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Abstract
Multiple breakdowns in liquids still remains obscure for its complex, non-equilibrium and transient dynamic process. We introduced three methods, namely, plasma imaging, light-scattering technique, and acoustic detection, to measure the multiple breakdown in water induced by focused nanosecond laser pulses simultaneously. Our results showed that linear dependence existed among the cavitation-bubble lifetime, the far-field peak pressure of the initial shock wave, and the corresponding plasma volume. Such a relationship can be used to evaluate the ideal size and energy of each bubble during multiple breakdown. The major bubble lifetime was hardly affected by the inevitable coalescence of cavitation bubbles, thereby confirming the availability of light-scattering technique on the estimation of bubble size during multiple breakdown. Whereas, the strength of collapse-shock-wave and the subsequent rebound of bubbles was strongly influenced, i.e., the occurrence of multiple breakdown suppressed the cavitation-bubble energy being converted into collapse-shock-wave energy but enhanced conversion into rebound-bubble energy. This study is a valuable contribution to research on the rapid mixing of microfluidics, damage control of microsurgery, and photoacoustic applications.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Pulsed-laser-induced optical breakdown in deionized water occurs and results in the generation of plasma when the irradiance reaches a sufficiently high level. The expanding plasma subsequently drives the shock-wave propagation and cavitation-bubble oscillation [1]. The mechanism and phenomena of optical breakdown induced by pulsed laser have been extensively studied because of its various applications in clinical surgery [2–7], photoacoustic applications [8–10], drug delivery [11–16], microsurgery [15,17–21], micromachining [22,23], laser-induced breakdown spectroscopy [24–26] and microfluidic operations [27–29]. The mechanism of plasma emission and expansion [30–35], shock-wave propagation [36–39], cavitation-bubble oscillation [1,40–42], breakdown threshold [42–44], and energy-conversion efficiency [45] during optical breakdown have also been widely studied over the last decades.
At low focusing angle (lower than 29.8° [46]), plasmas with multiple cores formed in multiple sites, which are induced by laser pulses, are usually discrete and irregular and are thus called multiple breakdown. Compared with single breakdown, multiple breakdown accompanying the formation of multiple plasmas, cavitation bubbles, shock waves, and jets result in a more complex, non-equilibrium and transient dynamic process. Hence, most studies on laser-induced optical breakdown in liquids are restricted to single breakdown. However, microjets resulting from anti-phase bubbles have prospective applications in cell optoporation [20] and microsurgery [47], and the interaction of multiple bubbles produce high Reynolds numbers for the rapid mixing of microfluidics [28,48]. The multiple shock waves originating from multiple plasmas also have applications in low-invasive medical treatments [49–51]. Accordingly, the dynamics of pulsed-laser-induced multiple breakdown in liquid is necessary to investigate.
The phenomenon of multiple breakdown has been observed decades ago [52]. The probability of multiple breakdown increase with increased energy input [53]. Tian et al. [46] has summarized the reasons for multiple breakdown, including impurities [54], the probabilistic property of optical breakdown [1], the “moving-breakdown” effect [35], the influence of optical aberrations [55,56], and the self-focusing effect [1,57,58]. Moreover, the focusing angle is critical for multiple breakdown, because increased focusing angle can reduce the probability of multiple breakdown [46,59]. Multiple plasmas are formed during multiple breakdown, and the starting time of each plasma decays with increasing distance from the focal point along the optical axis [35,60]. The plasma number barely influences its shielding efficiency [60]. The space interval of multiple plasmas induced by focused laser pulses is small. Increased focusing angle can reduce the plasma space interval and even convert discrete plasma into continuous linear plasma when the pulse energy is sufficiently large [58,59]. Evans et al. [57] has shown the influence of the ponderomotive self-focusing of a polarized laser beam on multiple breakdown. When multiple plasmas form, multiple cavitation bubbles and shock waves are generated. The quantities of initial bubbles and shock waves sometimes exceed the number of plasmas because of the formation of additional bubbles induced by the low-density plasma [61]. The mutual interaction of multiple bubbles leads to more complex behaviors, including bubble coalescence and jet formation [62–64]. The cavity dynamics of multiple bubbles induced by single focused pulse laser has been investigated by Nath et al. by using a shadowgraph [64]. Tinne et al. [65] has shown the interaction dynamics of two cavitation bubbles without coalescence. The energy conversion and jet emission of closely spaced multiple bubbles induced by femtosecond laser have been investigated by Potemkin et al. [66]. The spatial position, number, and size of multiple cavitation bubbles can be controlled with a digital hologram [67]. Arbitrarily shaped bubbles can be generated by multiple-bubble coalescence induced by a pulsed laser with the help of a spatial light modulator [68]. Unlike cavitation bubbles, the prorogation of each shock wave is almost independent from one another. The shock wave originating from the corresponding plasma is normally modeled as a spherical shock. Meanwhile, the spatial distribution of multiple breakdown causes the intensity and duration of multiple-shock-wave pressure to differ from the prorogation angle [59,69]. Accordingly, a cylindrical shock wave has been successfully created in water by the overlap of multiple shock waves induced by a tight focused femtosecond laser [70]. However, the relationships among multiple plasmas, multiple cavitation bubbles, and multiple shock waves during multiple breakdown, as well as their mutual interactions, remain unclear and require further study.
