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Predicting the maximum radius of an acoustically driven, explosively growing bubble in a viscoelastic medium

Baudouin Fonkwa*

Minki Kim†

Eric Johnsen

  • *Contact author: baudfonk@umich.edu
  • †Present address: School of Mechanical Engineering, Kookmin University, Seoul 02707, Republic of Korea.
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Phys. Rev. Fluids 11, 110501 – Published 5 November, 2026

DOI: https://doi.org/10.1103/9vsr-436t

Abstract

Cavitation can be exploited to create local and precise destruction of biological tissues. In applications such as histotripsy, cavitation bubbles are created by focused megahertz and megapascal pressure waves, grow, and inertially collapse, thereby inducing stresses that mechanically homogenize tissue. As the size of the damaged region has been shown to scale with the maximum size of the bubbles, we seek to determine the dependence of the maximum size of a bubble on the initial conditions, namely properties of the ultrasound and the tissue. For this purpose, the energy budget analysis for an oscillating bubble is extended to include viscoelasticity while also accounting for compressibility. By relating the bubble energy at maximum size to the initial energy, an analytical expression for the maximum radius can be obtained. The maximum radius is shown to decrease with increasing shear modulus of the medium, and to increase with increasing amplitude and wavelength of the wave. The proposed analytical model accurately predicts the maximum radius as long as the growth is explosive, i.e., the bubble velocity reaches an asymptotic constant value. Conditions for explosive growth are derived in terms of the pressure waveform amplitude and frequency.

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Outline

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Phys. Rev. Fluids 11, 110501– Published 5 November, 2026
  • Received 6 June 2025
  • Accepted 13 October 2026
Article part of CHORUS
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