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Abstract
Hydrostatic pressure is a key factor that influences laser-induced bubble dynamics in water. In this work, we investigated laser-induced bubble dynamics at high hydrostatic pressures up to 53.2 MPa, by using a high-pressure chamber combined with the shadowgraph imaging technique. It was shown that at the atmosphere pressure, the bubble evolution agrees well with the Keller-Miksis model during the free expansion and collapse phase. As the ambient pressure increases, both the size and the oscillation period of the bubble decreases dramatically as a consequence of faster dynamics. The maximum bubble radius, as well as the collapse time, decrease nonlinearly with the increasing pressure; while the pressurization effect on bubble expansion before 100 ns is negligible due to the high internal bubble pressure in the early stage. Time-resolved plasma emission images were also taken with an ICCD camera to illustrate the plasma evolution at high hydrostatic pressures. It was demonstrated that at a high pressure above 40 MPa, the plasma can gain energy from the bubble collapse, while the bubble will lose its energy, which may lead to a shorter collapse time than that obtained from the numerical calculation. This work provides insight into laser-induced bubble dynamics and the plasma-bubble interaction at high hydrostatic pressures.
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1. Introduction
Laser-induced cavitation is a phenomenon that when high energy pulse laser is focused into liquid, the plasma generates by multiphoton and cascade ionization [1], and then the cavitation bubble occurs and oscillates as subsequent shockwave is released and propagates in liquid [2]. The mechanism and phenomena of laser-induced cavitation have been extensively investigated since it is widely applied in various areas, such as in microsurgery [3], drug delivery [4], material synthesis [5], photoacoustic applications [6], surface cleaning [7], laser propulsion in water [8] and microfluidic operations [9].
Hydrostatic pressure is one of the critical parameters that influences the bubble dynamics. Not only the maximum bubble radius and bubble collapse time [10], but also the liquid jet formation and the water hammer pressure [11] are all influenced by the ambient pressure. Up to now, the pressure effects on bubble dynamics have been primarily concerned in two fields, i.e., the pulsed laser ablation in liquid (PLAL) for nanoparticles synthesis [5] and the underwater laser-induced breakdown spectroscopy (LIBS) for deep-sea exploration [12]. PLAL is a method for nanoparticles synthesis that when the immersed target is ablated by pulsed laser, the ablated materials are excited and react chemically with the liquid vapor and consequently become the products. The bubble can provide a perfect environment for nanoparticles formation, and the high pressure and temperature during bubble collapse may also lead to the mechanical materials ablation [5]. De Giacomo et al. have investigated the effect of external pressure in the range from 0.1 to 14.6 MPa on laser ablation of graphite target submerged in water, and demonstrated that the variation of external pressure plays a key role for nanoparticles generation [13]. Dell’ Aglio et al. have studied the pressure effect on laser-induced plasma and cavitation bubble dynamics during the production of silver nanoparticles in water [14]. They found that the bubble dynamics depends significantly on the external pressure and the random nanostructures formation is connected with the bubble collapse phase. They also illustrated that the nanoparticles ejection from the bubble depends strongly on the pressure inside bubble [15]. Sasaki et al. showed that the bubble dynamics at high hydrostatic pressure has great impacts on the features of nanoparticles synthesized by laser ablation in liquid [16].
On the other hand, LIBS is a spectroscopic method which utilizes the laser-induced plasma to vaporize, atomize and excite the analyzed materials, and the optical emission from plasma can be collected for analysis purpose [17]. With the advantages of multi-elemental, stand-off, and rapid detection capabilities, LIBS has been proven to be an attractive technique for the in-situ geochemical analysis in marine applications [12,18]. However, when applying LIBS into the deep-sea environment, the pressure effect caused by different ocean depth is inevitable that should be taken into consideration. In underwater LIBS, the plasma plume interacts with the surrounding cavitation bubble during its evolution, and the plasma emission characteristics are strongly influenced by the external pressure [19–25]. Several groups have performed the underwater LIBS studies at high pressure conditions with the aim to improve the laser irradiation schemes such as using the double-pulse or long-pulse lasers. Lawrence-Synder et al. firstly obtained the single-pulse LIBS signals at the pressures up to 27.6 MPa [19], and showed that when the ambient pressure is higher than 10 MPa, there is no significant enhancement on double-pulse LIBS signals [20]. They explained that the shorter bubble duration and smaller bubble size at higher pressures hinder the application of double-pulse LIBS in deep-sea [21]. Similar conclusion has also been reached by López-Claros et al. who investigated the double-pulse LIBS of immersed solid target in water [22]. Thornton et al. reported the use of long-pulse laser to improve the quality of LIBS signals at high pressures and obtained the bubble temporal evolutions in the range from 0.1 to 30 MPa [23–25].
