中国物理B ›› 2025, Vol. 34 ›› Issue (10): 104302-104302.doi: 10.1088/1674-1056/addce7

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Coupled oscillation model of spherical bubble cluster in liquid cavity wrapped by elastic shell

Xin-Yi Zuo(左馨怡), Rui Liu(刘睿), Zhao-Kang Lei(雷照康), Yu-Ting Wu(吴玉婷), Xiu-Ru Li(李秀如), and Cheng-Hui Wang(王成会)†   

  1. Institute of Shaanxi Key Laboratory of Ultrasonics, Shaanxi Normal University, Xi'an 710119, China
  • 收稿日期:2025-04-09 修回日期:2025-05-26 接受日期:2025-05-27 发布日期:2025-09-29
  • 通讯作者: Cheng-Hui Wang E-mail:wangld001@snnu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 12374441).

Coupled oscillation model of spherical bubble cluster in liquid cavity wrapped by elastic shell

Xin-Yi Zuo(左馨怡), Rui Liu(刘睿), Zhao-Kang Lei(雷照康), Yu-Ting Wu(吴玉婷), Xiu-Ru Li(李秀如), and Cheng-Hui Wang(王成会)†   

  1. Institute of Shaanxi Key Laboratory of Ultrasonics, Shaanxi Normal University, Xi'an 710119, China
  • Received:2025-04-09 Revised:2025-05-26 Accepted:2025-05-27 Published:2025-09-29
  • Contact: Cheng-Hui Wang E-mail:wangld001@snnu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 12374441).

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摘要： Bubbles within an elastic shell, which undergo ultrasound-driven oscillation to treat tumors and soft tissues, are frequently treated as viscoelastic media. Therefore, studying the dynamic behavior of bubbles wrapped in a viscoelastic medium while considering an elastic shell can provide theoretical support for ultrasound biotherapy. Bubbles are always in the form of clusters. Therefore, a model of spherical bubble clusters in a liquid cavity wrapped by an elastic shell was constructed, the coupled oscillation equations of bubbles were obtained by taking into account the dynamic effects of the elastic shell and the viscoelastic media outside the cavity, and the oscillation behaviors of the bubbles were analyzed. Acoustic waves at 1.5 MHz could cause bubbles with a radius of 1 μm to resonate. Increasing the number of bubbles increased the suppressing effect of bubble oscillation caused by bubble interaction. The bubble cluster oscillation caused the elastic shell to oscillate and be stressed, and the stress trend was the inverse of the bubble oscillation trend with maximal tensile and compressive stresses. Bubbles with an equilibrium radius of 2 μm exhibited the lowest inertial cavitation threshold, making inertial cavitation more likely under high-frequency acoustic excitation. The inertial cavitation threshold of bubbles was heavily influenced by the acoustic wave frequency, bubble number density, and bubble cluster radius. The nonspherical oscillation stability of bubbles was primarily affected by the driving acoustic pressure amplitude and frequency, bubble initial radius, bubble number density, and bubble cluster radius. The acoustic frequency and amplitude exhibited a synergistic effect, with a minimum unstable driving acoustic pressure threshold of approximately 0.13 MPa. The initial radius within the elastic shell affected the minimum unstable driving acoustic pressure threshold.

关键词: spherical bubble cluster, elastic shell, cavitation bubbles, coupled oscillations

Abstract: Bubbles within an elastic shell, which undergo ultrasound-driven oscillation to treat tumors and soft tissues, are frequently treated as viscoelastic media. Therefore, studying the dynamic behavior of bubbles wrapped in a viscoelastic medium while considering an elastic shell can provide theoretical support for ultrasound biotherapy. Bubbles are always in the form of clusters. Therefore, a model of spherical bubble clusters in a liquid cavity wrapped by an elastic shell was constructed, the coupled oscillation equations of bubbles were obtained by taking into account the dynamic effects of the elastic shell and the viscoelastic media outside the cavity, and the oscillation behaviors of the bubbles were analyzed. Acoustic waves at 1.5 MHz could cause bubbles with a radius of 1 μm to resonate. Increasing the number of bubbles increased the suppressing effect of bubble oscillation caused by bubble interaction. The bubble cluster oscillation caused the elastic shell to oscillate and be stressed, and the stress trend was the inverse of the bubble oscillation trend with maximal tensile and compressive stresses. Bubbles with an equilibrium radius of 2 μm exhibited the lowest inertial cavitation threshold, making inertial cavitation more likely under high-frequency acoustic excitation. The inertial cavitation threshold of bubbles was heavily influenced by the acoustic wave frequency, bubble number density, and bubble cluster radius. The nonspherical oscillation stability of bubbles was primarily affected by the driving acoustic pressure amplitude and frequency, bubble initial radius, bubble number density, and bubble cluster radius. The acoustic frequency and amplitude exhibited a synergistic effect, with a minimum unstable driving acoustic pressure threshold of approximately 0.13 MPa. The initial radius within the elastic shell affected the minimum unstable driving acoustic pressure threshold.

Key words: spherical bubble cluster, elastic shell, cavitation bubbles, coupled oscillations

中图分类号:  (Ultrasonics, quantum acoustics, and physical effects of sound)

  • 43.35.+d
43.25.+y (Nonlinear acoustics) 47.55.dp (Cavitation and boiling)