In the present study, we measured plasma distribution, cavitation-bubble oscillation, and the far-field peak pressure of shock waves during optical breakdown in water induced by focused nanosecond laser pulses to investigate the relationships among pulse energy and multiple plasmas, multiple cavitation bubbles, and shock-wave emission. Compared with single breakdown, the total plasma volume increased in an accelerating manner with pulse energy, whereas the volume of the major plasma was linearly proportional to pulse energy during optical breakdown. Considering that both initial bubbles and initial shock waves originated from the corresponding plasmas, we also found linear relationships among the following: ideal bubble size, which is the maximum radius that the cavitation bubble could reach if there was no interaction between multiple bubbles in a liquid of infinite extent; shock wave strength; and plasma volume. Moreover, the major bubble lifetime was barely affected by the bubble coalescence during multiple breakdown, which is crucial for estimating the ideal size of cavitation bubble. Then, the influences of mutual interaction among bubbles on the collapse shock wave and the subsequent rebound of bubbles during multiple-bubble oscillation were discussed.
2. Experimental setup
The experimental setup is shown in Fig. 1(a). A single-frequency-doubled Q-switched Nd: YAG laser (Quantel Q-smart 450; wavelength = 532 nm; pulse duration = 6 ns; repetition frequency = 10 Hz) pulse was used to induce optical breakdown in deionized water. A variable beam splitter (Thorlabs, VA5-532) consisting of a half-wave plate and a polarization beam splitter were used to control the incident pulse energy. A nonpolarizing beam splitter (Thorlabs, BS013) was used to split pulse beam into two parts. One part was reflected into an energy meter (Ophir, PE50-DIF-C), and the other was focused with a 40 × , 0.6 numerical aperture (NA) long-working-distance microscope objective (Daheng, GCO-2113) into a quartz cuvette filled with deionized water. The laser-induced plasma image signal was initially magnified with a 10 × , 0.6 NA long-working-distance microscope objective (Daheng, GCO-2132) at the side of a cuvette and then captured with an EMCCD camera (Andor, Xion3) having a neutral density filter (Thorlabs, ND06A) to avoid detector saturation. Two notch filters (Thorlabs, NF533-17, NF633-25) were used to block the scattering light from both excitation and probe beams. The spatial resolution of image was about 1.6 μm. Meanwhile, a type of optical-scattering technique was introduced to detect cavitation-bubble oscillation. A continuous probe beam emitted by a 2 mW He-Ne laser (Thorlabs, HNL020RB; wavelength = 633 nm) and expanded with a Galilean beam expander collinearly with the excitation pulse beam was focused into a cuvette. The transmitted probe beam was monitored by an AC-coupled amplified photodetector (APD) (FEMTO, 25 kHz-200 MHz bandwidth). During the process of cavitation bubble oscillation, the scattering was dynamically changing. when a CW beam passed through the cavitation bubble, the propagating beam was scattered by the bubble and the axial intensity of which was reduced during the bubble expansion stage and brought back to the base level during the stage of collapse. Thus, this time-resolved and bubble-specific response mode allowed us to detect the oscillation period of cavitation bubble and further characterize the bubble size. A piezoelectric transducer (Olympus, V324-N-SU) placed about 3.8 mm over the focal point was used to detect the pressure of shock waves produced by the plasma formation and cavitation-bubble collapse in the far field where the shock wave propagated as sonic wave. Pressure signal was amplified 500 times with a low-noise amplifier (Olympus, 5662PR). Both signals from the high-speed photodector and transducer were recorded with a digital oscilloscope (Rohde & Schwarz, PTE1204) with a temporal resolution of 0.5 ns. A delay generator (Stanford Research Systems Inc., DG645) was used to trigger the EMCCD camera and oscilloscope.
