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Ejection of Metal Particles into Superfluid He by Laser Ablation Xavier Buelna, Adam Freund, Daniel Gonzalez, Evgeny Popov, and Jussi Eloranta J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b06594 • Publication Date (Web): 05 Oct 2016 Downloaded from http://pubs.acs.org on October 11, 2016

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Ejection of Metal Particles into Superfluid 4He by Laser Ablation Xavier Buelna, Adam Freund, Daniel Gonzalez, Evgeny Popov, and Jussi Eloranta∗ Department of Chemistry and Biochemistry, California State University at Northridge, 18111 Nordhoff St., Northridge, CA 91330 E-mail: [email protected] Phone: +1 818 677 2677

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Abstract The dynamics following laser ablation of a metal target immersed in superfluid 4 He

is studied by time-resolved shadowgraph photography. The delayed ejection of

hot micrometer-sized particles from the target surface into the liquid was indirectly observed by monitoring the formation and growth of gaseous bubbles around the particles. The experimentally determined particle average velocity distribution appears similar as previously measured in vacuum but exhibits a sharp cutoff at the speed of sound of the liquid. The propagation of the subsonic particles terminates in slightly elongated non-spherical gas bubbles residing near the target whereas faster particles reveal an unusual hydrodynamic response of the liquid. Based on the previously established semi-empirical model developed for macroscopic objects, the ejected transonic particles exhibit supercavitating flow to reduce their hydrodynamic drag. Supersonic particles appear to follow a completely different propagation mechanism as they leave discrete and semi-continuous bubble trails in the liquid. The relatively low number density of the observed non-spherical gas bubbles indicates that only large micronsized particles are visualized in the experiments. Although the unique properties of superfluid helium allow a detailed characterization of these processes, the developed technique can be used to study the hydrodynamic response of any liquid to fast propagating objects on the micrometer-scale.

INTRODUCTION Laser ablation of metals in the liquid phase is a commonly applied method that can be used to produce relatively narrow size distributions of metal nanoparticles and other nanostructures such as nanodisks and nanowires. 1–9 The latter structures have been particularly well studied in superfluid 4 He as their formation is promoted by quantized vortex lines (diam. ca. 1 ˚ A), 10,11 which act as templates for the wire assembly. 12–16 Other cryogenic liquids were mainly employed to rapidly cool down and stabilize the products in an inert environment at low temperatures. 9,17 2

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The primary objective of early nanosecond laser ablation studies in superfluid helium was to implant atomic and molecular probes into the liquid for subsequent spectroscopic studies. 18–21 Such probes could, for example, be employed to interrogate the atomic-scale response of superfluid helium under confinement. 22 However, based on the recent advances in understanding the mechanism of nanosecond laser ablation as well as the dynamics of the surrounding superfluid bath, it appears to be difficult to produce isolated species by this method due to rapid clustering. 23 In our recent work, 23,24 we have demonstrated that superfluid helium is an ideal prototype liquid medium for developing new experimental techniques to analyze liquid phase laser ablation and the resulting product formation. For example, optical imaging of the gas bubbles formed around laser heated plasmonic nanoparticles has led to the development of a new in-situ method for observing the spatial locations and sizes of the particles in liquid phase. 24 It is noted that the presented approach is not limited to superfluid helium but can be applied to analyze plasmonic nanoparticles in any liquid as the developed relationship between the gas bubble and nanoparticle sizes is completely general. In addition to nanometer-scale particles, laser ablation of metals can also lead to the production of larger micron-sized particles, especially when rough ablation target surfaces are employed. 25,26 For example, such particles are an unwanted by-product of laser ablation in the preparation of thin films. While their size and velocity distributions have been thoroughly characterized in vacuum, the formation dynamics and interaction with a liquid environment has not been studied in detail before. Due to the high temperature and initial velocity of such particles, an unusual hydrodynamic response of the surrounding liquid is expected. For example, high particle temperature may lead to significant hydrodynamic drag reduction by supercavitation or, equivalently, the formation of Leidenfrost vapor layers. 27,28 To date, this effect has been studied experimentally down to the millimeter-scale. Furthermore, for micron-scale particles, the developed vapor layer may become significantly larger than the particle itself, which leads to complex interaction between the flexible gas bubble and the

