Bubble formation at variously inclined nozzles

Bubble formation at variously inclined submerged nozzles, fed with a continuous gas flow rate, is investigated. The average liquid velocity induced by bubble motion is determined, leading to a simple correlation for estimation of the liquid velocities induced by the repeated passage of bubbles. An effective model for the prediction of bubble sizes at their detachment from vertical nozzle orifices is presented which encompasses a bound expansion stage, followed by an accelerated expansion phase, and ends by an original bubble detachment criterion. The existence of a liquid-phase effective entrainment velocity, generated by the continuous passage of the bubble stream, is quantified and included in the model. Model predictions are found to correlate well with experimental and literature data.