It can be summarized that most studies of laser-induced bubble dynamics were carried out at the atmosphere pressure, while the bubble dynamics characterization at the high pressure conditions are rare. Moreover, very few attentions are paid on the plasma-bubble interaction and its effects on the bubble evolution. It is known that for a nanosecond laser-induced breakdown in water, the duration of plasma (∼ 1 µs) [26] is much shorter than that of the cavitation bubble (∼ hundreds of µs) at the atmosphere pressure [27], but when the pressure is getting higher, the bubble collapse time reduces significantly and it may be in the same order of magnitude as the plasma duration time. Recently in our previous work [28], we have shown that at the higher pressures above 30 MPa, the bubble collapses extremely fast and even earlier than the cooling of the plasma, which leads to an increase in the plasma temperature and electron density. Therefore, the bubble dynamics at high pressures plays a key role on the characterization of plasma emission and the corresponding LIBS signals [28–30]. In this work, we further investigate the nanosecond laser-induced bubble dynamics at different pressures from 0.1 to 53.2 MPa. By comparing between the shadowgraph imaging results and the numerical results based on Keller-Miksis model [31], we will show the characteristics of the bubble evolutions at different pressures and especially the effect of plasma-bubble interaction on bubble dynamics at the high pressure conditions.
2. Theoretical model
After the detachment of shock wave from the laser-induced plasma, there is a cavitation bubble left and begins to expand in the liquid [32]. Assuming that the pressure inside bubble is uniform and the chemical reaction is neglected, the temporal evolution of the bubble radius and the pressure inside bubble can be calculated by Keller-Miksis model [31]. Both the compressibility and viscosity of the liquid surrounding the bubble as well as the surface tension are taken into consideration by this model. The bubble dynamics can be described as below [33]:
When the bubble expands to the maximum radius, it begins to contract and eventually collapses. The interval from the bubble maximum to the subsequent minimum is defined as the bubble collapse time. It can be calculated by integrating the Rayleigh model and expressed as below [10]:
The constants used for water at a temperature of 20 °C in this work were water density $\rho = 998\; kg/{m^3}$, saturated vapor pressure ${p_v} = 2330\; Pa$, surface tension $\sigma = 0.072583\; N/m$, polytropic exponent $\gamma = 4/3$, coefficient of the dynamic shear viscosity $\mu = 0.001046\; Ns/{m^3}$, and sound speed in water $c = 1483\; m/s$ [34].
