Laser-induced elongated bubble in infinite surrounding

Based on the experimental setup in Chapter 3, in infinity surrounding, Fig. 4.1 shows the oscillation of an elongated bubble of about 1.4 mm in length induced by a nanosecond laser with 18 mJ. The frame interval is 10 μs with 1 μs exposure time.

The major axis of the elongated bubble is on the horizontal line or the incident optical path because the laser-induced plasma expands mainly on the optical path. We can see the oscillations of the bubble on major and minor axes are similar during the first period of expansion, which leads to a nearly spherical shape with diameter about 2.5 mm at its maximum size. Additionally, because the elongated bubble is cylindrical symmetry, the expansions of the bubble on the directions normal to the major axis are equal to each other. As a result, the elongated bubble shows a near sphere at its maximum size during the first expansion in an infinite surrounding despite that this bubble is not initially spherical symmetry in shape and velocity. In Fig. 4.1, upon the first collapse point, the bubble uniquely rebounds to a dumbbell due to the significant expansion on the major axis. Following the dumbbell, the bubble converts to elliptic and reaches the second collapse point. After the second collapse point, the bubble vibrates and decays in roughly spherical shape. The experimental result of Fig. 4.1 is conspicuously different to the bubble oscillation induced by a femtosecond laser as shown in the Fig. 33 of Ref [5].

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Fig. 4.1 The oscillation of an elongated bubble in infinite surrounding. The frame rate is 100,000 and the exposure time is 1μs.

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4.2 Experimental setup

A bubble is generated beneath a free surface by focusing a flash-pump pulsed laser (Nd:YAG, λ=1064 nm) with a pulse width 6 ns. The beam waist of the laser is 1.5 mm and is enlarged 10 times to 15 mm by employing a beam expander (Fig. 4.2).

Then, a lens with a focal length of 4.5 cm in air is used to focus the enlarged beam horizontally into a tap water at a room temperature 297K under atmospheric pressure.

The dimension of the water tank is 100^╳70^╳20 mm³ and the depth of water is 15 mm for alleviating the influence on the bubble from the bottom wall of the tank. The dynamic of the interaction between the bubble and the free surface is reproducible and is recorded by a high speed camera (NAC GX-3) which has maximum frame rate at 198,000 fps.

The plasma expansion in the early stage of a laser-induced breakdown is intimately correlated to the laser energy, and the plasma expands toward the incident laser beam due to the energy distribution on the incident optical path [6]. The higher the incident energy, the farther the initial plasma moves away from the focal point, which results a longer cavitation bubble. Furthermore, because the maximum size of the bubble gradually saturates when the laser energy is increased, the optimal stability in bubble size can be achieved at lager laser energy. As a result, for observing a stable water jet induced by an elongated bubble, the laser energy is set to 18 mJ which is the maximum laser energy measured just after the focusing lens with f = 4.5 cm.

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Fig. 4.2 The schematic experimental setup for observing the water jet on the free surface. Laser is horizontally focused into the water.

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4.3 Results and discussion

The water jet shows a sheet feature and this sheet structure gradually appears on each part of the water jet when the bubble depth is decreasing. In this section, we follow the sequence of the appearing of each part of the water jet with decreasing bubble depth.

Figures 4.3 and 4.4 show the behavior of a water jet on a flat water surface with 30,000 frame rate and 10μs exposure time, which is induced by an elongated bubble with γ = 1.18 and 0.76. This water jet is divided into a thin jet and a thick jet as depicted in Fig. 4.3 for discussing the feature of the water jet. The bubble depth is defined in stand-off parameter γ = D/Rmax, where D is the depth beneath the free surface and Rmax is the maximum bubble radius. Because the vertical expansion of the bubble is significantly influenced by the free surface, the maximum bubble radius is measured by the width of bubble in the picture and is around 0.9 mm to 0.99 mm for bubble depth between 0.5 mm and 1.5 mm. As a result, the maximum bubble radius is defined in 0.95 mm. The direction of the laser beam goes horizontally from left to right, and the major axis of the elongated bubble is parallel to the water surface plane.