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1.6 and 4.2 K at the corresponding saturated vapor pressure. 24 The cryostat vacuum shroud was evacuated down to ca. 10−6 torr by a turbo molecular pump (Pfeiffer model TPH 062; 56 L/s of N2 ) backed by a two-stage mechanical pump (Edwards model E2M2) and the helium vapors from the sample space were pumped through a throttle valve (MKS model 252 with feedback provided by MKS Baratron 622 capacitance manometer) by a single stage mechanical pump (Pompe Per Vuoto Rotant model EU65; 20 L/s). Optical access to the sample is provided through a set of five suprasil quartz windows used for the ablation laser, backlight (near infrared diode model Osram SPL PL90 driven by Intersil EL7104CN and Motorola MTP75N03HDL), and charge-coupled device (CCD) camera (ImagingSource DMK 23U445) equipped with imaging optics (180X zoom lens, working distance 95 mm). To improve the image contrast in selected experiments, the backlight was replaced by a diffuse laser beam obtained from a frequency doubled Nd-YAG laser (Surelite-II, 9 ns pulse length). The ablation laser, backlight, and camera shutter were triggered by two computer controlled delay generators (Stanford DG 535 and Berkeley Nucleonics BNC 565). 29 To image the products ejected from the target, the ablation laser pulse is followed by a backlight diode flash after a specified time delay. Within the range of applied drive pulse lengths, the backlight diode output could be varied from 10 ns to several microseconds as determined by a fast response photodiode (Thorlabs DET10A). The applied backlight diode is also capable of nanosecond timescale pulse sequencing, which can be used to record multiple timed images onto a single CCD frame. Analysis of the recorded shadowgraph images was carried out by using the Fiji software. 30,31

RESULTS Laser Ablation. Laser ablation of metals in the liquid phase is known to create rapidly expanding confined plasma adjacent to the ablation target. 1 Under the present experimental conditions, initial plasma expansion for up to ca. 50 ns can be observed, followed by emission

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nanoparticles through their plasmon resonance led to the formation of spherical gas bubbles around them, which were subsequently observed through time-resolved shadowgraph photography. Such bubbles grew within 3 µs of the heating laser pulse and disappeared from the optical view in 20 µs. 24 In contrast to our previous work, 24 the present experiments employ higher ablation laser powers (> 10 GW/cm2 ) to increase the size of metal particles ejected from the ablation zone. Within the first 5 µs from the ablation laser pulse, the recorded time-resolved shadowgraph images show delayed material ejection from the target (see top panel of Figure 2). Note that each shadowgraph image frame originates from a different ablation laser pulse and hence the observed dynamics must be consistent from pulse to pulse. Formation of Gas Bubbles. Several millimeters from the ablation target (typically > 2 mm), non-spherical gas bubbles, which possess geometries consistent with particle propagation away from the target, are observed as shown in Figure 3. The number density of these bubbles peaks around 25 µs after the ablation laser pulse but they can be observed up to 100 µs (see, e.g., Figure 3A). Note that these non-spherical bubbles appear much later in time as compared with the above mentioned spherical bubbles that form around the dissolved metal nanoparticles. Furthermore, their density is independent of the ablation laser repetition rate (1 - 10 Hz), which eliminates the possible involvement of previous laser pulses in the process. The present study focuses specifically on analyzing the properties of these non-spherical gas bubbles (“bullets”) formed after the ablation event. The fact that the above mentioned bullets can only be observed a couple of millimeters away from the ablation target indicates that they require some time to grow before becoming visible in the shadowgraph images. At early times, as demonstrated in Figure 3B, some bullets possess a strongly elongated geometry with the characteristic expanding tail structure. On the other hand, bullets observed farther away from the target typically show less pronounced elongation (see Figure 3C) and exhibit noticeable fluctuations in their orientation with respect to the ablation target (i.e., not consistently from left to right in Figure 3C).

