Features of bubble formation and bubbling regimes
Four typical bubbling patterns are observed and distinguished by the bubble coalescence and microbubble generation during injecting gas through the downward-pointing nozzle, as shown in Figure 2. At very low gas flow rate as shown in Figure 2(a), only a single bubble forms in a single cycle (regime I: no bubble coalescence). With its growth, the bubble moves towards one side of the nozzle and then a neck is formed. Different from that with injecting gas from an upward-pointing nozzle, the neck of the bubble is not a cylindrical symmetry. When the size reaches a critical value, the bubble detaches from the nozzle and its neck contracts suddenly in normal direction of gas injection. Afterwards, this bubble begins to spin around the orifice wall until it leaves the nozzle.
As the gas flow rate increases as shown in Figure 2(b), one or two small bubbles form rapidly and merge into the previous departed one and no satellite bubbles are generated (regime II: coalescence without pinch-off). The small trailing bubble and the large departed bubble that would coalesce are termed as mother and father bubbles, respectively (Figure 1). This coalescence process is similar to that observed in experiments of injecting gas through an upward-pointing nozzle, and would not occur when the inner radius of the nozzle is larger than 0.25 mm.
With further increasing the flow rate as shown in Figure 2(c)-(e), a series of microbubbles is generated during the bubble formation and departure process (regime III: coalescence with microbubbles). The mother bubble size increases but the number of the mother bubble formed in one father-bubble cycle reduces as the gas flow rate increases (see in Figures S1-S2 in supplementary material). Accordingly, several microbubbles are generated in one father-bubble cycle at low gas flow rate, but only one is observed at high flow rate. At very high gas flow rate as shown in Figure 2(f), the mother bubble becomes very small and irregular, and continues to penetrate the departed one rapidly without generation of microbubbles (regime IV: irregular bubble coalescence).
Mechanism for generation of microbubbles from capillary nozzle
Figure 3 show a close-up view of bubble coalescence and detailed formation process of the microbubble. It is clear from the Figure 3(a)-(b) that the pinched-off microbubbles arise from the convergence of the capillary waves. These capillary waves are generated from the expansion of the neck connecting two coalesced bubbles, and propagate along the mother-bubble surface. The wave speed of the last surface waves in Figure 3(b) is estimated to be 1.3-1.5 m/s. As the last capillary waves converge at the apex, a cylindrical protrusion with a small neck is formed, as shown in Figure 3(b) at 0.82 ms. This protrusion stretches the mother bubble and delays the collapse of the mother bubble into the father in direction of drainage flow, giving enough time to pinch off a satellite bubble, as reported by Blanchette and Bigioni12. Figure 4 presents the superimposed profiles spanning the travel of the capillary waves and pinch-off process in Figure 3(b), clearly showing the surface stretch by the capillary waves. The generated microbubble that blocks the vapor-liquid interface in the previous frames is removed in Figure 4(b). In addition, Zhang et al.15 found that the draining from the mother bubble to the father further pulled the surface protrusion towards the mother bubble. This would thin the neck induced by the capillary waves and also promotes the pinch-off. Unlike that in previous studies12-14,16 the capillary waves traveled freely in all directions, in the present experiments they are clearly limited and delayed by the nozzle, as shown in Figure 3(b). Therefore, the capillary waves no longer propagate axisymmetrically about the axis of the two parent-bubble centers, while the pinch-off of the microbubble still takes place. Because the bubble inclines preferentially towards one side of the nozzle at the late growth stage, the angle between the injection direction of gas and that of the drainage of the coalescing bubbles is changed from around zero when the gas is injected through an upward-pointing nozzle to 45-135o in the downward-pointing nozzle experiments. This change effectively delays the bubble shrinkage in the drainage flow direction, and it ensures the propagation and convergence of capillary waves at the apex, thereby leading to pinch-off of the microbubble. The ejected microbubbles have a high speed of around 1.5 m/s because it gained considerable momentum from its mother bubble, thereby making it easier to collect the produced microbubbles. Figure 3(c) shows the bubble coalescence process from another side-view, allowing us to clearly observe the internal liquid jet and the propagation of the surface waves after the pinch-off. The formed liquid jet and the surface waves can accelerate the departure of the mother bubble and hasten the next coalescence, thereby generating more microbubbles in one father-bubble cycle.
Typical process of bubble growth and departure from an upward-pointing capillary nozzle at relatively high gas flow rate is shown in Figure 5. It is clear that the departure of the lower trailing bubble and its coalescence with the upper departed one occur nearly simultaneously, and a liquid jet is generated after departure of the lower trailing bubble, with the same direction to that of the drainage flow inside the bubbles. Therefore, one reason for no generation of microbubble may be the block of the nozzle orifice to the development of capillary waves across the trailing bubbles before departure. More importantly, the inward concave of its lower surface and the accelerated drainage process inside the bubbles withstand the convergence of capillary waves, leading to no pinch-off of the satellite bubble.