In other words, the morphology of the water jet is not cylindrical symmetry. When the bubble gradually approaches to the water surface, this asymmetrical effect from the bubble first apparently appears on the top of the thick jet which has a pair of ear, as shown in the Fig. 4.3 with γ = 1.18. It should be noticed, this ear is parallel to the major axis of the bubble. This formation of the ear will be discussed later because the experimental results about this mechanism are clearer when the interaction between the bubble and free surface is increased by decreasing the bubble depth.

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These ears significantly grow into a structure similar as a pair of opposite arm when the bubble gradually approaches to the water surface, as shown in Fig. 4.4 with γ = 0.76. In addition to the significant water splashes of the two arms, there is a short cyclic splash shaped like a cup connected between the two arms and the top of the thick jet, as shown by the last few pictures of the second row in Fig. 4.4. Comparing this experimental result with the case when the expansion of the bubble on the direction parallel to the free surface is symmetrical, for example, vertically focusing the laser beam into a water as measured in our previous work in which the two arms are not exist and the edge of a cup is uniform [7]. As a result, we consider that the structure consisted of the arms and the cup is an asymmetry crown-shaped water jet which has great speed on the direction parallel to the major axis of the bubble.

Additionally, the structure of a thick jet induced by a spark bubble is similar to the case of Fig. 4.4, which has two-arm splash parallel to the electrodes of spark discharge [8,9].

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Fig. 4.3 The water jet for γ = 1.18. The major axis of the bubble is parallel to the water surface. The frame rate is 30,000 and the exposure time is 10μs.

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Fig. 4.4 The water jet for γ = 0.76. The time (in μs) is indicated at the bottom of each frame. The top of the thick jet shows an asymmetry crown-shape water jet.

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Beside the growth of the ear to a two-arm splash, the thin jet appears an interesting feature which is analogously a rotating drill. As labeled by an arrow in Fig.

4.5(a) with γ = 0.73, the thin jet rotates in 180° with about 0.2 ms. Generally, a rotating jet could be generated artificially by a rotating pressurized chamber in which the jet is expelled tangentially [1]. However, in our experimental setup, there is no angular force for inducing the circular rotation from the bubble. Thus, we explain this rotating jet analogously by the mechanism of circular or elliptical polarization of an electromagnetic wave as followed. When a stream of fluid is generated, no metter how smooth the stream is, there always exists instability began from any tiny perturbation in the stream, referred to as Plateau–Rayleigh instability [10,11]. This instability causes a waving on the surface of the stream, and finally, this stream breaks into smaller droplets [1,10,11], as shown in Fig. 4.6. Figure 4.6 shows the thick part of the water jet induced by vertically focusing the laser beam into the water (the setup in Chapter 3). As we can see, the vibration on the surface of the thick jet is cylindrical symmetry and the thick jet gradually breaks up into server drops. Additionally, the breakup of thin part of the water jet in Fig. 4.6 has similar result which is not shown.

However, when the laser is horizontally focused into the water, the waving on the thin jet with directions parallel to the major and minor axes of the bubble, as depicted in Fig. 4.7(a), will be different to each other due to the great energy distributions of the water breakdown and the bubble parallel to the optical path. This difference can be in phase or amplitude and is similar to the circular or elliptical polarization of an electromagnetic wave. A schematic picture of a circular polarization is shown in Fig.

4.7(b). As a result, the thin jet is rotating or twisting.

As mentioned above, the mechanism of the two arms is apparent when bubble depth is decreased. In Fig. 4.5(a), the frame at the time of 133.3μs clearly shows the feature of a surface depression about the formation of the two-arm splash. In Chapter

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3, when a laser is focused vertically into the water, a thick jet shows a crown-like structure on its top. We discussed the process of such crown-like structure as followed.

The pressure in the bubble is decreasing during its first expansion, and then the bubble start to collapse because its pressure can not counterbalance the external pressure. Such downward collapsing of bubble leads to a depression of the free surface upper the bubble [13,14]. Upon the surface depressing to its maximum depth, the surrounding water flows into the crater of the surface depression and a water jet rises on the free surface [7,13]. Compared to the general case which is only a crater formed during the surface depression [14-17], a thin jet extruded by the first expansion of the bubble causes that a ring-shaped crater is generated around the thin jet, as shown in Fig. 3.6. The collapse of this ring-shaped crater will generate the crown-like water jet. However, the cross image of the ring-shaped crater as shown in the Fig. 3.5 is difficult to observe in the experimental results, as shown in the Fig. 3.4.

