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Ultrason Sonochem
Ultrason Sonochem
Ultrasonics Sonochemistry
1350-4177
1873-2828
Elsevier

S1350-4177(24)00271-2
10.1016/j.ultsonch.2024.107023
107023
Original Research Article
Optic generation and perpetuation of acoustic bubble clusters
Mur Jaka ab
Reuter Fabian a
Agrež Vid b
Petkovšek Rok rok.petkovsek@fs.uni-lj.si
b⁎
Ohl Claus-Dieter claus-dieter.ohl@ovgu.de
a⁎
a Faculty of Natural Sciences, Institute for Physics, Otto-von-Guericke-University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
b Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva 6, SI-1000 Ljubljana, Slovenia
⁎ Corresponding authors. rok.petkovsek@fs.uni-lj.siclaus-dieter.ohl@ovgu.de
15 8 2024
11 2024
15 8 2024
110 10702313 6 2024
29 7 2024
8 8 2024
© 2024 The Author(s)
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Laser-induced cavitation bubbles offer precise control of the flow in space and time, but they are rarely used for the mechanical and chemical processing of liquids. Instead, strong acoustic fields are commonly used to nucleate and drive cavitation bubbles for liquid process applications. While acoustic field creates many more cavitation events, the resulting chaotic dynamics offers little control on the fluid mechanics, i.e., where and how bubbles deliver their energy. Here we present a method that utilizes a laser to nucleate a single cavitation bubble, which is then driven into violent oscillations by the ultrasound field, resulting in splitting of the bubble followed by formation of a cluster of cavitation bubbles. This combination offers means for cavitation control not available in conventional acoustic cavitation. Here, the cavitation bubble is generated with a custom build pulsed laser that is focused below a sonotrode driven at 20 kHz. In absence of the acoustic driving the bubble reaches a maximum diameter of 130 µm with a lifetime of approximately 10 µs. In the presence of the acoustic field the first few expansions and bubble collapses are strongly affected by the phase of nucleation. Over successive acoustic cycles a small bubble cluster develops that loses its connection with the phase of generation. We study the dynamics in the free field and constrained by a rigid boundary. For both geometries the cluster over many acoustic cycles dies off, yet through repetitive optical bubble seeding the cluster lifetime and its location can be controlled.
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pmc1 Introduction

Laser-induced single cavitation bubbles have been established as means of controlled cavitation for applications in medicine [1] and material processing [2]. The precisely defined timing and properties of such bubbles have found wide use in fundamental studies, from shock wave [3] and plasma formation [4], bubble dynamics and related phenomena [5], sonoluminescence studies [6] to collapses in various geometries [7]. The versatility of the laser-induced cavitation is somewhat limited by the laser focusing conditions and event repetitions possible. For example, a laser-induced bubble near a solid surface may cause material erosion under certain conditions [8].

Acoustic cavitation is induced by irradiating a liquid with a high-pressure ultrasound wave. Here, the use of a vibrating tip (the sonotrode) has become an established technique for liquid processing in chemistry and biology labs. At the tip bubble clusters form then collapse violently [9]. Acoustic cavitation is used for example for surface cleaning [10], emulsification [11], in sonochemistry [12], and for therapeutic treatment [13], [14]. It falls short when precise control is needed, as complex bubble–bubble interaction prevents control of the bubble cluster. The easily accessible control variables such as driving amplitude and the number of oscillation cycles are not sufficient to prepare similar bubble clusters for repeated runs. For example, the cluster formation on the sonotrode tip does not start immediately and does not stop at the end of the driving, as the sonotrode exhibits mechanical inertia and continues with damped oscillations once the driving signal is stopped [15].

Single bubbles in a periodic pressure field have been studied previously, with one of the motivations stemming mainly from the use of microbubbles as ultrasound contrast agents [16], [17] and drug delivery mediators [18], [19]. Earlier research in the field was motivated by the possible enhancement of energy focusing at the bubble collapse [20] connected with the emission of light, i.e. sonoluminescence [21], [22]. But not only the amplitude of driving but also pressure gradients affect the bubble dynamics resulting in jetting along the acoustic pressure gradients [23]. We can separate the existing work mostly in the fields of simulations [16], [22], [24], [25], [26], [27] or mostly experiments [19], [20], [21], [23], [28] with very few connecting experiments with simulations [29].