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size distribution was observed, consisting of small particles less than 100 nm in diameter and large particles in the range of 0.3 - 3 µm. 26 The dynamics of material ejection from the ablation spot in superfluid helium is shown in the top panel of Figure 2 where a sharp tip-like feature is first seen to develop at t = 3.43 µs, followed by its penetration through the ablation bubble surface within 200 ns. The timing of these events is consistent with the onset of the micron-sized particle ejection discussed above and indicates that the metal surface remains in molten state up to several microseconds after the ablation laser pulse. The geometry of the sharp tip (ca. 15 µm thick) reflects the size and angular distribution of the ejected particles. Once the expanding ablation bubble has reached its maximum radius, it becomes unstable and exhibits strong fluctuations in both geometry and volume. 33 With the typical laser powers applied in this study, this regime is reached in a couple of milliseconds after the ablation laser pulse. The observed violent explosive events near the target (see bottom panel of Figure 2) can contribute to this previously reported ablation bubble instability during its contraction phase. Note that the whole region shown in the figure near the target overlaps with the ablation bubble and hence only gas should be present there. One plausible explanation for these events is that the original hot ablation spot (as compared to the standard boiling point of liquid helium, 4.2 K) suddenly becomes accessible for the liquid from the side, causing explosive boiling and sudden expansion. Presence of such highdensity gas can provide contrast in the shadowgraph images. Although no particle ejection from these events is observed, they may, for example, contribute to roughening of the metal surface over time. Propagation of Subsonic Metal Particles. Once the spherical gas bubbles produced by laser heated metal nanoparticles have disappeared from the view, 24 the properties of nonspherical gas bubbles can be studied. Analogous to the heated nanoparticles, hot micronsized metal particles can also form gaseous bubbles around them with a characteristic growth time. Furthermore, these bubbles show elongated structure, which is consistent with particle

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Speed of sound (approx. 230 m/s) Normalized particle count

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0.8 2

Vacuum: Al (355 nm, 4 J/cm ) 2 Liquid: Cu (355 nm, 6 J/cm )

0.6

0.4

Rare individual bubbles and continuous tracks

0.2

0 0

200

400

600

800

1000

1200

Velocity (m/s)

Figure 6: Comparison between the observed velocity distributions in superfluid helium (Cu target; total particle count 250 obtained from 62 separate video frames recorded at 25 µs after the ablation; 10 torr external pressure, 1.7 K; red line with circles) and vacuum (Al/vacuum; black line) obtained by 355 nm laser ablation. 25 Note that the two experiments employ slightly different incident laser powers as indicated in the caption. Particle Average Velocity Distribution. The angular particle distribution from laser ablation in vacuum was previously observed to be very narrow (i.e., cos24 (φ) with φ being the angle with respect to the ablation laser beam). 25 Such a narrow angular distribution was also observed in the present experiments (see, e.g., Figure 3A). While the previously measured micrometer-size particle velocity distributions in vacuum vary slightly with respect to the target material, surface roughness, and the applied ablation laser power, they typically show a characteristic maximum between 100 and 200 m/s with wings that spread to both the low and high velocity sides. 25 If the position of each non-spherical gas bubble observed in the shadowgraph images is taken to correspond to the location of the metal particle itself at a given time, the particle average velocity distribution can be obtained by analyzing a sequence of images such as those shown in Figure 3. A comparison between Cu (superfluid helium) and Al (vacuum) 25 velocity distributions is shown in Figure 6. The distributions appear very similar but with the following notable differences in the liquid phase: 1) the

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maximum of the distribution is shifted slightly towards higher velocity and 2) a cutoff is present at both low and high velocity ends of the distribution. The shift in the velocity maximum can be attributed to the different metal and surface quality of the ablation target as well as the slightly higher ablation laser power applied in this work. The second point is more interesting as the distribution is seen to cut off abruptly at the speed of sound in superfluid helium (ca. 230 m/s). In this velocity regime, only a small number of bubbles are observed and they mostly appear as semi-continuous tracks, indicating that their mode of propagation is different than for subsonic particles. The low velocity cutoff may simply reflect the inability of the low kinetic energy particles to escape the vicinity of the ablation bubble. Propagation of Supersonic Metal Particles. The shadowgraph images discussed above represent instantaneous snapshots of the fast moving metal particles. On the other hand, experiments employing multiple backlight pulses or, alternatively, long exposure times can reveal their local dynamics. This technique was used to determine the mechanism of 1) fast particle propagation (bubble trails) and 2) particle localization at the end of their trajectories. Considering the first process, it is known that fast propagating macroscopic objects in classical liquids (e.g., fast bullet propagating underwater) leave a trail of gas bubbles behind them. Following this analogy, the bubble progression shown in Figure 4A can be interpreted as the individual bubbles left behind by a fast moving metal particle, which itself has already passed by the observation window. Each bubble that was left behind still carries some momentum originating from the particle that traveled inside it and hence the bubble keeps traveling slowly in the same direction as the particle itself (see Figure 4A). A closeup of the particle hopping event towards the end of a bubble trail is shown in Figure 4B where, in addition to the spherical bubble being left behind, the next bubble appears highly distorted due to particle escape. In general, the observation of these bubble trails is a rather rare event, which indicates that they originate from the high end of the particle velocity distribution beyond the speed of sound (see Figure 6). These fast particles are also likely the

