# Numerical Simulations of the Nonlinear Interaction of a Bubble Cloud and a High Intensity Focused Ultrasound Field

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Schematic diagram of the problem. (

**b**) Pressure waveform situated at $\mathrm{z}=6.48\mathrm{cm}$ on the symmetry axis in front of the cloud before transmitting into the bubble cloud at low ($\mathrm{P}=25\mathrm{W}$) and high ($\mathrm{P}=300\mathrm{W}$) powers. (

**c**) Void fraction in the focal area showing the bubble cloud (${\mathrm{V}}_{\mathrm{f}}=0.45\%$).

**Figure 2.**First three harmonics of acoustic pressure in the focal area at $\mathrm{P}=300\text{}\mathrm{W}$. (

**a**) Without bubbles and (

**b**) with bubble cloud (${\mathrm{V}}_{\mathrm{f}}=0.45\%$).

**Figure 3.**Mechanical index in the focal area at $\mathrm{P}=300\text{}\mathrm{W}$. (

**a**) Without bubbles and (

**b**) with bubble cloud (${\mathrm{V}}_{\mathrm{f}}=0.45\%$).

**Figure 4.**Maximum mechanical index values. (

**a**) versus acoustical power ($\mathrm{P}=25\u2013300\text{}\mathrm{W}$), with (${\mathrm{V}}_{\mathrm{f}}=0.45\%$) and without bubble cloud. (

**b**) versus bubble density in the cloud (${\mathrm{V}}_{\mathrm{f}}=0.0018\u20130.45\%$), with $\mathrm{P}=300\text{}\mathrm{W}$.

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**MDPI and ACS Style**

Vanhille, C.; Hynynen, K. Numerical Simulations of the Nonlinear Interaction of a Bubble Cloud and a High Intensity Focused Ultrasound Field. *Acoustics* **2019**, *1*, 825-836.
https://doi.org/10.3390/acoustics1040049

**AMA Style**

Vanhille C, Hynynen K. Numerical Simulations of the Nonlinear Interaction of a Bubble Cloud and a High Intensity Focused Ultrasound Field. *Acoustics*. 2019; 1(4):825-836.
https://doi.org/10.3390/acoustics1040049

**Chicago/Turabian Style**

Vanhille, Christian, and Kullervo Hynynen. 2019. "Numerical Simulations of the Nonlinear Interaction of a Bubble Cloud and a High Intensity Focused Ultrasound Field" *Acoustics* 1, no. 4: 825-836.
https://doi.org/10.3390/acoustics1040049