The pioneering works of generating a laser-induced bubble in an acoustic pressure field [20], [21] have established the effect of acoustic pressure influence on the time of collapse and bubble radius, both as a function of the acoustic phase. In this work, we build on these foundations, studying the single bubble dynamics with high spatial and temporal resolutions, and for the first time observe and quantify the transition from a single laser-induced bubble to an acoustically driven bubble cluster.

An acoustic field was generated using a small-diameter sonotrode tip (2 mm), which was operated at low amplitudes, below the threshold for acoustic cavitation [15]. A bubble was seeded optically in the thereby generated oscillatory pressure field with a pulsed laser beam focused around 0.35 mm below the tip where we expect the pressure anti-node. The laser focus was centered below the sonotrode, where pressure wave fronts are nearly planar due to the geometry of excitation. The laser energy was set just above the optical breakdown threshold, optimized for repeatable generation of relatively small cavitation bubbles. The bubble dynamics is imaged with two high-speed cameras, one operating at kHz frame rates that allows long observation times and one with MHz frame rates for short times using shadowgraphy. We start with an investigation of the effect of the acoustic pressure field on the bubble dynamics through switching on and off the sound field. Further, the transition from a single laser-induced bubble to an acoustic driven bubble cluster that is formed after a few collapses is investigated. The lifetime of the bubble cluster is approx. two orders of magnitude longer than that of a single bubble in absence of an acoustic field. This is the case in a semi-infinite geometry with an unconstrained liquid for centimeters below the sonotrode and within a narrow gap formed by the sonotrode tip and a glass plate. Finally, we report on sustaining the bubble cluster further through repetitive nucleation of laser-induced bubbles.

2 Methods

The experimental setup consisted of an ultrasonic emitter for acoustic cavitation, a custom-built picosecond laser source for laser-induced cavitation, and the imaging setup able to record the events simultaneously with two high-speed cameras, one supported by a custom build laser-based illumination system. Additionally, we used Gilmore-NASG-model single bubble modelling.

2.1 Acoustic cavitation methods

The ultrasonic emitter for acoustic cavitation was a sonotrode horn (Bandelin SONOPULS TS 102) connected to an electric amplifier. The 2 mm diameter sonotrode tip and the glass-plate sample were inserted into a glass-cuvette with a volume of 25 ml, while being separated by h=0.7-1.0mm. The schematic of the experiment is depicted in Fig. 1a. The sonotrode is driven with an amplified sinusoidal electric signal, matched to its resonance frequency, which is 20.05 ± 0.05 kHz. The drift in frequency is mainly due to temperature changes of the environment, i.e. water and air. A suitable voltage for driving the sonotrode was experimentally obtained to be around 20 % below the threshold voltage needed to generate continuous acoustic cavitation. This results in a vertical sonotrode tip amplitude of about 17 ± 2 µm as measured with the high-speed cameras. This tip oscillation amplitude is used to obtain the acoustic pressure through simulations. A direct measurement of the pressure below the sonotrode is hampered by the large size of a suitable hydrophone. The simulations implement the geometry using the finite element solver COMSOL Multiphysics together with the acoustics toolbox. There the measured sonotrode tip motion was set as a boundary condition assuming an ideal sinusoidal behavior that has been confirmed with high-speed imaging. The simulation predicts a pressure amplitude of 140 ± 10 kPa at the position of the laser-induced bubble for 15 µm sonotrode oscillation amplitude, which is in line with being just below the acoustic cavitation threshold as established in the literature [30]. A hydrophone was added to the setup for monitoring of the acoustic cavitation bubble clusters strength at approx. 3.5 mm away from the laser-induced bubble position. We used a Müller-Platte needle probe hydrophone with 90° angled tip (response 0.8 mV/bar), allowing for relative comparison of acoustic bubble shock wave pressures in different conditions.Fig. 1 a) schematic representation of the experimental setup. b) sample image from Photron camera (kHz recording), showing the initial spherical laser-induced bubble. Dashed lines indicate the initial sonotrode position (upper line) and the glass surface (bottom line). c) The timing diagram of events: sonotrode driving starts ca. 2000 oscillation periods before the ps laser pulse, to allow the sonotrode to reach the full oscillation amplitude. Both kHz (Photron) and MHz (Shimadzu) frame rate cameras start shortly before the ps laser pulse, capturing the initial bubble evolution. The kHz recording continues to capture the bubble-cluster evolution.