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origin of the continuous tracks that can sometimes be observed well ahead of the shock wave created by the fast expanding confined plasma. Such a track is expected to appear near the termination phase of fast particle trajectory. The above observations point to the following general mechanism for fast particle propagation above the speed of sound in superfluid helium. As a hot metal particle travels in the liquid, heat transfer to the liquid continuously increases the surrounding gas bubble size. Once the hydrodynamic drag of this bubble becomes too high, the hot metal particle penetrates through the front part of the bubble, leaving the original bubble behind. Provided that the particle is still at a sufficiently high temperature, it can start growing another bubble around it, which could then detach again if the hydrodynamic drag becomes sufficiently large. The energy of breaking the bubble into two parts is essentially dictated by the liquid surface tension, which is very low for superfluid helium. A schematic drawing of this bubble hopping mechanism for supersonic particles is shown in the bottom part of Figure 5. As a general note, this mode of particle propagation appears similar to that observed in the classical “bubble chamber” experiment where analogous bubble trails have been used to detect and analyze incident high energy particles. 39 Dissipation of Particle Kinetic Energy. Dissipation of kinetic energy for the moving metal particles in superfluid helium can arise from the following sources: 1) emission of sound (acceleration/deceleration only), 2) viscous response (i.e., scattering by thermal phonons/rotons), and 3) creation of vortex rings with diameters comparable to the object size when the velocity exceeds the Landau critical value (vc ≈ 60 m/s). 40 Since the viscosity of superfluid helium is very low and most of the ejected particles have velocities exceeding vc (cf. Figure 6), the dominant mechanism for energy loss is the vortex ring emission process. Vortex ring energy, Ering , with a radius, Rv , in superfluid helium can be estimated from: 40,41 ρ0 h 2 R v Ering (Rv ) = 2mHe

    8Rv ln − 1.67 a

(1)

where ρ0 is the bulk liquid density (145.3 kg/m3 at 1.7 K), 42 h is the Planck’s constant, 14

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mHe is the 4 He atom mass, and a = 0.74 ˚ A is the vortex core parameter. 16 For example, a 1 µm diameter spherical copper particle (density ca. 9×103 kg/m3 ) propagating at 100 m/s has enough kinetic energy to create almost 107 vortex rings of the same diameter. This estimate shows that vortex ring creation is also a rather inefficient channel for energy loss. Based on the previous time-dependent density functional theory simulations, the time scale for vortex ring emission can be estimated as 20 ps. 43 Therefore, the time required to dissipate the particle excess kinetic energy is approximately 20 ps × 107 = 200 µs, which is comparable to the time scale of the present experiments. This highlights the fact that the dissipative response of superfluid helium is not instantaneous and, depending on the particle excess kinetic energy available, this process can take a significant amount of time. In contrast, the Landau critical velocity can be reached nearly instantaneously over a few nanometer distances at small particle kinetic energies. 44 Finally, it should be noted that the bubble growth around the particle is a dynamic process and the energetics of vortex ring formation varies accordingly as a function of the moving bubble radius. Furthermore, the process should stop once the velocity falls below vc . Particle Trajectory Termination. The termination phase of hot particle trajectories is shown in Figure 4C. The main body of the bubble is nearly spherical but a pronounced neck is present due to the particle pressing onto the front of the bubble. The penetration depth is dictated by the liquid surface tension, which acts as the final stopping force for the particle. Particle localization at end of the neck signifies that this image corresponds to its cool down phase and, furthermore, the terminating step for the trajectory. Due to their large hydrodynamic mass and the loss of particle kinetic energy, these bubbles move very slowly (ca. 1 - 2 m/s). Although the energy of vortex ring creation around micronsized particles is very small compared to their initial kinetic energy, this dissipation channel may become increasingly important during the slowdown phase just before the velocity drops below the Landau critical value. One possible interpretation of the periodic variations in the neck diameter observed in Figure 4C is the emission of a large number of micron-