Fig. 1 Schematic of the experimental setup and measured signals. (a) Schematic of the experimental setup used to measure laser-induced optical breakdown. (b) Schematic of multipl-breakdown structure model and multiple plasmas emiting multiple bubbles and shock waves. Differently colored arrows demonstrate the various paths of shock waves propagating to the transducer. (c) Diagram of optical-scattering technique. (d) Image of multiple plasmas generated in water. The light is incident from right. (e) Light-scattering response of cavitation-bubble oscillation. (f) Typical acoustic data of multiple breakdown.
The image of multiple plasmas was shown in Fig. 1(d). Notably, the camera’s exposure time of 10 μs of was much longer than the plasma’s lifetime. Thus, the plasma’s image showed the morphology of expanded plasmas. The cavitation-bubble oscillation induced the change of probe-beam intensity was shown in Fig. 1(e). The first oscillation period (FOP) represents the lifetime of the major bubble, which was barely influenced by the mutual interaction of bubbles. The second oscillation period represents the rebound-bubble lifetime. For about 10 mm of the transducer diameter and the spherical spreading of shock waves, the acoustic reflections of the transducer and the bottom of cuvette was significant. the shock-wave response signal was shown in Fig. 1(f). The peak signals I, II, and IV corresponded to the same initial shock waves propagating to the transducer at different moments, which were caused by the reflection of transducer and cuvette bottom. As shown in Fig. 1(b), when shock waves formed, the upward part initially reached the transducer (red arrow). The downward part was reflected by the bottom of the cuvette and then propagated to the transducer (orange arrow). Finally, the upward part reflected by the transducer and the bottom of the cuvette reached the transducer (green arrow). Moreover, the peak signals III, V, and VI corresponding to the collapse shock wave reached the transducer at different moments. Notably, the time interval t0 between signals II and IV or signals V and VI was invariant, and the distance d0 between the transducer and the focal point can be calculated by because of the reflection of detector and cuvette, where c denotes the acoustic velocity in water (set to 1500 m/s).
3. Results and discussion
3.1 Multiple-plasma formation
Two kinds of plasma were suggested to form during optical breakdown, namely, low- and high-density plasmas. However, optical breakdown with low-density plasma formation induced by a nanosecond laser barely occurs in deionized water without impurities at low numerical apertures (NA<0.8) [61]. Thus, in the present case, we did not consider the influence of low-density plasma formation in the next discussion. Plasma location, number, and size were investigated by taking photographs with an EMCCD camera. As Fig. 1(d) shows, four discret plasmas with different size are generated along the optical axis. The quantity of plasmas per pulse as a function of pulse energy is shown in Fig. 2(a). Each black star represents a single independent pulse experiment. Both the probability of optical breakdown (red sphere) and the quantity of discrete plasmas (black star) increased with increasing pulse energy. However, the ratio of the occurrence frequency of single breakdown to that of optical breakdown decreased with increasing pulse energy despite the increased probability of optical breakdown (blue sphere). Considering that most of the plasmas generated during multiple breakdown were discrete, instead of the axial length of plasmas, the plasma volume was calculated to characterize the plasmas in consideration of the plasma’s cylindrical symmetry along the optical axis. The calculated volume of plasmas as a function of pulse energy was plotted in Fig. 2(b). With increased pulse energy, the plasma volume of single breakdown (black sphere) almost linearly increased, whereas the total volume of plasmas during multiple breakdown (blue sphere) acceleratingly increased. For the pulse energy higher than 350 µJ, where the single breakdown almost disappear, the volume distribution of plasmas was more dispersive due to the increased probability of multiple breakdown. Then, the volume of the major plasma with the maximum size was calculated and plotted (red sphere). Unlike the total plasma-volume distribution, the change tendency of major plasma volume was linearly proportional to the pulse energy, similar to that of single breakdown. According to the plasma images of our experiments, the most of major plasmas were generated around the focal point and had the strongest luminescence, as shown in Fig. 2(c). The speed of plasma extension along the direction of laser propagation was also far faster than that along the opposite direction of laser propagation with increased pulse energy.
Fig. 2 Evolution of optical breakdown on laser pulse energy. (a) Number and probability of optical breakdown as a function of pulse energy. The black star represents the plasma number per pulse experiment, the red sphere represents the probability of breakdown, and the blue sphere represents the ratio of single breakdown to optical breakdown. (b) Plasma volume as a function of pulse energy. The black sphere represents the plasma volume of single breakdown, the blue sphere represents the total volume of plasmas during multiple breakdown, and the red sphere represents the major plasma volume of multiple breakdown. The line corresponds to linear dependence of both single breakdown and multiple breakdown. (c) Images of plasmas along the optical axis where averages of all images in the presence of plasma formation within each energy range are shown. The beam is incident from above.
