Figure 1

Schematic of the experimental setup. The dimensions are indicated in the rectangular box on the right. Here $R_m$ is the maximum radius of the bubble, $R_h$ is the radius of the hole in the plate, and $H$ is the distance between the center of the bubble and the bottom of the plate. The thickness of the plate is denoted by $L$.Reuse & Permissions

Figure 2

Overall sequence of events leading to the formation of two impacting jets and their resultant breakup due to an oscillating bubble near a holed plate. The time (in ms) is indicated at the bottom of each frame. The plate has a thickness of $L=12$ mm and a hole of radius $R_h=0.5$ mm. Note the formation of an initial primary jet as the bubble expands into the hole ($t=0.53$ and 0.97 ms) and a tapering of its bottom portion and the formation of an air gap at the top of the hole as the bubble shrinks ($t=1.27$, 1.70, and 1.73 ms). The bubble collapse leads to a perturbation propagating upward through the hole between $t=1.77$ and 1.87 ms (see Fig. 3 for a zoom into the hole). The liquid present in the hole is pushed against the air gap and emerges as short spray bursts that impact on the primary jet and cause perturbations in the jet as shown at $t=2.13$ ms (described in greater detail in Fig. 3). The primary jet subsequently breaks up into fine droplets ($t=2.53$–4.13 ms) as it moves forward pushed by the fluid pumped by the collapsed bubble. A concentric jet of liquid characterized by two side jets (in the planar view) emerges later, as seen clearly at $t=3.50$ ms. This results from expansion of the gas from the remnants of the bubble as it emerges out of the hole along with fluid. The darker color of the liquid immediately following the side jets (indicated by the arrow at $t=4.13$ ms) is due to the bubble or electrode remnants. Later, further liquid is pumped by the bubble and comes out as a thicker continuous column ($t=5.80$ ms). This liquid is distinct from the initial primary jet. The scale bar corresponds to a length of 2 mm. The maximum radius of the bubble obtained is $R_m=6.3$ mm.Reuse & Permissions

Figure 3

Images from the case study in Fig. 2 between time $t=1.77$ and 3.27 ms shown (with background subtracted) to get a clear picture of the mechanism within the hole subsequent to bubble collapse. The numbers in each frame indicate the time in ms. The bubble collapse at $t=1.77$ ms leads to a perturbation propagating through the hole seen as a faint dark vertical line within the hole at $t=1.77$ ms. Alternating air gaps (dark) and liquid packets (gray) are also formed within the hole (indicated by arrows at $t=1.80$ ms). The collapsed bubble pumps liquid into the hole due to jetting induced upon collapse. This pumped liquid is seen as a dark line moving forward at the bottom of the hole from $t=1.90$ ms onward (indicated by the black arrow at $t=1.90$ ms). The pumped liquid also pushes the liquid originally present within the hole upward (gray region indicated by the black arrow at $t=2.00$ ms). The moving liquid packets remove the air gaps and emerge in the form of short bursts of spray (formed by air-liquid interaction) and impact the primary jet as indicated at $t=1.87$, 1.90, 2.00, and 2.13 ms (white arrows). The impacts lead to perturbations on the jet and its breakup into fine droplets and a spray as it moves forward, being pushed by the pumped liquid ($t=2.13$–3.27 ms). At $t=2.97$ ms a concentric jet (noted as two side jets in the planar image) can be seen to emerge from the hole. This is due to the gas from the remnants of the collapsed bubble that expands as it emerges out of the hole. The scale bar corresponds to a length of 2 mm.Reuse & Permissions