3. Experimental setup
The schematic diagram of the experimental setup used in this work is shown in Fig. 1. A Q-switched Nd:YAG laser (Beamtech Optronics, Dawa 200, pulse duration 10 ns) was operated at the fundamental wavelength of 1064 nm with a repetition rate of 10 Hz. The laser beam passed through a half-wave plate and a Glan prism for a fine adjustment of the laser energy. A portion of each laser pulse (∼8%) was reflected by the beam splitter and sent to a photodiode connected with an oscilloscope to monitor the laser energy. The experiments of bubble dynamics at the atmosphere pressure were carried out in a quartz cuvette (size 5×5×5 cm, wall thickness 2 mm) filled with water solution. The laser beam with a moderate energy of 5 mJ was focused into the quartz cuvette to generate the plasma. The focusing lens L1 was consisted of an achromatic doublet (f = 75 mm) and a meniscus lens (f = 100 mm) in order to minimize the spherical aberrations and to realize a relatively large focusing angle. With this arrangement, well-localized plasmas can be obtained in water [35,36]. The water solution used in this work was made of CaCl2 dissolved in deionized water with the Ca concentration of 2000ppm, in order to have a longer plasma duration time which benefits the study of plasma-bubble interaction. Shadowgraph images of the laser-induced bubble were recorded by using an ICCD camera (Andor Technology, iStar DH 734i) combined with a probe laser beam (Laser 2, Big Sky, ULTRA CFR). Laser 2 was operated at the wavelength of 532 nm with a pulse duration of 10 ns. The probe laser beam was expanded by a pair of plano-concave lens L2 (f = −30 mm) and plano-convex lens L3 (f = 60 mm) for back illumination. The bubble images were then collected by a pair of achromatic doublet lenses L4 (f = 50 mm) and L5 (f = 150 mm) and captured by the ICCD camera. An interferential filter with the center wavelength of 532 nm (1 nm bandwidth) was placed in front of the ICCD camera to block the spontaneous emissions from the plasma and only 532 nm laser light was detected. Meanwhile, the plasma emission images can also be recorded by removing the probe laser, and in the case, the interferential filter was replaced by a neutral density filter to avoid the saturation of the camera.
Fig. 1. Experimental setup for the imaging of laser-induced bubble and plasma in water at different pressure conditions. A quartz cuvette is used for the experiment at atmosphere pressure, and a high-pressure chamber (shown in the inset) is used to realize the high pressures up to 60 MPa. The meanings of abbreviations in the figure are presented below: HWP: half wave plate, GP: Glan prism, BS: beam splitter, M: mirror, L: lens, PD: photodiode, OSC: oscilloscope, DG: delay generator, SW: sapphire window, PS: pressure sensor, F: filter, ICCD: intensified CCD.
The experiments of bubble dynamics at high pressure conditions were carried out in a home-made high-pressure chamber, as shown in the inset in Fig. 1. The chamber was a stainless-steel cube with a volume of 27 mL (size 3×3×3 cm). The laser beam was focused into the center of the chamber through a sapphire window (diameter 10 mm, thickness 14 mm) to generate the plasma. Another two sapphire windows equipped in the lateral side of the chamber were used for the probe laser beam entrance as well as for the imaging measurement. The imaging system at high pressure was the same as the atmosphere pressure. The way of chamber pressurization was realized by applying a mechanical pump to a maximum of 60 MPa with a precision of 0.1 MPa. A USB pressure sensor mounted inside the chamber was used to monitor the pressure values during the experiments. The timings between the two lasers and the ICCD camera were controlled by a delay generator (Stanford Research System, DG645). With this system, the time-resolved bubble shadowgraph images as well as the plasma emission images at different pressures can be obtained.
4. Results and discussion
4.1 Bubble evolution at atmosphere pressure
We firstly obtained the shadowgraph images of laser-induced bubble at atmosphere pressure during the early stage (from 16 ns to 1800ns) and the bubble oscillation period (from 2 µs to 163 µs), as shown in Fig. 2. We can see that at the early stage of bubble evolution, the shock wave detaches from the bubble immediately after the laser pulse and becomes a rather oval in shape. The bubble shows a non-isotropic expansion behavior with a higher bubble wall velocity towards the incident laser. The evolutions of bubble and shock wave during this period are in good agreement with the work of Vogel et al., where the dynamics of bubble and shock wave have been well described [34]. What we are focusing here is the comparison of bubble dynamics before plasma quenches (shown in Fig. 2(a)) and after plasma quenches (shown in Fig. 2(b)). During the passage of the laser pulse, the pressure and temperature of the initial plasma are extremely high due to the direct absorption of laser energy in the breakdown region [37]. The high inner pressure drives the bubble expansion and the plasma dynamics has a remarkable impact on bubble evolution at the early stage before plasma quenches. Therefore, the bubble non-isotropic expansion behavior observed in Fig. 2(a) at different directions is mainly contributed by the plasma growth and expansion. However, in the next step after plasma quenches, the bubble wall velocity in different directions is nearly the same and the bubble has a regular spherical shape, as shown in the images of the first bubble oscillation period (2 µs ∼ 163 µs) in Fig. 2(b). Here, we mention that the white spot in the middle of the bubble image in Fig. 2 is actually caused from an experimental issue instead of the realistic plasma emission. It is due to the fact that the excitation light (from Laser 2) used for the shadowgraph passes through the bubble where the incident light is perpendicular to the bubble surface.
