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Minnaert resonances and higher-order acoustic modes for bubbles in a viscous fluid with surface tension

by H. Ammari and X. Fu and W. Jing and H. Li

(Report number 2026-22)

Abstract
The aim of this paper is to account for viscosity, surface tension, and interactions between micro-bubbles in approximating their resonant behavior in the ultrasonic regime. Original asymptotic formulas for the resonance frequencies are derived in terms of the difference in the acoustic impedance at the interface between the gas and the fluid. Both low-frequency resonances (Minnaert resonances) and higher-frequency resonances, i.e., beyond the subwavelength regime, are considered. We also provide a resonant characterization for a system of several micro-bubbles.

Keywords: micro-bubble, Minnaert resonance, higher-order acoustic mode, viscosity, surface tension, hydrodynamic layer potential, asymptotic formula

@Techreport{AFJL26_1177,
  author = {H. Ammari and X. Fu and W. Jing and H. Li},
  title = {Minnaert resonances and higher-order acoustic modes for bubbles in a viscous fluid with surface tension},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2026-22},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2026/2026-22.pdf },
  year = {2026}
}

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