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Bubble formation and detachment in liquid cross-flow widely existed in industrial systems. In this work, an integrated theoretical model based on a global force balance on the bubble detaching from a wall orifice in high liquid cross-flow is established to give a comprehensive description of bubble detaching process. The bubble detachment diameter are predicted by the model, and the effect of variation forces acing on bubble surface caused by liquid velocity, air flow rate and orifice diameter on bubble detachment is analyzed. Predictions of the theoretical model compare well with the previous experiment. In the horizontal direction, the liquid inertia force is the main detaching force, and the liquid drag force plays an important role in the early stage of bubble detachment. Because of the different liquid flow rate, the resultant force change has great influence on bubble detachment. However, due to the difference of gas flow rate and orifice diameter, the change of resultant force has little effect on bubble detachment. The relationship between gas–liquid momentum ratio, orifice diameter and bubble detachment diameter is fitted. When the ratio is less than 0.2, the liquid inertia force and drag force caused by liquid velocity has a great influence on bubble detachment diameter. When the ratio is greater than 0.2, the effect of liquid velocity is gradually weakened, and the bubble detachment becomes difficult due to the increase of air flow.

Theoretical study for bubble diameter prediction at detachment from an orifice in high liquid velocity cross-flow