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.