Fig. 2. Shadowgraph images of laser-induced bubble at atmosphere pressure during the early stage from 16 ns to 1800ns (a) and in the first oscillation period from 2 µs to 163 µs (b).
Quantitative evaluation of the shadowgraph series of bubble radius is shown in Fig. 3. In Fig. 3(a), the distance of the bubble wall from the optical axis is plotted as a function of delay time from 5 ns to 2 µs. The black line of bubble radius is fitted through the experimental data points with a curve fitting software (Table curve, Jandel Scientific). From the bubble radius curve, the pressure inside bubble as a function of time is derived by Eq. (2) of the Keller-Miksis model (shown as the red line in Fig. 3(a)). We can see that along with the early-stage bubble expansion, the pressure inside bubble decreases rapidly due to the pressure transient between the inside bubble and the outside. The initial pressure inside bubble reaches over 8000 MPa which is much higher than the outside (atmosphere pressure). In Fig. 3(b), we used the Keller-Miksis model to calculate the temporal evaluation of the bubble radius and pressure during the bubble expansion and collapse stage. A fourth-order Runge-Kutta method was applied to numerically integrate the differential Eq. (1) and Eq. (2) and the calculation results of the bubble radius and pressure are shown in Fig. 3(b) as the black line and red line respectively. The calculations start with an initial bubble radius ${R_0} = 150\; \mu m$ at ${t_0} = 100\; ns$, where the value of ${R_0}$ is identified from the bubble shadowgraph image at the delay time of 100 ns. The equilibrium radius ${R_n} = 325\; \mu m$ is determined when the calculated maximum bubble radius equals the value experimentally obtained (shown in Fig. 3(b)). We can see that the bubble expands to the maximum at the delay time of 80 µs and the pressure inside bubble decreases to the minimum correspondingly. And at this time, the pressure inside bubble is much lower than the outside and the bubble begins to shrink. After that, the pressure inside bubble increases sharply during the bubble collapse phase. From these results above, we can conclude that at the atmosphere pressure, the bubble expansion is driven by the plasma growth at the early stage, while the plasma impact on bubble dynamics is negligible at the bubble free expansion stage and the experimental results agree well with the Keller-Miksis model. However, when the hydrostatic pressure becomes higher, we can expect that the bubble expansion will be greatly suppressed with a much-reduced size and lifetime. In this case, the effect of plasma-bubble interaction on bubble dynamics may be questionable that should be taken into account even in the late stage as shown in the follows.
Fig. 3. Bubble radius as a function of delay time at atmosphere pressure during the early stage (a) and the late stage (b). Numerical calculations of the pressure inside bubble are also shown in the figure as the red line.
4.2 Bubble evolution at high hydrostatic pressure
In order to investigate the pressure effect on bubble dynamics, a high-pressure chamber with a maximum pressure of 60 MPa was used as described in the experimental section. Time-resolved shadowgraph images of the bubble at high hydrostatic pressures of 2.0 MPa, 10.2 MPa, 20.5 MPa, 31.6 MPa, 41.6 MPa and 53.2 MPa were obtained and shown in Fig. 4. We can see first that the elongated and multiple bubbles were formed along the laser focal axis and shown with a relatively large pulse-to-pulse fluctuation. This is because that the focusing quality of the laser beam is much reduced under the use of the high-pressure chamber compared with that of the quartz cuvette, i.e., a large focusing angle and low spherical aberration cannot be achieved due to the limitation of the aperture and thickness of the sapphire window equipped in the high-pressure chamber which leads to a multiple independent breakdown phenomenon in water [38]. Although the stability of bubble images is degraded under the high-pressure conditions, we can still see clearly in Fig. 4 the strong dependence of the bubble expansion on hydrostatic pressures. Both the size and lifetime of the bubble decrease dramatically with the increasing hydrostatic pressure. For example, at 2.0 MPa, the bubble undergoes a rapid expansion at 1 µs and it expands to the maximum at 16 µs. The multiple cavities tend to be merged into a single one during the expansion. Whereas for 10.2 MPa, the bubble reaches the maximum at 2 µs with a much smaller size compared with that of the 2.0 MPa. When the hydrostatic pressure is up to 53.2 MPa, the bubble doesn’t exhibit an obvious expansion behavior and the bubble dynamic is extremely fast with a collapse time less than 1 µs. However, at a short delay time of 100 ns, no obvious difference was observed for the pressures from 2.0 to 53.2 MPa, indicating a weak dependence of the bubble on hydrostatic pressures at the early stages.
