Formation of ellipsoidal bubbles at a free-standing nozzle

Abstract When gas is injected at high velocity into liquid, the bubbles formed at the nozzle are elongated in the direction of gas flow due to the axial momentum of the gas. In this paper, the bubble is modelled as a prolate ellipsoid growing at a nozzle which projects vertically upwards into a body of inviscid liquid. The shape of the bubble is defined in terms of axial ellipticity, as determined by an energy balance on the gas jet enclosed by the expanding envelope. The time of growth and hence the free bubble volume is derived from the familiar inertial model of bubble motion in which the bubble hydrodynamic mass is presented as a function of axial ellipticity. Theoretical predictions of bubble shape and size at the detachment stage are presented in terms of the injection number, N I , a dimensionless representation of the gas dispersion forces. There is good agreement with experimental observation of air and helium injection into water. Over a range of N I from 0.17 to 1.5 which embraces the energetic injection conditions encountered commercially, bubble ellipticity at detachment increases parabolically whereas the dimensionless bubble volume decreases steadily. The bubble detachment volume under these conditions shows a linear relationship with the gas injection rate. The implications of these findings for gas-liquid contacting and for nozzle design are briefly considered.