On the other hand, there are two arms significantly formed on the thick jet when the major axis of the elongated bubble is parallel to the surface plane, which leads to easily measure the off-axis craters located aside the thin jet. The zoom-in pictures around the surface depression of Fig. 4.5(a) is shown in Fig. 4.5(b). We can clearly see that the surface depression is not only a crater appeared on the free surface. The thin jet at the center of the surface depression causes a pair of off-axis crater, which has radially outward motion during its collapse, as indicated by the two outward arrows in Fig. 3.5.

When the bubble depth is further decreased to γ = 0.63, the bottom of the thin jet becomes a sheet of isosceles triangle with top angle about 24°, as shown in the first low of Fig. 4.8. This structure is confirmed in sheet because the back light can directly penetrate though a plane except the edge of the plane which reflects the back light and appears in dark. For this sheet formation, as mentioned above, the elongated bubble

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firstly expands to a near spherical bubble in infinite surrounding and the thin jet is extruded during this first expansion when the bubble is beneath a free surface. Thus the thin jet should be initially in cylindrical symmetry. Next, as shown in the frames at 133μs to 166μs in Fig. 4.8, the bottom of the thin jet becomes “fat” after the rising of the thick jet. Furthermore, when the two arms are not symmetry to each other, the thin jet will not be an isosceles triangle, as shown in Fig. 4.9 in which the focus length of laser is altered to be 120mm. In the first frame in Fig. 4.9, the shape of the elongated bubble is twist compared to Fig. 4.4 due to the energy distribution around the focus volume induced by increasing the focus length, and then the two arms will not symmetry to each other. As a result, we consider that the thin jet could be pulled outward by the opposite arms and becomes a sheet in structure. The sheet part of the thin jet gradually shrinks and mixes with the upward moving thick jet, and finally, the thin jet converts back to a cylindrical shape, as shown in the second low of Fig. 4.8 which shows that the isosceles triangle analogously sinks into the thick jet. When bubble depth γ = 0.55, due to the raising of surface interaction between the bubble and free surface, the third row of Fig. 4.10 shows that the thick jet is also pulled into a plane structure. The surface tension of the thick jet tends to decrease the area of the plane by shrinking the thick jet back to a cylinder-like structure. Finally, for more shallow bubble depth, the two-arm splash has no definite structure and the thin jet rapidly breaks into multiple drops, as shown in the second row of Fig. 4.10.

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Fig. 4.5(a) The water jet for γ = 0.73. The exposure time is 10μs and the time (in μs) is indicated at the bottom of each frame. The thin jet analogously rotates like drill. (b) The zoom-in pictures around the surface depression. The frame rate is 50,000 and the shutter speed is 3μs. The time (in μs) is indicated at the bottom of each frame.

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Fig. 4.6 The breakup of the thick part of the water jet induced by vertically focusing the laser beam beneath the free water surface. The waving on the thick jet is cylindrical symmetry and the thick jet gradually breaks up into several drops.

Additionally, the breakup of the thin part of the water jet has similar result.

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(a)

(b)

Fig. 4.7(a) The vibrations on the thin jet with directions on major and minor axes are unmatched to each other. (b) The schematic of the circular polarized of an electromagnetic wave.

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Fig. 4.8 The water jet for γ = 0.63. The exposure time is 10μs and the time (in μs) is indicated at the bottom of each frame. The thin jet is pulled outward by the two arms and forms a sheet structure.

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Fig. 4.9 A sheet thin jet with shape in non-isosceles triangle is generated when the laser is focused with focus length in 120mm. As we can see in the first frame, the shape of the elongated bubble is twist due to the energy distribution around the focus volume induced by increasing the focus length.

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Fig. 4.10 The water jet for γ = 0.55. The exposure time is 10μs and the time (in μs) is indicated at the bottom of each frame. The thick jet shows a sheet structure and gradually shrinks back to a cylinder-like structure.

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