2.2 Optical cavitation and imaging methods

Optical cavitation is initiated by the custom build picosecond fiber laser source (wavelength 1030 nm) [31], causing a laser-induced breakdown in water that results in a controlled cavitation event 0.35–0.70 mm below the sonotrode tip depending on geometry, using pulse energies of up to 100 μJ. This was accomplished with a long working distance microscope objective (NA = 0.45). The resulting laser-induced bubble has a maximum radius of 67 ± 3 µm, and a corresponding first oscillation period of around 10 µs without operating the sonotrode in the free field geometry. The picture of the bubble at maximum expansion reached in the acoustic field (approx. 170 µm) is shown in Fig. 1b where the upper boundary (white line) is the sonotrode tip, the center of mass of the laser-induced bubble 0.70 mm below the tip, and additional a glass plate (bottom white line) mounted below the sonotrode tip and the bubble.

The first, i.e. “standard”, high-speed camera ensure a visualization of the relatively long-lived bubble clusters at 100–200 kHz frame rates and the relatively short-lived initial laser-induced cavitation bubble recorded at a frame rate of 5 MHz by a second, i.e. “ultra-high-speed”, camera. The standard high-speed camera images through macro-objectives, either 105 mm f/2.8 with macro rings at 2.0x magnification or 65 mm f/2.8 at 2.6x magnification. The ultra-high-speed camera images through a 5x magnification microscope objective and has a resolution of 400 × 250 pixels. A custom-built short-pulse illumination system was used for synchronized illumination of the ultra-high speed camera frames. Each frame was illuminated with two light pulses of 0.3 ns duration each and separated by an interval of 18.75 ns [32]. The standard high-speed camera was illuminated with a continuous high-power white LED source.

The timing of the experiment is critical and sketched in the diagram in Fig. 1c. First, the sonotrode oscillations were started such they reach the desired amplitude and a stable acoustic pressure. Due to the high quality of resonance of the sonotrode around 2000 oscillations are needed for stable oscillation amplitude and were thus waited prior to the optical initiation of the cavitation bubble. The standard high-speed camera was started earlier to make sure that no acoustic cavitation was induced. The laser pulse was synchronized to the function generator driving the sonotrode, allowing for a selection of the phase between the acoustic field for the time of bubble generation. The second, ultra-high-speed camera captures the initial 64 µs of the bubble evolution in the case of typical frame rate of 2 MHz. The standard high-speed camera then records the longer dynamics, in particular the formation and evolution of the bubble cluster.

2.3 Single bubble experiment

The single bubble experiment was characterized using ultra-high-speed imaging, where Fig. 2a depicts representative frames from a single event taken at a 2 MHz frame rate. The double-pulse illumination scheme is visible in the first frame where a shock wave is imaged twice that is emitted from the laser breakdown site near the center of the image. Yet for the comparable slow bubble dynamics, this illumination does not cause motion blurring. Fig. 2b depicts the bubble radius evolution. The bubble radius presented on the graph was calculated as the equivalent volumetric radius – perpendicular long and short axis were defined for the bubble area and further treated as the main axis of an ellipsoid. Its volume was calculated and taken as equal to a spherical bubble with the presented radius. Fig. 2c shows graphs of the sonotrode tip position as a function of time with fitted sine-function for pressure reconstruction using COMSOL simulation results (pressure trace shown in orange).Fig. 2 a) ultra-high speed camera imaging of the single-bubble dynamics during the first two oscillations, recorded at a 2 MHz frame rate. The frames at 35.5 µs and 48.0 µs time stamps are the closest frames available to the first and second bubble collapses, respectively. The video is available in Supplementary, Video 1. b) Extracted volumetric-equivalent bubble radius for the video, and c) extracted sonotrode position with a sinusoidal function best fit and an acoustic pressure oscillation corresponding to the sonotrode positions.

In the sequence shown in Fig. 2a, the first bubble collapse happens close to the 35.5 µs timestamp and reveals liquid jetting away from the sonotrode tip surface. This direction of jetting is different as in the absence of an acoustic field, the bubble would be attracted to the sonotrode surface and thus would jet upwards [33]. In our case, the bubble is positioned around γ=3, where γ is the normalized stand-off distance defined as the ratio between the maximal bubble radius, Rmax , and the distance from bubble center to the surface, hb thus, γ=Rmax/hb. We explain this jetting away from the solid sonotrode surface with the acoustic pressure gradient being stronger than the pressure gradient caused by the solid boundary. The jetting observed also occurs at an angle from the sonotrode symmetry axis, due to the bubble position being approximately 150 µm away from the sonotrode symmetry axis along the laser-propagation axis.