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sized vortex ring bundles, which can also form in classical liquids in their non-quantized form. However, an uneven particle heat distribution during its thermalization could also produce such periodic variations. Finally, considering the rather low number density of these supercavitating particles in the field-of-view over time, their total concentration must be significantly lower than the ejected metal nanoparticles (diam. < 100 nm) from the target. 24 Hydrodynamic Analysis Based on Supercavitation. When a fast moving object is embedded inside a gaseous cavity (supercavitation), the skin friction drag is greatly reduced and, for example, propagation velocities for macroscopic objects near the speed of sound (up to Mach 0.77) have been achieved in water. 27 For supercavitation to persist, the object must be able to maintain the gaseous layer around it. For large macroscopic objects, this is typically achieved by employing a special nozzle that produces gas bubbles in the front, which join to form a cavity around the object. 45,48 In the following, we consider a scenario where the hot metal particles from laser ablation produce gaseous cavities around them naturally (“Leidenfrost vapor layer”) 28 and the supercavitation effect facilitates their propagation at velocities near the speed of sound. The unique properties of superfluid helium 24 allow the detailed study of such dynamics in the liquid phase and, consequently, the determination of optimal cavity shapes that minimize the hydrodynamic drag. To provide a qualitative analysis of the experimental results, we employ the general supercavitation model, which was originally developed for describing this phenomenon in water. 45 A more accurate description of the problem should employ a true hydrodynamic simulation, which includes the dissipative behavior of superfluid helium at the appropriate length scale. When the propagating dynamically growing particle–gas bubble system is captured at early times (see Figure 3B), it exhibits the characteristic features of supercavitation. 45–48 The elongated body 48 along with the complex tail structure and turbulence in the wake are present in the shadowgraph images. Here the supercavitated particle resides inside the

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gas bubble (cavity), which lowers the overall skin friction drag. 48 In general, to create and maintain such a cavity, the object must contain a cavitator or include an internal heat source. 45,48 In the present case, the object corresponds to a hot metal particle, which itself is able to maintain a semi-stationary gaseous cavity around it for tens of microseconds. For the cavity to reach the desired elongated geometry, the hydrodynamic forces due to the particle must apply to the foremost point of the cavity, which is located far ahead of the system center of mass. 48 To understand the supercavitating flow of the experimentally observed hot metal particles in superfluid helium, it is instructive to first calculate the relevant hydrodynamic quantities. Based on the particle average velocity distribution shown in Figure 6, nearly half of the ejected particles have velocities between Mach 0.7 and 1.0. The Reynolds number (Re) for cavitating flows is defined as: 27

Re =

ρvd η

(2)

where ρ is the liquid density (145.3 kg/m3 at 1.7 K), v is the object velocity (m/s), d is the cavitator diameter perpendicular to the flow (m), and η is the liquid viscosity (3.0×10−7 Pa s at 1.7 K). 42 To establish a first estimate, we take the cavitator diameter to be equal to the cavity front diameter (dm ), d = dm ≈ 50 µm (see Figure 3B). For metal particles traveling at Mach 1 in superfluid helium at 1.7 K, Eq. (2) gives Re = 6 × 106 indicating a strongly turbulent flow. However, we note that this is an upper limit estimate as one expects d < dm and we will return to this point later. Furthermore, because of the very low surface tension of superfluid helium, the Weber number is approximately 105 , which clearly shows that surface tension effects can be neglected. The key parameter describing supercavitating flows is the cavitation number σ: 45

σ=

2 (P − Pc ) ρv 2

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where P − Pc represents the pressure differential outside vs. inside the cavity. The typical criterion used for identifying a supercavitating flow is σ < 0.1. 48 An approximate relationship connecting the cavity length (L) and its diameter (dm ) to cavitation number is given by: 49 σ + 0.008 L = dm σ (0.066 + 1.7σ)