Fig. 4. Time-resolved shadowgraph images of the laser-induced bubble generated in water at the hydrostatic pressures of 2.0 MPa, 10.2 MPa, 20.5 MPa, 31.6 MPa, 41.6 MPa and 53.2 MPa. The corresponding delay time is indicated at the bottom of each figure.
Figure 5 shows the bubble radius as a function of delay time at different hydrostatic pressures. Due to the elongated feature of the bubble, the bubble radius was defined as the half of the maximum distance of bubble wall perpendicular to the optical axis. From Fig. 4 and Fig. 5, we showed that the pressurization has little impact on bubble expansion at the early times but huge impact at the late times. This can be explained by the fact that during the nanosecond laser-induced breakdown process in water, the initial plasma inside bubble is heated by the laser pulse to a quite high temperature and pressure [34,37]. The influence of the hydrostatic pressure is negligible for the early-stage bubble expansion. After that, the high temperature and pressure generated inside the bubble drive a rapid expansion of the bubble in all directions. Along with the increase of the bubble volume, the pressure inside bubble decreases with time rapidly, and when the bubble reaches its maximum volume, the pressure inside is much lower than the hydrostatic pressure and then the bubble undergoes the collapse phase. Therefore, it is clear that the bubble expansion and collapse at the late stage depend strongly on the hydrostatic pressure.
Fig. 5. Bubble radius as a function of delay time at different hydrostatic pressures of 2.0 MPa, 10.2 MPa, 20.5 MPa, 31.6 MPa, 41.6 MPa, 53.2 MPa.
Figure 6 further gives the maximum bubble radius as a function of hydrostatic pressure. We can see that the maximum bubble radius decreases nonlinearly as the pressure increases, and its decreasing trend is smaller when the hydrostatic pressure is higher. E.g., the bubble’s maximal radius decreases from 837 to 284 µm with an average decreasing velocity of 29.9 µm/MPa, when the pressures increase from 2.0 to 20.5 MPa. While from 20.5 to 53.2 MPa, the maximal radius decreases from 284 to 206 µm with a much lower average decreasing velocity of 2.4 µm/MPa. This nonlinear behavior agrees well with the work of Li et al. [10] where the ambient pressure effects on bubble dynamics were investigated within a relatively small pressure range of 0.1-0.35 MPa.