According to Vogel et al. [31], the generation of free electrons of plasmas induced by a nanosecond laser is a combination of avalanche and multiphoton ionization. The initial “seed electrons,” which are essential to triggering avalanche ionization, are supplied by multiphoton ionization. However, the majority of free electrons are generated by avalanche ionization. The occurrence of optical breakdown is probabilistic especially around the threshold fluence, and its probability increases with increased pulse energy. The probabilistic feature of optical breakdown plays an important role in the multiple breakdown. The lens aberration effects caused by the objective further result in several other discrete focused regions along the light axis in the neighborhood of the lens focus [55,56], which greatly increase the probability of multiple breakdown. Hence, in the present work, more discrete focused regions where fluences exceeded the breakdown threshold occurred with increased pulse energy and resulted in decreased probability of single breakdown but increased probability of multiple breakdown. Laser-light transmission through the plasma region is known to be strongly reduced for the plasma shielding effect [32]. The dominant mechanism of shielding effect induced by nanosecond laser in water was by the absorption, with relatively little energy lost to reflection or scattering. The fluence ahead of the plasma region along the optical axis was strongly decreased by the plasma absorption, which suppressed the generation of new plasma, thereby further enhancing the occurrence of multiple breakdown. The plasma absorption is positively related to the density of free electrons. Hence, the highest absorption of major plasma and the weaker fluence ahead of the focal point together suppressed the size and luminance of discrete plasma ahead of the focal point, as shown in Fig. 2(c). The plasma is initially generated at the focal point where the fluence is the highest and first exceeds the threshold. Besides, no extra plasma is generated behind the focal point along the optics axis. The major plasma free of the plasma shielding was scarcely influenced by the occurrence of multiple breakdown. Hence, there was no significant difference of major plasma volume distribution between multiple breakdown and single breakdown, where major plasma volume showed a linear dependence of excitation energy regardless of the breakdown case, as shown in Fig. 2(b).
The position of multiple discrete focused regions, which were determined by the focusing objective, was fixed. The location of each plasma usually generated around focused regions during multiple breakdown also stayed almost constant, as shown in Fig. 2(c). Hence, the increase in pulse energy can strongly affect the volume and number of plasma, but it barely affects the plasma’s position in our experiment. With regards to the control of multiple breakdown, Quinto-Su et al. [67] showed that a spatial light modulator can control the position, number, and size of multiple bubbles. In our experiments, the constant space interval of multiple plasmas during multiple breakdown conferred ease in studying the influence of multiple breakdown on bubble oscillation and shock waves because the influence of space interval was removed.
3.2 Multiple cavitation-bubble oscillation
When multiple breakdown occurs, multiple-plasma formation and expansion for their high pressures and temperatures resulted in the formation of multiple initial cavitation bubbles along the direction of the laser beam. These initial bubbles then began to expand and soon experienced bubble interaction for their close space. The interaction among bubbles resulted in a more complex oscillation of multiple bubbles, such as jet formation, which was influenced by bubble-size difference, phase difference, and the distance between bubbles [71]. The typical difference in bubble oscillation between single breakdown and multiple breakdown is shown in Fig. 3. A sequence of bubble pictures was captured using a high-speed camera (Photron, Fastcam SA-Z) instead of EMCCD (an extra LED was added to the setup as the exposure source of the camera, as shown in Fig. 1(a)). When only a single bubble formed in a liquid of infinite extent, jets were barely formed during bubble collapse. At the end of bubble oscillation, a stable microbubble was generated around the plasma center, as shown in Fig. 3(a). For multiple breakdown, as shown in Fig. 3(b), several bubbles were generated along the optical axis. Soon, bubble coalescence occurred, resulting in a single shock-wave formation during bubble collapse. Then, two jets were formed, and the coalesced bubble was split into two big-size bubbles and some other small bubbles. Two major bubbles moving away from each other continued to oscillate. In the end, higher number of stable small bubbles than single breakdown existed at the focal region. Even if the starting time was almost synchronous, these bubbles were still regarded as out-of-phase bubbles because of their different lifetimes. The interaction of out-of-phase bubbles resulted in the formation of two high-speed jets collinear to the optic axes with opposite directions [72,73].
Fig. 3 Dynamics of cavitation bubbles in water induced by nanosecond laser pulses. The frame rate was 2.1 × 105 fps, and the exposure time was about 3.15 μs. (a) Oscillation dynamics of single bubble. (b) Oscillation dynamics of multiple bubbles.