2.4 Single bubble modelling

Bubble radius measurements are compared to modelling of a spherical cavitation bubble in an unbounded liquid driven by an oscillating acoustic pressure in the far field. This allows obtaining a better insight into bubble size evolution within the first acoustic pressure period, although it is limited as nearby surfaces and the pressure gradient on the bubble resulting to jetting is neglected. We chose the Gilmore model [34] for viscous compressible liquid for the simulation. The model describes bubble radius R through a second order ordinary differential equation:(1) RR¨1-RCL˙+32R˙21-R˙CL=H1-RCL˙+H˙RCL1-RCL˙

where CL is the speed of sound in liquid at the bubble wall, H is the enthalpy difference of the liquid at the bubble wall and the infinity. The implementation of the model is given in [35] with the Noble-Abel-stiffened-gas (NASG) equations of state (EOS). In the reference [35], the model is applied on the initially small (micrometer scale) bubble at rest, meaning the gas pressure inside the bubble pG is in a steady state defined by the initial bubble radius R0 surface tension with the coefficient σ and liquid pressure pL:(2) pG=pL+2σR0

For water the surface tension is σ=0.073N/m and the liquid pressure is set to static ambient pressure of pL=100kPa. The initial conditions used in the simulation were set for initial bubble wall velocity (v0=1150m/s), initial bubble radius (R0=3.00μm), equilibrium bubble radius (Req=6.00μm), sound pressure amplitude (pac=120kPa), and sound frequency (fac=20.0kHz).

3 Results and discussion

The results section is divided into two subsections, the first is dealing with the laser-induced bubble in a periodic acoustic field, and the second is dealing with the transition of the laser-induced cavitation bubble towards an acoustically driven bubble, and finally, an acoustically driven bubble cluster.

3.1 Laser-induced bubble driven with an ultrasound field

First, the seeding phase position of the optically induced bubble with respect to the acoustic driving was varied. This timing is further referred to as the generation phase, calculated as φ=360°Δtt0, where Δt is the timing difference and t0 is the acoustic period. Zero phase is set to the point when bubble generation coincides with minimum pressure (negative amplitude of pressure). The method reveals how the bubble generation phase affects the observed bubble dynamics. Therefore, we collect the experimental radius-time curves for different generation phases into a 2D-plot as shown in Fig. 3a, which is compared to Fig. 3b, where the dynamics is predicted with the Gilmore model. It is important to note that in the experiment, bubble splitting often occurred after only a few bubble oscillations, in some cases already at the first collapse. The experimental bubble radius curves in those cases are only shown to the point of bubble splitting. Considering the relatively slow pressure variation compared to the unperturbed laser-induced cavitation bubble oscillation (sound field period 50 µs vs. 10 µs bubble lifetime, respectively), the bubble dynamics and its time dependent radius evolution follow different paths from generation to the maximal bubble radius as a function of the generation phase. The simulations shown in Fig. 3b support the findings qualitatively. The spherical Gilmore bubble exhibits both the large variation of the maximum radii achieved as a function of the generation phase, and a pronounced region of prolonged bubble oscillations coupled with large radii similar with the experimental findings. The experimentally generated bubble is also not spherical (as shown by the jetting in Fig. 2), thus limiting the expected Gilmore model match after the first bubble collapse [37] to the experimental data.Fig. 3 Color-coded bubble radius as function of time (horizontally) for different phases of bubble generation (vertical axis), as a) measured in the experiments, and b) modelled using the Gilmore model. Qualitative agreement between the two graphs shows a pronounced effect of the generation phase during first bubble oscillation.

