# Observation of the Formation of Multiple Shock Waves at the Collapse of Cavitation Bubbles for Improvement of Energy Convergence

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- Rebound bubbles arise when the bubble bounces off the enclosed gas [3].
- (2)
- (3)
- (4)

## 2. Experimental Setup

^{2}at 532 nm allow the shock waves to be visible on the high-speed video. The spatial resolution of the photo is 1.1 µm/pixel so that the shock wave thickness of 7.5 µm (7 pixels) can be clearly imaged. The videos presented in this paper are taken at 5 or 10 million frames per second, with a magnification of 300 times.

_{max}is the bubble maximum radius, t

_{coll}is the collapse time, P

_{∞}is the pressure in the liquid, and ρ is the liquid density. In Figure 2, the maximum radius of the bubble, the first rebound, and the second rebound are 2.0, 1.4, and 0.6 mm, respectively. The size of the bubble and its rebounds is large enough to cover the surface of the photodiode (1 × 1 mm

^{2}).

## 3. Results

#### 3.1. Type-A: Quasi-Spherical Bubbles

#### 3.2. Type-B: Elongated Bubbles

#### 3.3. Type-C: Toroidal Bubble

## 4. Discussion

_{max}> 1, where d is the distance between the bubble center and the wall, and R

_{max}the bubble maximum radius). In our experiment, the bubble is deformed in one direction because of the initial shape of the plasma generating the bubble. In the case of the bubble close to a solid surface, the presence of the surface deforms the bubble in the normal direction. Both deformations lead to the formation of a microjet and multiple shock waves. The formation of a water hammer shock wave followed by the compression shock wave has already been observed experimentally [4,5] and confirmed numerically [24,25] in the case of bubbles near a solid surface. The use of a microscope lens in our setup improves the spatial resolution. We can observe that the shock fronts are not as sharp as expected. Several fronts seem to follow each other (successive dark and clear lines over small distances on the photos) originating from the same location. This particular multi-front structure suggests that the shock waves are not released as one sharp single front, but that several pressure peaks form from one small area of the bubble. These multiple fronts could be due to waves or instabilities at the bubble interface, where—even within a local area on the bubble interface—several shocks might be formed. Multiple fronts are not observed with numerical studies due to implementation of a smooth interface, leading to a local single shock front. They may not be observed experimentally if the spatial resolution is insufficiently large. The formation of the two distinct shockwaves has also been reported in the case of a bubble near a free surface, with shadow graphic images of the shockwaves, and the corresponding front light images revealing the dynamics of the microjet within the bubble [26]. The multiple fronts are visible at the collapse of the toroidal part of the bubble.

## 5. Conclusions

- (A)
- Quasi-spherical bubbles, where two types of shock wave were observed. When the bubble shrunk to nearly a width of 200 µm and a height of 80 µm, a water hammer shock wave formed during the impact between the microjet and the diametrically opposed bubble interface, followed by a compression shock wave at the collapse of the remaining toroidal bubble.
- (B)
- Elongated bubbles, although assumed to be one single volume, displayed two independent collapses or several collapses. The two-independent cases show that the first shock wave was emitted at the top, then the second shock at the bottom of the bubble was emitted 200 ns later from the first shock.
- (C)
- Toroidal bubbles, where multiple shock waves are generated along the large torus, occur over a longer period of time of 500 ns than for cases (1) and (2).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Experimental setup: (

**a**) Side view: Pulsed laser, and high-speed camera and backlit illumination laser, (

**b**) Top view: laser-photodiode synchronization system, and high-speed camera and backlit illumination laser.

**Figure 2.**(Black solid line) Photodiode signal for the collapsing bubble, (red dotted line) trigger level for the beginning of high−speed video, (blue dash line) video start (t = 0), (green boxed) zoom in the t = 0 region. (

**1**) Intensity peak due to the flash of the laser generating the bubble, (

**2**) first bubble, (

**3**) rebound bubble, and (

**4**) second rebound bubble.

**Figure 3.**(

**a**) Graph of the estimated bubble radius as a function of time for the average, the average plus standard deviation, and the average minus standard deviation bubble. The interval of time when the collapse can occur is 94 µs. (

**b**) Zoom in and superposition of the collapse curves, as if the trigger was set at 20% of the average maximum radius. The interval of time when the collapse can occur is drastically reduced from 94 µs to 0.65 µs.

**Figure 4.**High−speed video imaging of the collapse of a quasi-spherical bubble. The series of photos are numbered 1 to 12 over time. The collapse is not perfectly spherical, which denotes the formation of a microjet. Several shock waves are visible at the collapse (photo 12, magnified photo 12), and drawn on the sketch of the main shock waves and the collapse bubble (sketched photo 12 (bottom-right)). The shocks are assumed to be a water hammer shock wave (1) and compression shocks waves (2) and (3) in the sketch. This collapse type is classified to the quasi-spherical bubbles. Camera settings are: 5 million frames/s, and 5 ns exposure time. The scale bar is 200 µm.

**Figure 5.**High-speed video imaging of a vertically elongated bubble. The series of photos are numbered 1 to 12 over time. A first shock wave is formed at the top of the bubble in photo 5, followed by a second shock wave at the bottom of the bubble in photo 7. This collapse type is classified to the elongated bubbles. Camera settings are: 5 million frames/s, and 5 ns exposure time. The scale bar is 200 µm.

**Figure 6.**High-speed video imaging of a toroidal bubble. The series of photos are numbered 1 to 12 over time. A first shock wave is visible at the bottom of the bubble in photo 1. Shock waves are then formed at the top of the bubble in photo 3. This collapse type is classified to the elongated bubbles. Camera settings are: 10 million frames/s, and 5 ns exposure time. The scale bar is 200 µm.

**Figure 7.**High-speed video imaging of the formation of multiple shock waves at the collapse of a large toroidal bubble. The series of photos are numbered 1 to 12 over time. This collapse type is classified to the toroidal bubble. Camera settings are: 10 million frames/s, and 5 ns exposure time. The scale bar is 200 µm.

**Figure 8.**High-speed video imaging of the formation of multiple shock waves at the collapse of a large toroidal bubble. The series of photos are numbered 1 to 12 over time. This collapse type is classified to the toroidal bubble. Camera settings are: 10 million frames/s, and 5 ns exposure time. The scale bar is 200 µm.

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**MDPI and ACS Style**

Tinguely, M.; Ohtani, K.; Farhat, M.; Sato, T.
Observation of the Formation of Multiple Shock Waves at the Collapse of Cavitation Bubbles for Improvement of Energy Convergence. *Energies* **2022**, *15*, 2305.
https://doi.org/10.3390/en15072305

**AMA Style**

Tinguely M, Ohtani K, Farhat M, Sato T.
Observation of the Formation of Multiple Shock Waves at the Collapse of Cavitation Bubbles for Improvement of Energy Convergence. *Energies*. 2022; 15(7):2305.
https://doi.org/10.3390/en15072305

**Chicago/Turabian Style**

Tinguely, Marc, Kiyonobu Ohtani, Mohamed Farhat, and Takehiko Sato.
2022. "Observation of the Formation of Multiple Shock Waves at the Collapse of Cavitation Bubbles for Improvement of Energy Convergence" *Energies* 15, no. 7: 2305.
https://doi.org/10.3390/en15072305