To study the mutual interaction of cavitation bubbles induced by multiple breakdown, the initial distance between bubbles, the ideal maximum radius (Rmax), and the lifetime (Tosc) of each bubble were necessary to acquire. The initial distance between bubbles can be easily extracted from the plasmas images. By contrast, the Rmax and Tosc of each bubble for the mutual interaction of bubbles during multiple breakdown was difficult to directly measure. Given that the cavitation bubbles originated from the plasma, we calculated Rmax and Tosc of each bubble from the corresponding plasma volume, as long as the relationships among bubble lifetime, maximum radius, and plasma volume were known. The FOP measured by light-scattering technique represented the lifetime of coalesced bubbles during multiple breakdown. First, the FOP versus laser pulse energy was plotted in Fig. 4(a). Weak breakdowns with short-lifetime-bubble formation but without visible plasma generation at low pulse energy were ignored in this study. Such minute-bubble generation was due to the expansion of nonluminescent low-density plasma that cannot be captured with an EMCCD camera [61,74]. This indicated that the number of bubbles may have been higher than the bright plasma number when multiple breakdown occurred. However, influence of such small bubble on other large bubbles induced by high-density plasma was insignificant for its small size. According to Fig. 4(a), the FOP of both single breakdown and multiple breakdown almost linearly increased with increased pulse energy, which meant that the coalesced-bubble lifetime was barely affected by the occurrence of multiple breakdown. Considering the cavitation bubble originating from the plasma and the linear relationship among FOP, major plasma volume, and pulse energy, we assumed that the coalescence of bubbles did not influence the major-bubble lifetime. Hence, the measured FOP represented the major-bubble lifetime originating from the major plasma. Then, we plotted the FOP as a function of major plasma volume, as shown in Fig. 4(b) with the increase of major plasma volume, the FOP linearly increased for both single and multiple breakdown, and there was no significant difference in their trends. This finding indicated the reasonability of our assumption that the measured FOP represented the major-bubble lifetime was linearly proportional to the corresponding plasma and barely influenced by the bubble coalescence. Although this result differed from that obtained by Cui et al. [75], who stated that lifetime is increased by the bubble coalescence, the discrepancy may be ascribed to the different starting times of multiple bubbles. In our experiment, the starting time of each bubble was almost simultaneous, whereas a huge delay of starting time existed among multiple bubbles during Cui et al.’s research. Hence, the lifetime of other smaller bubbles simultaneously formed during the multiple breakdown can be calculated through the corresponding plasma volume. When the bubble size is no less than a few micrometers, the Rmax of single bubble in a liquid of infinite extent is related to its lifetime Tosc by Rayleigh’s formula [76], as follows:
Where ρ = 998 kg/m3 is the density of the liquid, Ps = 98.07 kPa is the static pressure and Pv = 2.98 kPa is the vapor pressure of the liquid. The ideal maximum radius of each bubble, except that induced by low-density plasma, can then be calculated. Under our experimental conditions, owing to the much smaller distance among adjacent plasmas than the sum of the corresponding bubble radius, bubble coalescence was inevitable mostly during multiple breakdown, as further confirmed by the fact that only single first collapse shock wave was detected during multiple breakdown.Fig. 4 FOP of cavitation bubbles. (a) FOP as a function of pulse energy. (b) FOP as a function of major plasma volume.
Multiple-bubble coalescence and jet formation resulting in the split of coalesced bubbles influenced the subsequent oscillation process. Accordingly, we next studied the influence of multiple breakdown on the rebound of bubbles. Given that the bubble ideal size was linearly related to the corresponding plasma volume, the volume ratio of major plasma to total plasma (VROMPTTP) was introduced to characterize the bubble-size difference. The rebound-bubble lifetime, which was measured and plotted as a function of FOP as shown in Fig. 5(a). A positive correlation obviously existed between the rebound-bubble lifetime and the major bubble oscillation period considering that the rebound bubbles evolved from the major bubble. However, an obvious difference was found between single breakdown and multiple breakdown that the rebound-bubble lifetime was enhanced during multiple breakdown. As the inset of Fig. 5(a) shows, the rebound-bubble lifetime linearly increased with FOP during single breakdown (blue spheres). For multiple breakdown, when the VROMPTTP was greater than 0.9 (red spheres), the distribution of rebound-bubble lifetime was more dispersed, but its trend was similar when compared with single breakdown. With further reduction of VROMPTTP, the distribution of rebound-bubble lifetime was not consistent with that of single breakdown, rebound-bubble lifetime was gradually increased when compared with single breakdown at equal FOP. VROMPTTP was crucial to the cavitation-bubble rebound. The maximum radius of split bubble was still calculated through its lifetime, because the bubble oscillation period was largely related to its volume and was not affected significantly by its shape [77]. Hence, a longer lifetime meant a larger bubble size. For single breakdown, only single bubble formed around the plasma, and its oscillation process without bubble interaction was simple. All the rebound-bubble energy was inherited from the major bubble and the rebound-bubble lifetime was linearly proportional to its FOP. Meanwhile, for multiple breakdown, bubble coalescence caused the rebound-bubble energy to originate from both the major cavitation bubble and other small bubbles. Hence, the reduction of VROMPTTP at same FOP, which meant equal major bubble ideal size, i.e., the increase in size and energy of other bubbles, led to the increased energy of other bubbles converted into the rebound-bubble energy through the multiple-bubble coalescence and to the increased in rebound-bubble lifetime. Hence, for the VROMPTPP lower than 0.7, we found an obviously negative correlation between rebound-bubble lifetime and VROMPTPP at same FOPs during multiple breakdown, as shown in Fig. 5(b). It was worth noting that two rebound bubbles were generated during multiple breakdown, but only the major one with longer lifetime can be detected. The increased rebound-bubble energy caused by the bubble coalescence might be not more than the energy of the minor rebound-bubble at high VROMPTPP, which result in a similar distribution of the measured rebound-bubble lifetime with that of single breakdown, as shown in the inset of Fig. 5(a).