The observed dynamics reveals that the acoustic pressure is strongly affecting the bubble dynamics in terms of maximum bubble radius (from 1/2-smaller to 2-times larger depending on the generation phase) and the shape of the radius-time curve. An unperturbed cavitation bubble always reaches the maximum bubble radius during the first oscillation [37], while the periodic pressure field for certain generation phases may lead to larger radii after the first collapse. For bubbles generated between the minimum low pressure and the steepest increasing pressure (phases 0° to 90°), multiple short oscillations lead to consecutive collapses, in turn reducing the total bubble energy such that these bubbles reach a maximum radius that is smaller than reference bubble radius. On the other hand, for bubbles generated in the phase interval from 135° to 225°, i.e., in the last 1/8 of the period before the maximum positive pressures and up to 1/8 of that afterwards, the acoustic pressure prolongs the bubble oscillation well beyond the unperturbed maximum radius of around 60 µm. The effect decreases at higher phases, gradually converging to a behavior comparable to unperturbed dynamics within the first few bubble oscillations around phase 270°. A notable difference to the unperturbed case is observable in the second acoustic pressure cycle. The acoustic pressure oscillations are shorter than bubble dissolution times (milliseconds for radii above 0.5 µm [36]), expanding the micrometer sized residual bubble that is again subjected to expanding pressures.

The transition from a laser-induced bubble to an acoustically driven bubble was assessed using the time-dependent bubble radius data presented in Fig. 3a spanning the first sonotrode oscillation period. Within that time span, we analyzed the phase delay of the maximum bubble radius occurrence with respect to the peak-negative acoustic pressure and the maximum bubble radius reached, both plotted versus the bubble generation phase. The data is shown in graphs in Fig. 4a and b, respectively. The maximum bubble radius occurs within a 6 µs window or equally within about 40° of the entire acoustic phase cycle for all generation phases. The delay distribution shows no significant trends that could be recognized from the measurement noise across the whole phase range and would also satisfy the periodic boundary condition, i.e., data at the beginning of the period should approximately match the end of the period. According to this observation, we calculated the average of all measurements, finding that the maximum bubble radius occurs at −37 ± 14° or 5.2 ± 1.9 µs before the peak negative acoustic pressure position, i.e., within approx. 7 % of the acoustic pressure oscillation. On the other hand, the bubble generation phase has a pronounced effect on the maximum bubble radius reached from the beginning of bubble dynamics. The single bubbles generated during the steepest transition from low to high pressure, i.e., around phase 90°, reach maximal radius as small as 25 µm, while bubbles generated in phase with a high-pressure maximum, i.e. around phase 180°, reach a maximum radius of more than 120 µm as visualized in the graph in Fig. 4b. The graph offers an alternative visualization of the maximum bubble radius for all generation phases, clearly revealing a region of enlarged radii between the generation phases 135° and 225°. The opposite holds for bubbles generated in anti-phase to the specified phase interval.Fig. 4 a) the phase delay graph between the peak negative pressure timing and the maximum bubble timing. the latter precedes the peak negative pressure position by 37 ° or 5.2 µs and remains near-constant regardless of the bubble generation phase. b) The maximal bubble radius graph within the first period of the acoustic pressure oscillation, as a function of the bubble generation timing.

While bubbles can be generated anywhere within the generation phase space, and the maximum radius reached differs by up to a factor of 3 for varied generation phases, the delay between the pressure minimum and the maximum radius remains constant. This points to a conclusion that the bubble becomes acoustically driven within the first pressure period after its laser-based generation.

3.2 Transition to acoustic bubble cluster formation

Following the detailed measurements of early single bubble dynamics in the first 64 µs as presented in the previous section we continued to observe the formation of a bubble cluster. With acoustic driving and on a typical timescale of milliseconds, the single bubble splits and coalesces multiple times, thereby forming a collection of individual bubbles that we describe as a cluster of bubbles. Measuring bubbles within the cluster is challenging, we therefore characterize the overall cluster dynamics by measuring the number of dark pixels within the area of interest as a function of time. The area of interest always started just below the sonotrode tip and was either bounded by the bottom of the camera frame or by the position of the glass plate surface introduced below the initial bubble position. The glass plate was introduced for two reasons, as the controlled acoustic cavitation below the sonotrode tip would typically be used near surface in real applications and as a means of constraining the acoustic bubble cluster.

