass forming liquids. The amounts of gas dissolved in the liquid are determined using the chemical equilibrium involving oxidation–reduction reactions. The gravitational bubble rising is used to write the coalescence kernel for which a collision efficiency is also introduced. Based on a Direct Quadrature Method of Moments (DQMOM), a numerical method is developed. This numerical tool is applied to melting of borosilicate glass beads for which temperature and residence time of the sample in a crucible are investigated. The bubble density decreases sharply at short times. This early stage decrease is well explained and quantified when the coalescence is taken into account in numerical computations. The bubble size density is very well described with a log-normal distribution. Using the first three moments, the bubble size distribution obtained numerically is in good agreement with experimental data. Numerical computations are also applied to soda-lime-silica glass in which the bubble release is driven by the mass transfer between the two phases. The faster decrease of bubble density than would be expected by temperature is reproduced by the numerical computation. The enhancement of the bubble release rate is mainly due to the increase of dissolved gas species with temperature.