Fig. 5 Rebound-bubble lifetime. (a) Rebound-bubble lifetime as a function of FOP. Different color represent different VROMPTTP: single breakdown (blue sphere); VROMPTTP over 0.9 (red sphere), range from 0.7 to 0.9 (green sphere), range from 0.5 to 0.7 (magenta sphere), and range below 0.5 (olive sphere). (b) Rebound-bubble lifetime as a function of VROMPTTP at the same FOP of 25.5 μs.
The interactions of cavitation bubbles originating from multiple breakdown strongly influence the subsequent oscillating dynamics and resulted in increased lifetime of rebound bubbles by converting other bubble energies into rebound-bubble energy. Thus, we needed to determine whether the conversion efficiency η of cavitation-bubble energy into rebound-bubble energy was affected by the bubble coalescence during multiple breakdown. The energy of each cavitation bubble Eb is given by [78], as follows:
For multiple breakdown, given that the cavitation-bubble lifetime is linearly proportional to plasma volume, we can calculate the total energy of cavitation bubbles Ebt through plasma volume. The multiple-bubble coalescence and jet formation resulted in the rebound of two major bubbles. However, only the energy of the larger one (Ebb) was calculated through the second oscillation period. Hence, the actual rebound-bubble energy was higher than Ebb but lower than double Ebb. The calculated conversion efficiency was lower than the actual conversion efficiency when multiple breakdown occurs. The calculated conversion efficiency η as a function of total cavitation-bubble energy was shown in Fig. 6(a). The conversion efficiency was related to the cavitation-bubble energy and was heightened by the occurrence of multiple breakdown. For single breakdown, less than 5% of cavitation-bubble energy was converted into the rebound-bubble energy, and the conversion efficiency decreased with increasing cavitation-bubble energy. During multiple breakdown, for the VROMPTTP higher than 0.9, which meant that other bubbles had much smaller size and energy than the major bubble. The weak influence of bubble coalescence on the major bubble oscillation resulted in the similar calculated conversion efficiency with single breakdown. It should be noticed that the actual conversion efficiency during multiple breakdown was higher than the measured because of the formation of two major rebound bubbles. The conversion efficiency was strongly enhanced and exceeded over 20% at low VROMPTTP, which meant the actual conversion efficiency was higher than 20% but lower than 40%. VROMPTTP was crucial for the conversion efficiency of cavitation-bubble energy to rebound-bubble energy. As shown in Fig. 6(b), at same total cavitation-bubble energy of 2 μJ, the conversion efficiency decreased with increasing VROMPTTP. The decrease in VROMPTTP signified the reduction of size difference between major bubble and other bubbles, thereby enhancing bubble coalescence. More bubble energy conversion into the rebound bubbles increased conversion efficiency and the rebound-bubble lifetime. Meanwhile, the duration of bubble oscillation was extended with increasing rebound-bubble lifetime during multiple breakdown, and a smaller size difference among multiple bubbles meant a longer bubble-oscillation duration.Fig. 6 Conversion efficiency of cavitation-bubble energy into rebound-bubble energy. (a) Efficiency η as a function of total bubble energy. Different color symbols represent different VROMPTTP range. (b) Cavitation-bubble energy of 2 μJ, conversion efficiency η as a function of VROMPTTP.
