Temporal evolution of laser-induced water jet

The time evolution of a water jet generated by a nanosecond laser induced water breakdown is presented with different depths beneath a flat free surface. Figure 3.10 shows a typical experimental result for the morphological variations in the temporal evolution of the water jet generated by laser-induced breakdown at a depth of γ = 0.9.

The crown-shaped structure can be seen to be a nearly circular cup. This cylindrical symmetry is quite different from the structure of two-arm splash induced by a spark bubble [10]. The cylindrical symmetry leads to the net force on the wall of the crown-shaped water jet to be uniform in the radial direction. The surface tension of the crown-shaped water jet tends to decrease the surface area by shrinking the diameter of the crown structure. As seen in the fourth row of Fig. 3.10, the crown-shaped water jet is getting closed by over time and forms an air bubble to surround the prior thin jet. The closing motion of the crown-shaped water jet can be analogously imaged as the process of a flower closing the petals. Note that the flat free surface is important for generating the cylindrically crown-shaped water jet with closing motion because the curvature of free surface critically determines the structure of the water jet. In the earlier investigations, it has been found that a cylindrical free surface generally leads to the structure of the two-arm splash with only opening motion [15,16], whereas a spherical surface usually cannot results in the generation of the cup-shaped splash [15]. Just after the closing motion, the top rim of the cup-shaped jet pinches the prior thin jet into two segments to form an air bubble with a vertically elongated toroidal shape. In other words, the circular wall of the crown-shaped jet turns into the boundary of the air bubble and the enclosing segment of the prior thin jet develops into the central pillar of the toroidal air bubble. Followed closely by, the elongated shape of the toroidal air bubble starts to become a near

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spherical shape owing to the surface tension to shrink the surface area. During the shrinking of the air bubble, the central pillar of the toroidal air bubble breaks into multiple water drops inside the air bubble, as shown in the last row of Fig. 3.10. The breakup into smaller packets from a stream of fluid, referred to as Plateau–Rayleigh instability [17,18], is rich with varieties of phenomena and applications [19]. A well-known example related to Plateau–Rayleigh instability is the formation of small droplets when water is dripping from a faucet. The last row of Fig. 3.10 also depicts that the enclosed drops oscillate, collide and recombine to each other; finally only a drop of water with a diameter about 0.33 mm survives in the spherical air bubble.

Interestingly, the final water drop keeps moving upward and bounces between the top and bottom walls of the air bubble. Eventually, the water drop stays on the bottom wall of the air bubble and is stably dragged up by the air bubble, as shown in the last picture of Fig. 3.10. The comprehensive evolution of the water jet can be seen from the Supplemental Material [20] for the movie corresponding to Fig. 3.10.

The morphological variations of the water jet in the temporal evolution are significantly dependent on the depth of the cavitation bubble. The scenario shown in Fig. 3.10 for displaying an air bubble enclosing a water drop generally occurs for the depth in the range of 0.8 ≤ γ ≤ 1.03. There are another two types of morphological changes of the water jets generated in the depths of 0.6 < γ < 0.8 and 1.03 < γ < 1.1, respectively. Figure 3.11 shows a typical result for the morphological variations in the temporal evolution of the water jet generated at a depth of γ = 0.7. In the early stages, the volume of the crown-shaped water jet can be seen to grow considerably. One might naturally expect that a stretched air bubble could enclose the prior thin jet to display a similar phenomenon of the formation shown in Fig. 3.10. However, the thin

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Fig. 3.10 A typical result for the experimental result for the morphological variations in the temporal evolution of the water jet generated by laser-induced breakdown at a depth of γ = 0.9. The time (in μs) is indicated at the bottom of each frame.

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jet is usually bending owing to the strong interaction between the cavitation bubble and the free flat surface. The bent thin jet generally inclines to the sidewall of the crown-shaped jet. As a consequence, only an air bubble without any water drop can be formed in the final stages. The comprehensive evolution can be seen from the Supplemental Material [21] for the movie corresponding to Fig. 3.11. On the other hand, for the depth in the range of 1.03 < γ < 1.1, the wall of the crown-shaped water jet is not high enough to enclose the thin jet with sufficient volume to form a water drop inside the air bubble. Figure 3.12 shows a typical result for the morphological variations of the water jet generated by the laser-induced water breakdown at a depth of γ = 1.04. The comprehensive evolution can be seen from the Supplemental Material [22] for the movie corresponding to Fig. 3.12.

Based on thorough experimental observations, the dependence of the pinched altitude H of the crown-shaped water jet on the depth parameter γ in the range of 0.6-1.1 is shown in Fig. 3.13. Note that there is no crown-shaped water jet to be generated for γ < 0.6 or γ > 1.1. It can be seen that the highest pinched altitude occurs near the region of γ = 0.8 and its value is approximately 2.3 mm. The decrease of the pinched altitude H for the depth in the range of 0.8 < γ < 1.1 arises from the reduction of the interaction between the cavitation bubble and the free flat surface. The scopes for the three types of morphological variations of the water jet in the temporal evolution are depicted in Fig. 3.13. In brief, the condition for the formation of an air bubble enclosing a water drop is a straight thin jet with a sufficient pinched altitude for the crown-shaped water jet.

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Fig. 3.11 A typical result for the morphological variations in the temporal evolution of the water jet generated at a depth of γ = 0.7. The time (in μs) is indicated at the bottom of each frame.

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Fig. 3.12 A typical result for the morphological variations in the temporal evolution of the water jet generated at a depth of γ = 1.04. The time (in μs) is indicated at the bottom of each frame.

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Fig. 3.13 Dependence of the pinched altitude H of the crown-shaped water jet on the depth parameter γ in the range of 0.6-1.1.

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[20] http://dpss.servehttp.com/  Publications  Graduation Thesis: the movie 1 of the attachment of this graduation thesis corresponding to the results shown in Fig.

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[21] http://dpss.servehttp.com/  Publications  Graduation Thesis: the movie 2 of

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the attachment of this graduation thesis corresponding to the results shown in Fig.

3.11.

[22] http://dpss.servehttp.com/  Publications  Graduation Thesis: the movie 3 of the attachment of this graduation thesis corresponding to the results shown in Fig.

3.12.

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Chapter 4. Laser-induced breakdown