Meniscus dynamics in bubble formation. Part II: Model

A mathematical model was developed to describe the subsequent bubble formation from a single orifice on a perforated plate above a gas plenum. Special attention was paid to the behaviour of the meniscus inside the orifice and its role in the bubble formation process. The model is based on the mass and momentum balances and has two stages. The first bubbling stage A involves the bubble growth, ascent, and detachment. The second waiting stage B concerns the meniscus oscillations and the simultaneous plenum pressurization. The oscillating meniscus is approximated with a simple mechanical analogue, a liquid piston. The model agrees well with the experimental data reported in Part I of this study. In particular, the model is able to describe and explain the hysteresis phenomenon observed in the measurements.