(4)

which has been observed to be nearly independent of the cavitator shape. 47 Based on the dimensions shown in Figure 3B, L = 340 µm and dm = 50 µm. Inserting these values into Eq. (4) gives σ = 0.06 < 0.1, which indicates a supercavitating flow. According to Eq. (3), this yields the pressure differential, P − Pc , as 2 MPa, assuming that the bullet shown in Figure 3B propagates at Mach 1. The drag coefficient, Cd , can be related to the cavitation number by the following empirical relation: 45

Cd = 0.82 (1 + σ)

(5)

which assumes a disk shaped cavitator. However, if the cavitator has a spherical geometry (i.e., a spherical particle), the drag coefficient value is reduced significantly. For example, at cavitation number 0.06 the drag coefficient is lowered to 0.27 (spherical) vs. the estimate of 0.87 (disk) provided by Eq. (5). 46 In principle, a disk cavitator shape could result from the dynamic shaping of a molten particle by the hydrodynamic forces pressing onto its front during the propagation in the liquid. The drag coefficient, in turn, can be used to estimate the cavitator diameter, d: 45

d = dm



σ − 0.132σ 8/7 Cd

1/2

(6)

This equation gives d = 13 µm with Cd = 0.87 (disk) or d = 23 µm with Cd = 0.27 (sphere). These diameters are sufficiently large that the particles should be visible in the shadowgraph images and they also appear slightly larger than observed under vacuum in previously 18

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published experiments. 25 This either means that the value of d should be interpreted as an effective diameter (i.e., metal particle and dense gas layer around it) or the applied empirical hydrodynamic equations are no longer very accurate at this length scale. Finally, turning the attention back to the calculation of the Reynolds number (i.e., Eq. (2)), with the above values for d, we obtain Re = 1×106 - 3×106 (vs. the initial estimate of 6 × 106 ), which are still clearly in the highly turbulent flow regime. In addition to the observed characteristic cavity shapes, sudden changes in the propagation direction of the bullets can also be observed as demonstrated in Figure 3C. This indicates that under some circumstances non-uniform forces are applied to the front of the cavity, which causes the apparent directional instability. Analogously, a similar effect has also been reported for supercavitated macroscopic objects propagating in water. 50 Since the gaseous cavity surrounding the hot metal particles is much larger than the particle itself, it is flexible to adjust its geometrical shape to minimize the resistance to liquid flow. The elongated shape is common to all supercavitating flows, but, additionally, the widening of the cavity towards the tail is clearly visible in Figure 3B. Since the recorded shadowgraph images are 2-D projections, the tail structure could arise from a 3-D hollow cone geometry, which is also typical for supercavitation. 48 In this case, the dark region appearing between the tail fins (see Figure 3B) is indicative of turbulent flow in this region. These observations can be compared with an earlier hydrodynamic simulation where a similar tail structure was predicted. 51 While the features observed in the present experiments and in that reference are not fully identical, they demonstrate the basic features of the cavity geometry and the presence of the turbulence. However, these two processes are not entirely comparable as the numerical study models the water entry stage of a projectile and, in that sense, the general consideration of Savchenko 48 would provide a more direct comparison for the cavity geometry. Note that the presence of the tail section could also be related to the “wings” that have been reported for traveling cavitation bubbles. 52

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CONCLUSIONS It was shown that fast moving hot metal particles produced by laser ablation can be used to study the hydrodynamic response of liquids on the micrometer scale. In particular, the particles that propagate near the speed of sound exhibit the supercavitation phenomenon that greatly reduces their skin friction drag. Depending on the time of image capture, this method can be used to study the various hydrodynamic regimes of the moving particle–gas bubble system. Due to the large size difference between the rigid micro-particle and the surrounding flexible gas bubble, shadowgraph photography can reveal the optimal cavity shape that minimizes the hydrodynamic drag at a given velocity. Supersonic particles follow a completely different propagation mechanism as they leave slowly drifting bubble trails behind them. The developed experimental techniques to generate fast moving hot particles and visualize them by time-resolved shadowgraph photography are completely general and can be used to study the associated hydrodynamic phenomena in any liquid.

Acknowledgement Financial support from the National Science Foundation grants CHE-1262306 and DMR1205734 are gratefully acknowledged.

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