4.3 Bubble collapse and plasma-bubble interaction
To better understand the pressure effect on bubble dynamics, the temporal evolutions of the bubble radius and pressure inside bubble at different hydrostatic pressures are numerically investigated based on the Keller-Miksis model and the results are shown in Fig. 7. The calculations start at 100 ns with an initial bubble radius ${R_0} = 150\; \mu m$, which is measured from the bubble shadowgraph images. ${R_n}$ is determined when the calculated maximum bubble radius equals the value experimentally obtained for each hydrostatic pressure, that is $270\; \mu m$ for 2.0 MPa, $140\; \mu m$ for 10.2 MPa, $135\; \mu m$ for 20.5 MPa, $132\; \mu m$ for 31.6 MPa, $130\; \mu m$ for 41.6 MPa, $and\; 128\; \mu m$ for 53.2 MPa. It is shown that ${R_n}\; $decreases with the hydrostatic pressure, since ${R_n}$ is the equilibrium radius of the bubble where the pressure inside the bubble equals the hydrostatic pressure. We can see from Fig. 7(a) and Fig. 7(b) that at the early state of bubble expansion, the bubble radius and bubble wall velocity have no distinguishable difference, and the pressure inside bubble is much higher than the ambient pressure. The pressure inside bubble immediately after the laser pulse can be as high as 103-104 MPa, and it reduces rapidly down to the hydrostatic pressure during the bubble expansion. After several oscillation periods, the bubble evolves until it reaches a pressure value equal to the hydrostatic pressure. This proves in a numerical way that the effect of the ambient pressure is to reduce the bubble oscillation period and the bubble size as a consequence of faster dynamics, while the external pressure varying in the range of tens MPa has negligible effect on the bubble expansion at the early stages. However, when comparing the numerical result in Fig. 7(a) and the experimental result in Fig. 5, we can see a discrepancy that no re-expansion of the bubble was observed at high pressure conditions due to the great energy loss during the bubble collapse phase. Another important difference is that the bubble collapse time, which is defined as the interval time from the maximum radius to the subsequent minimum, is smaller for the experimental result shown in Fig. 5. This means that under a certain hydrostatic pressure, the bubble collapses faster in experiment than in numerical calculation.
Fig. 7. Numerical#calculations of bubble radius (a) and bubble pressure (b) as a function of delay time at different hydrostatic pressures of 2.0 MPa, 10.2 MPa, 20.5 MPa, 31.6 MPa, 41.6 MPa, 53.2 MPa.
Figure 8 gives the bubble collapse time as a function of hydrostatic pressure obtained from the numerical calculation (black) and the experimental data (red), respectively. We can see that both the experimental and numerical collapse times show a nonlinear decreasing trend with the increasing pressure, which is similar to the maximum bubble radius (shown as Fig. 6). This can be explained by the Rayleigh model which is illustrated by the Eq. (3), that the maximum bubble radius is proportional to the corresponding collapse time. We can thus conclude that higher hydrostatic pressure drives faster bubble dynamics, and the maximum bubble radius as well as the collapse time decrease nonlinearly when increasing the ambient pressure. As for the discrepancy between the experimental and numerical results in Fig. 8, it can be explained by the following aspects. In the first, the Keller-Miksis model used in this work is based on some assumptions that the bubble remains to be spherical and there is no energy dissipation during the bubble oscillation period [31]. And they are obviously not the case of this work at high pressures, where the bubbles are elongated due to the multi-breakdown in water. Due to the high pressure, the bubble collapses too fast to be merged into a single spherical one and there is no re-expansion. Secondly, the impact of the plasma inside bubble is not taken into consideration. We know that at atmosphere pressure, the duration of plasma is much shorter than that of the bubble. The impact of plasma on the bubble free expansion stage is negligible and the experimental results agree well with the Keller-Miksis model. However, when the ambient pressure is higher, the bubble duration time is greatly suppressed that may even be shorter than the plasma duration. As can be seen from Fig. 5, when the pressure is higher than 20.5 MPa, the bubble duration is shorter than 2 µs, which is comparable to the duration time of plasma radiation [28]. Therefore, the plasma impact on bubble dynamics may not be neglected in this case.
Fig. 8. Bubble collapse time as a function of hydrostatic pressure obtained from the numerical calculation (black) and the experimental data (red).
The time-resolved plasma emission images were then taken with the ICCD camera to illustrate the plasma impact on bubble dynamics at high pressure conditions. Figure 9 shows the plasma images at the delays of 100 ns, 500 ns, 800 ns and 1100 ns with a gate width of 50 ns. Each image was an average of 100 laser shots. Two different color scales were used for a clear presentation of the emission distribution. From Fig. 9, we can see first that under all the pressures from 2 to 40 MPa, the plasma morphology and brightness have no significant difference at the delay of 100 ns. This proves again that the hydrostatic pressure has negligible influence on the bubble at the early stages as observed in Fig. 4 and Fig. 5. Note that the laser is incident from the right, and we can find a slight shift of the plasma position at points farther up the laser path when increasing the pressure. This is because that the refractive index of water is larger at higher pressure [39] which leads to a longer focal distance in water.
