Bubble formation regimes in forced co-axial air-water jets

Abstract

We report a detailed experimental characterization of the periodic bubbling regimes that take place in an axisymmetric air-water jet when the inner air stream is forced by periodic modulations of the pressure at the upstream air feeding chamber. When the forcing pressure amplitude is larger than a critical value, the bubble formation process is controlled by the forcing frequency, leading to the formation of nearly monodisperse bubbles whose volume is reduced as the forcing rate increases. We reveal the existence of two different breakup modes, M1 and M2, under effective forcing conditions. The bubble formation in mode M1 resembles the natural bubbling process, featuring an initial radial expansion of an air ligament attached to the injector, whose initial length is smaller than the wavelength of a small interfacial perturbation induced by the oscillating air flow rate. The expansion stage is followed by a ligament collapse stage, which begins with the formation of an incipient neck that propagates downstream while collapsing radially inwards, leading to the pinch-off of a new bubble. These two stages take place faster than in the unforced case due to the air flow modulation induced by the forcing system. The breakup mode M2 takes place with an intact ligament longer than one disturbance wavelength, whereby the interface already presents a local necking region at pinch-off, and leads to the formation of bubbles from the tip of an elongated air filament without an expansion stage. Scaling laws that provide closed expressions for the bubble volume, the intact ligament length, and the transition from the M1 breakup mode to the M2, as functions of the relevant governing parameters, are deduced from the experimental data. In particular, it has been found that the transition from mode M1 to mode M2 occurs at (StfΛWe)c=0.25 and that the intact ligament scales as li/ro∝Stf−1Λ1/5We1/4 within the breakup mode M1. Here ro is the radius of the gas stream, Λ the water-to-air velocity ratio, We the Weber number and Stf the dimensionless forcing frequency.