Figure 4

Effect of varying the plate thickness on the characteristics of the jet and the bubble at the bottom. The plates used here have thicknesses of (a) $L=2$ mm, (b) $L=5$ mm, and (c) $L=12$ mm. The hole radius is $R_h=1.0$ mm in all the plates. The water level within the hole in all the cases is coincident with the top face of the plate. In (a) note the total ejection of the liquid in the hole due to the bubble expansion ($t=0.80$ ms). The subsequent bubble dynamics is different from that of a submerged nonequilibrium bubble. The maximum bubble radius is $R_m=3.9$ mm. In (b) the bubble splits into two upon collapse. The jet characteristics are similar to that of Fig. 2 but driven by the top half of the split bubble. The bottom portion of the split bubble moves away from the plate. The maximum bubble radius $R_m=5.3$ mm in this case. In (c) both the jet and bubble characteristics are similar to that in Fig. 2. The primary jet, the spray impacting the jet, and the subsequent continuous liquid column are thicker here due to the larger hole radius used as compared to Fig. 2. The bubble reaches a maximum radius $R_m=5.1$ mm. The scale bar corresponds to a length of 2 mm.Reuse & Permissions

Figure 5

Effect of varying the water level with respect to the plate on the jet characteristics (a)–(c). The images are shown after background subtraction. The plate used had a thickness of $L=12$ mm and hole radius of $R_h=0.5$ mm. The water level is indicated with a dash-dotted horizontal line: (a) plate just submerged, (b) plate half submerged, and (c) plate just above the water surface. Note the absence of the primary jet due to bubble expansion in (a). The maximum radius of the bubble was $R_m=5.6$ mm. In (b) the sequence of events is similar to that in Fig. 2. The air gap is indicated by a white arrow at $t=1.67$ ms. The side jets are also indicated at $t=2.97$ ms (white arrow). The maximum bubble radius attained was $R_m=5.7$ mm. In (c) the bubble expansion pushes some liquid into the hole and causes it to come out as a primary jet ($t=0.77$, 1.37, 1.43, and 1.53 ms). A faint spray impacting the primary jet could be distinguished upon bubble collapse ($t=1.97$ ms). A small amount of fluid is subsequently pumped through the hole by the jet induced by the collapsed bubble, which can be seen as a faint vertical line at the bottom of the hole at $t=4.13$ ms (indicated by the white arrow). The maximum bubble radius obtained was $R_m=5.0$ mm. The scale bar corresponds to a length of 2 mm.Reuse & Permissions

Figure 6

Effect of varying the hole radius $R_h$ in the plate on the jet characteristics. The images are shown after background subtraction. The hole radii used and the bubble maximum radii attained are, respectively, (a) $R_h=2.0$ mm and $R_m=4.1$ mm, (b) $R_h=3.0$ mm and $R_m=3.5$ mm, (c) $R_h=6.0$ mm and $R_m=4.7$ mm, (d) $R_h=7.5$ mm and $R_m=5.5$ mm, (e) $R_h=9.0$ mm and $R_m=2.7$ mm, and (f) $R_h=12.0$ mm and $R_m=3.1$ mm. In (a) the sequence is similar to that of Fig. 2 with a primary jet (from $t=0.77$ to 1.47 ms), a subsequent spray impacting the primary jet and perturbing it (from $t=1.67$ to 2.77 ms), and finally the continuous thicker liquid column through the hole (from $t=3.87$ and 6.47 ms). (b)–(d) show a similar behavior: The bubble first expands into the hole but only a very weak or hardly visible primary jet is distinguishable. This is due to the large volume of liquid in the hole (due to large $R_h$) relative to the volume displaced by the bubble. During bubble shrinkage, an air gap is formed on top of the hole in all three cases [$t=1.10$ ms in (b), $t=1.23$ ms in (c), and $t=1.30$ ms in (d)]. A crownlike structure is observed on top of the hole in all three cases upon bubble collapse (due to spray impact with primary jet). In (e) the bubble collapses and oscillates almost spherically. Due to the large hole radius $R_h$, the presence of the plate and the free surface simultaneously near the bubble leads to opposing influences on the bubble to form a jet and the bubble simply oscillates. In (f) the bubble behaves as if near a free surface and forms a jet away from the plate. All the plates used had a thickness of $L=12$ mm. The scale bar in the first frame of each sequence corresponds to a length of 2 mm.Reuse & Permissions