In brief, bubble coalescence during multiple breakdowns can enhance the rebound-bubble lifetime through two ways, i.e., by adding the other bubble energy into the rebound-bubble energy and by increasing the conversion efficiency η. According to Hellman et al. [28], pulsed laser-induced breakdown can be used for the rapid and localized mixing of fluids in microfluidic channels which was driven by the cavitation-bubble oscillation and jets. Hence, more complex bubble oscillation process with strong jet formation and inevitable bubble coalescence due to the confined space interval during multiple breakdown, which resulted in higher Reynolds number at localized region, can possibly enhance the rapid mixing of fluids. In addition, the extension of bubble oscillation process may further enhance the fluids mixing efficiency by increasing the mixing time.
3.3 Far-field pressure of shock waves
During the underwater optical breakdown, both the plasma expansion and cavitation-bubble collapse generated shock waves. The peak pressure of shock wave with supersonic speed decays approximately proportional to r−2 (r is the distance from plasma center) after shock front formation and about 50 ns later, when the shock wave propagating as sonic wave for rapid energy dissipation and the peak pressure of which is proportional to r [37,38,59]. Hence, in the far field, where the shock pressure decay is shower than that in the near field, the pressure measurement is more accurate and easier to perform. Multiple breakdowns accompanied with the formation of the multiple shock waves. The pressure strength and profile were strongly related to the measure angle even at same distance from the focal point during multiple breakdown [59]. In our experiments, the ultrasonic transducer placed about 3.8 mm over the focal point was used to measure the shock waves induced by plasma formation and bubbles collapse. The initial multiple shock waves almost simultaneously spread to the detector because of the far larger diameter of about 10 mm of the detector than the multiple-plasma length. Hence, the pressure of initial shock waves measured by the transducer was the overlap of multiple shock waves. The peak pressure of the initial shock waves in the far-field induced by plasmas versus plasma volume was plotted in Fig. 7. We found that the peak pressure almost linearly increased with increasing plasma volume for both single breakdown (blue sphere) and multiple breakdown (red sphere). For multiple breakdown, each shock wave originating from the corresponding plasma formation simultaneously spread to the detector. The superposition principle can be used, because the shock waves behaved acoustically in the far field. Hence, the measured peak pressure was the sum of multiple shock wave peak. According to Fig. 7, the far-field peak pressure of the initial shock wave was linearly proportional to the corresponding plasma, which was similar to bubble ideal size. Note that the total volume of plasmas exponentially increased with pulse energy. The far-field peak pressure of initial shock waves perpendicular to the laser beam was linearly proportional to the plasma volume but nonlinearly scaled with the pulse energy.
The collapse shock wave was different from the initial shock wave. However, as shown in Fig. 1(e), the third peak signal representing the first collapse shock wave (FCSW) originated from the first collapse of cavitation bubbles. Even though multiple cavitation bubbles formed, only a single FCSW was detected during the first collapse. We attributed single FCSW formation to the inevitable multiple-bubble coalescence with different lifetimes. Equal number of FCSW should be formed if the oscillation of each bubble was independent. However, the collapse of smaller bubbles was overlapped for the multiple-bubble coalescence, which resulted in the elimination of the FCSWs from other smaller bubbles and the formation of single FCSW from major bubble with lower peak pressure. The peak pressure of FCSW as a function of maximum radius of the major bubble was shown in Fig. 8(a). In the case of single breakdown, the FCSW strength in the far-field was almost linearly proportional to the major bubble maximum radius as shown in Fig. 8(b), which was in accordance with the previous studies which discussed the linear relationship between the FCSW strength and the maximum radius of cavitation bubbles [36,78,79]. When the multiple breakdown occurs, the multiple bubble interaction influenced the strength of FCSW. For the VROMPTTP higher than 0.7 (red and blue sphere), the peak pressure of FCSW was similar to that of single breakdown for the weak influence of bubble coalescence on the collapse of major bubble. When the VROMPTTP ranged from 0.5 to 0.7, the influence of bubble coalescence on the collapse of major bubble was enhanced with increasing energy of the other bubbles, thereby resulting in the lower peak pressure distribution of FCSW (magenta sphere in Fig. 8(a)) compared with single breakdown. With the further reduction of VROMPTTP, the multiple-bubble coalescence was further enhanced and led to a more obvious decrease in the peak pressure of FCSW, the peak pressure distribution was much more dispersive than that of single breakdown, and the peak pressure strength was much smaller.
Fig. 8 Peak pressure distribution of FCSW in the far field. (a) Peak pressure of collapse shock waves in the far-field as a function of plasma volume. (b) Linear fitting of the peak pressure of FCSW with error bars. Different color symbols represent different VROMPTTP ranges. (c) The peak pressure of FCSW distribution with the same major bubble ideal size (maximum radius of 170 μm).(d) With the same cavitation-bubble energy of 2.2 µJ, the peak pressure of FCSW in the far-field as a function of rebound-bubble lifetime.