The bubble cluster was optically seeded with a single cavitation bubble generated at a generation phase of approximately 150°, i.e., one that expands beyond the maximal bubble radius of the unperturbed bubble in the first oscillation. Several acoustically driven bubble clusters have been seeded this way and their respective cross section development is plotted in Fig. 5a and b. Plots follow its growth and its disappearance in a) an unbounded geometry and b) within a gap consisting of the sonotrode tip surface and the glass plate. The measurements in Fig. 5a and b were averaged across one period of the acoustic pressure field to better reflect the total bubble cluster cross sectional area in the frame, not each successive growth and collapse cycle dynamics. While each cluster shows distinct complex behavior, commonly the peak bubble cluster area is reached 1–2 ms after the seeding, and it decays in the next few milliseconds. About 5 ms after the generation, the clusters disappeared, and cavitation bubbles are not observed anymore. The bubble cluster shape, size, and position evolution are illustrated with selected frames from a recording taken in an unbounded geometry and within a gap, see Fig. 5c and d, respectively.Fig. 5 The graphs show long-term bubble cluster development due to a single laser-induced bubble seeding in a) an unbounded liquid below the sonotrode and b) in a gap bounded by a glass plate at the bottom of the camera frame. The bubble cluster slowly wanes as the acoustic cavitation is not sustained, which can be seen in the chosen frames from the sequence in panels c) and d) for an unbounded liquid and within a gap, respectively. Full videos are available in Supplementary, Videos 2 and 3. The number in the upper right in c) and d) is the number of cycles of acoustic driving.

The behavior observed after the introduction of a gap also shows a similar trend, though on even shorter time scales. A large bubble cluster, as seen in the second frame of Fig. 5d, forms earlier compared in the unbounded geometry. A more scattered cluster of bubbles oscillating near the glass plate surface is found for up to 3 ms or 67 cycles, seen in the last three frames in Fig. 5d. Regardless of the geometry, the acoustic energy input into the bubble cluster is not high enough at the sonotrode amplitude settings used to counteract the energy losses to sustain the cluster oscillations. In the unbounded geometry, the bubble cluster is slowly pushed away from the sonotrode due to acoustic streaming [29] and directional jetting due to both acoustic streaming and an acoustic pressure gradient, thus moving to the lower pressure amplitude regions. In the gap, the energy is likely dissipated due to the bubble cluster being both pushed towards the surface by the same acoustic streaming and the secondary Bjerknes force, as well as by interacting with the surface during the collapses. Further research would be needed to understand dissipation mechanisms in more detail.

At last, a method for temporal control of the bubble cluster was developed. The bubble cluster life could be sustained by using repeated laser bubble generation within the gap, as the acoustic streaming was recognized as the main cluster dissipation factor in an unbound geometry due to the cluster being pushed to low pressure regions. Therefore, the ps-laser emits pulses at a fixed repetition rate of 20.3 kHz, resulting in approx. one laser pulse for each acoustic field period. Due to the unpredictable bubble cluster dynamics, not every laser pulse results in laser-induced cavitation, as blockage of the laser pulse by the bubble cluster often occurs, or the focal volume was already occupied by a gaseous cavity. Nevertheless, if the bubble cluster has moved away, similarly as observed from 20th cycle onwards in Fig. 5d, a new laser-induced bubble can be formed, adding a new seed for the bubble cluster and its reformation and development. The resulting optical bubble seeding frequency is 3–5 times lower than the laser pulse repetition rate. This approach resulted in a sustained bubble cluster below the sonotrode for as long as the picosecond laser pulses was activated. The graph in Fig. 6a shows the corresponding time-dependent evolution of the bubble cluster in a gap. This data is not time-averaged, showing periodic growth and collapse of the bubble cluster. The bubble cluster grows to a quasi-stationary size within the first few milliseconds after initiation and is then continuously sustained (chosen frames shown in Fig. 6b-e).Fig. 6 Quasi-periodic seeding of optical bubbles results in an indefinitely sustained bubble cluster. a) Analysis of three separate recordings. The bubble cluster shows complex acoustic behavior rather distinct to the dynamics of a single laser induced bubble. Sample images are shown for b) the first laser induced bubble, c) bubble shape after a few sonotrode cycles, and d), e) bubble cluster evolution at later times. The video is available in Supplementary, Video 4.

Thus, the acoustic bubble cluster can be seeded and controlled using laser-induced cavitation to start and sustain the process. Hydrophone measurements added a relative comparison of bubble cluster strength. At the hydrophone position, the acoustic pressure amplitude from the sonotrode was approx. 50 kPa, the collapse shock wave from a single acoustically driven bubble reached 200 kPa peak pressure (first collapse in Fig. 2 and similar events), and bubble cluster collapses emitted multiple shock waves reaching up to 400 kPa peak pressures. The initial picosecond laser-induced breakdown shock wave is below noise levels in these measurements.

