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Theoretical research on the motion of spherical bubbles with surface tension

考虑表面张力的球泡运动的理论解研究

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Abstract

The Rayleigh-Plesset equation is the fundamental model of bubble dynamics and is widely used in the study of cavitation mechanisms. Since cavitation bubble often occurs at the micro-scale, the effect of surface tension will have an important influence on the bubble motion. Based on the Sundman transformation and Weierstrass elliptic function theory, this paper studies the Rayleigh-Plesset equation considering surface tension, and establishes the parametric theoretical solutions of vapor bubble and gas bubble respectively. The results show that the vapor-bubble and gas-bubble dynamic equations can be solved theoretically. Further, based on the theoretical solutions, the effects of the surface tension on the motion of vapor bubbles and gas bubbles are studied in detail. For the two types of bubbles, the influence of the surface tension on the bubble motion will increase gradually as the scale of the bubble gets smaller. Especially when the bubble scale is reduced to 10 µm, the effect of the surface tension becomes too significant to be negligible.

摘要

Rayleigh-Plesset方程是气泡动力学的基本模型, 被广泛应用于空化机理的研究中. 由于空化气泡经常发生在微观尺度上, 表面张力的影响将对气泡的运动产生重要的影响. 基于Sundman变换和Weierstrass椭圆函数理论, 研究了考虑表面张力的Rayleigh-Plesset方程, 并分别建立了蒸汽气泡和气泡的参数理论解. 结果表明, 蒸汽泡和气体泡动力学方程可以从理论上得到求解. 在理论解的基础上,进一步研究了表面张力对蒸汽气泡和气泡运动的影响. 对于这两种气泡, 随着气泡尺度的减小, 表面张力对气泡运动的影响会逐渐增大. 特别是当气泡尺度减小到10 μm时, 表面张力的影响变得更加显著, 不可忽略.

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Acknowledgements

This work was supported by the State Key Program of the National Natural Science of China (Grant No. 91852204) and the National Natural Science Foundation of China (Grant No. 11772298).

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Authors and Affiliations

  1. State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Engineering Mechanics, Zhejiang University, Hangzhou, 310027, China

    Kaitao Guo  (郭凯涛), Di Zhao  (赵迪) & Lingxin Zhang  (张凌新)

  2. Xi’an Aerospace Propulsion Test Technology Institute, Xi’an, 710000, China

    Kaitao Guo  (郭凯涛)

Authors
  1. Kaitao Guo  (郭凯涛)
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  2. Di Zhao  (赵迪)
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  3. Lingxin Zhang  (张凌新)
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Correspondence to Lingxin Zhang  (张凌新).

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Author contributions

Lingxin Zhang designed the research. Kaitao Guo and Di Zhao wrote the first draft of the manuscript. Kaitao Guo performed the theoretical analysis and processed the data. Di Zhao helped organize the manuscript. Lingxin Zhang and Di Zhao revised and edited the final version.

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Guo, K., Zhao, D. & Zhang, L. Theoretical research on the motion of spherical bubbles with surface tension. Acta Mech. Sin. 39, 322341 (2023). https://doi.org/10.1007/s10409-022-22341-x

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