Fig. 9. Time-resolved plasma emission images at different hydrostatic pressures of 2 MPa, 10 MPa, 20 MPa, 30 MPa and 40 MPa. The images were acquired at the delays of 100 ns, 500 ns, 800 ns and 1100 ns with a gate width of 50 ns. Each image was an average of 100 laser shots. Two different color scales were used for a clear presentation of the emission intensity distribution. The laser was incident from the right.
While for the delay of 500 ns, we can see that the plasma emission intensity is clearly enhanced at higher pressures. For the delays from 500 to 1100 ns, the plasma emission is gradually reduced during the cooling of the plasma. And such reduction becomes slower when the pressure is higher. In particular, at 40 MPa, the plasma emission intensity decreases first and then increases, with a maximum count value of $\textrm{1}\mathrm{.01\ \times 1}{\textrm{0}^\textrm{3}}$ at 500 ns, $\textrm{0}\mathrm{.82\ \times 1}{\textrm{0}^\textrm{3}}$ at 800 ns and $\textrm{1}\mathrm{.96\ \times 1}{\textrm{0}^\textrm{3}}$ at 1100 ns. The plasma size is also reduced at longer delay times. These results correspond well with the bubble images above. At the pressures below 10 MPa, the bubble expansion time is long enough to complete the plasma radiation so that the plasma emission intensity decreases as a function of delay. At higher pressures, due to the fast collapse of the bubble, the plasma volume decreases quickly and the particle density inside the plasma increases. The plasma suffers a confinement effect caused by the compressed bubble which leads to an increase in the emission intensity. We can see that the bubble collapses to its minimum size at about 1100 ns of 40 MPa which corresponds to the increased emission intensity at this time. These results also agree well with our previous work that a spectroscopic measurement was performed at the high pressures up to 40 MPa, and the plasma temperature and electron density were deduced based on the spectral results [28]. From an energy balance point of view, during the bubble collapse phase, the plasma inside the bubble is compressed to a higher temperature and density, and thus a part of bubble kinetic energy is transformed into the plasma. The plasma will gain energy from the bubble collapse while in turn the bubble will lose its energy. That is why we can observe a significant increase in brightness at the late stage of plasma emission, and may also be the reason for the quicker bubble collapse time in the experimental results. These results may provide us better understandings of the bubble dynamics and the plasma-bubble interaction at high pressures.
5. Conclusions
In conclusion, we have investigated laser-induced bubble dynamics at the atmosphere pressure and at the high hydrostatic pressures up to 53.2 MPa. At the atmosphere pressure, the bubble shows a non-isotropic expansion behavior at the early stage which can be mainly contributed by the plasma growth and expansion inside the bubble. During the bubble free expansion stage, the bubble has a regular spherical shape and its evolution agrees well with the Keller-Miksis model. When increasing the ambient pressure, both the bubble size and the oscillation period decrease dramatically as a consequence of faster dynamics. The maximum bubble radius as well as the collapse time decrease nonlinearly with the increasing pressure, while the pressurization effect on the bubble before 100 ns is negligible due to the high internal pressure inside bubble at the early stage. The time-resolved plasma emission images were also taken with the ICCD camera to illustrate the plasma evolution at high hydrostatic pressures. It was demonstrated that at a high pressure above 40 MPa, the plasma can gain energy from the bubble collapse phase while the bubble will lose its energy, which may lead to a shorter collapse time than that obtained from the numerical calculation. This work provides some insights into the laser-induced bubble dynamics and the plasma-bubble interaction at high hydrostatic pressures, which may promote some relevant applications such as the PLAL for nanoparticles synthesis in high pressure conditions or the underwater LIBS for deep-sea investigations.
Funding
National Natural Science Foundation of China (61975190, 12174359); Key Technology Research and Development Program of Shandong (2019GHZ010).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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