The cavitation below the sonotrode tip was additionally analyzed in the frequency domain, to recognize and observe the main periodic behaviors of the bubble cluster. Data of the bubble cluster size changes during oscillations in an unbound liquid, in a gap, and in a gap including repetitive quasi periodic optical bubble seeding, were processed using a Fast Fourier Transform algorithm in Matlab. The obtained frequency spectra were averaged across all recorded repetitions (shown in Fig. 7, 30-40 events for unseeded cluster), with all graphs exhibiting one common feature − the main maximum of the spectrum is located at approx. 20.1 kHz position (data step 0.1–0.25 kHz), corresponding to the sonotrode driving frequency. Additional peaks are in all cases observed at higher harmonics of the driving frequency (40.1 kHz). The graph for bubble cluster dynamics in an unbound liquid shows some less pronounced peaks at frequencies lower than the driving frequency. These peaks correspond to bubble cluster dynamics exhibiting a larger expansion every n-th period of the acoustic pressure oscillation, with n being an integer between 2 and 5. Further research is needed to analyze the feature in detail to provide an explanation for it.Fig. 7 Frequency spectrum graphs obtained using FFT algorithm on bubble cluster oscillation data in an unbound liquid, in a gap, and in a gap including repetitive (quasi-periodic) optical bubble seeding. Each spectrum is averaged across all recorded repetitions.

The finding indicates that the details of the initial laser-induced cavitation bubble dynamics generated below the sonotrode does not play a critical role for the consecutive bubble cluster evolution. In fact, the periodic acoustic pressure field acts as the main bubble driver, regardless of the conditions applied.

4 Conclusion

We demonstrate the nucleation of repeatable acoustic cavitation clusters through seeding the acoustic field with laser-induced cavitation bubbles. This technique overcomes the unpredictable cavitation cloud activity common in ultrasound cavitation applications. The lifetime of the laser-induced cavitation bubble is shorter than the acoustic cycle which results in strong alteration of the bubble dynamics until the first collapse. The phase of bubble seeding determines if the bubble expands much larger or much smaller compared to bubbles in a stagnant liquid. The short lifetime and high repetition rates are achieved through a low-energy picosecond duration pulse. In most experiments, after the first collapse the bubble disintegrates into smaller bubbles. These bubble fragments are the nuclei for the built up of the cavitation cluster with a typical diameter of about 1 mm. Through the high reproducibility of the first bubble oscillation and fragmentation we can achieve a reproducible cavitation cluster. This is revealed by high-speed camera microscopy at kHz and MHz frame rates simultaneously. Two geometries are studied: the cluster dynamics in an unbounded liquid and the sonotrode oscillating at 0.7–1.0 mm away from a rigid boundary. We find comparable lifetimes of the cluster with about 30–50 cycles in both geometries.

To expand the lifetime of the cluster, we explored quasi-periodic seeding of optical bubbles. Here we could show infinite bubble cluster lifetimes with an optical bubble generated every 3–5 acoustic cycles, with further reduction possible to 10–20 cycles considering typical bubble cluster decay times.

In general, the control of acoustic cavitation is challenging. We report on a technique that connects acoustic cavitation with laser-induced cavitation showing that it is possible to improve the repeatability of acoustic cavitation. Applications of repeatable cavitation clusters may be the cleaning of sensitive surfaces where the operation range between applying a sufficient force to remove a contaminant from a substrate and the forceful destruction of the sample is very narrow.

CRediT authorship contribution statement

Jaka Mur: Writing – original draft, Methodology, Investigation, Formal analysis, Data curation. Fabian Reuter: Writing – review & editing, Methodology, Investigation, Funding acquisition, Conceptualization. Vid Agrež: Writing – review & editing, Methodology, Investigation, Formal analysis. Rok Petkovšek: Writing – review & editing, Validation, Supervision, Resources, Funding acquisition. Claus-Dieter Ohl: Writing – review & editing, Supervision, Resources, Funding acquisition, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A Supplementary data

The following are the Supplementary data to this article:Supplementary video 1

Supplementary video 2

Supplementary video 3

Supplementary video 4

Acknowledgements

We acknowledge support from the German Ministry for Education and Research (BMBF) in the framework of the “Programm des Projektbezogenen Personenaustauschs Slowenien 2023–2025” (Project ID 57656970), and Slovenian Research and Innovation Agency ARIS (Project IDs P2-0270 and L2-3171).

Appendix A Supplementary data to this article can be found online at https://doi.org/10.1016/j.ultsonch.2024.107023.
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