As mentioned above, when the VROMPTTP lower than 0.7, with equal major bubble ideal size, the rebound-bubble lifetime decreased with the increasing of VROMPTTP for the higher conversion efficiency of multiple bubble energy to rebound-bubble energy induced by the bubble coalescence. However, the change tendency of the peak pressure of FCSW showed the opposite trend. As shown in Fig. 8(c), with the same major bubble ideal size (maximum radius of 170 μm), the peak pressure of FCSW linearly increased with VROMPTTP. With decreased VROMPTTP, even the cavitation-bubble energy increased, the strength of FCSW induced by the collapse of major bubble was increasingly suppressed. In addition to the decrease in FCSW induced by the major bubble collapse, the FCSWs of other smaller bubbles were eliminated by the inevitable bubble coalescence. The part of vanished and reduced collapse shock waves energy was converted into the rebound-bubble energy, which resulted in increased conversion efficiency of cavitation-bubble energy into rebound-bubble energy and increased rebound-bubble lifetime. A remarkably negative linear relationship existed between the peak pressure of FCSW and the rebound-bubble lifetime with equal cavitation-bubble energy, as shown in Fig. 8(d). Unfortunately, we failed to estimate the efficiency of reduced shock wave energy into rebound-bubble energy for the non-linear propagation in the near-field but far-field measurement of shock waves. In conclusion, for multiple breakdown, decreased VROMPTTP meant reduced bubble size difference between the major bubble and other bubbles. Accordingly, the enhancement of bubble coalescence resulted in increased conversion efficiency of the initial bubble energy into rebound-bubble energy, as well as decreased strength of FCSW.
4. Conclusion
The plasma distribution, cavitation-bubble oscillation, and far-field peak pressure of shock waves during optical breakdown were measured simultaneously to investigate the multiple breakdown in deionized water induced by focused nanosecond laser pulses. According to plasma images, we found that both the probability of multiple breakdown and the breakdown quantity increased with pulse energy. The occurrence of multiple breakdown resulted in the accelerating increase of total plasma volume with increasing pulse energy. However, the plasma generated around focal point was barely affected by the occurrence of multiple breakdown, and its volume was linearly proportional to pulse energy. Considering that cavitation bubbles and shock waves originated from the plasma expansion, we found linear dependence among the bubble lifetime, far-field peak pressure of the initial shock wave, and the volume of the corresponding plasma. This finding may be useful for the further study of multiple breakdown and mutual interaction of multiple bubbles.
Out-of-phase multiple bubbles formation and the following coalescence of bubbles during multiple breakdown resulted in two high-speed jet formation and two major split bubbles generation. The first oscillation period that represented the lifetime of the major bubble originating from the major plasma was barely influenced by the bubble coalescence, which was of importance in calculating the maximum radius and energy of cavitation bubbles through light-scattering technique under the condition in which multiple bubbles may be formed. For example, vapor bubbles in gold nanoparticle solutions. Meanwhile, the mutual interactions of multiple bubbles strongly affected the rebound of bubbles and the strength of the collapse shock wave. The rebound-bubble lifetime which was linearly proportional to the first oscillation period for single breakdown was markedly increased by the multiple-bubble coalescence during multiple breakdown. The degree of the increase was dependent on VROMPTTP. Low value of VROMPTTP indicated longer rebound-bubble lifetime. The conversion efficiency of cavitation-bubble energy into the rebound-bubble energy was also enhanced during multiple breakdowns. The increased energy of rebound bubbles may have originated from the vanished and reduced FCSWs energy. During multiple breakdowns, the same number of FCSWs with bubbles should be formed if no interaction occurred between multiple bubbles. However, due to the confined space interval of multiple bubbles, FSCWs originating from other bubbles was eliminated and only single FCSW was formed during the first collapse of cavitation bubbles because of the inevitable bubble coalescence, and the peak pressure linearly proportional to the bubble size during single breakdown was significantly weakened. The part of vanished and reduced shock wave energy was transferred into rebound-bubble energy, thereby resulting in increased conversion efficiency of cavitation bubbles into rebound-bubble energy. Hence, at same cavitation-bubble energy, the FSCW strength linearly decreased with rebound-bubble lifetime. The inevitable bubble coalescence dynamics and the extension of bubble-oscillation duration during multiple breakdown may be useful for the enhancement of microfluidic mixing. Moreover, the increased rebound-bubble lifetime and decreased collapse-shock-wave strength caused by the bubble coalescence may be useful for photoacoustic applications.
Funding
National Natural Science Foundation of China (NSFC) (61335012, 61727823, 61575156, 61705177, 61775178, and 61505159).
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