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Sub-wavelength focusing of acoustic waves in bubbly media

by H. Ammari and B. Fitzpatrick and D. Gontier and H. Lee and H. Zhang

(Report number 2017-28)

Abstract
The purpose of this paper is to investigate acoustic wave scattering by a large number of bubbles in a liquid at frequencies near the Minnaert resonance frequency. This bubbly media has been exploited in practice to obtain super-focusing of acoustic waves. Using layer potential techniques we derive the scattering function for a single spherical bubble excited by an incident wave in the low frequency regime. We then derive the point scatter approximation for multiple scattering by \(N\) bubbles. We describe several numerical experiments based on the point scatterer approximation that demonstrate the possibility of achieving super-focusing using bubbly media.

Keywords: Minnaert resonance, system of bubbles, sub-wavelength focusing.

@Techreport{AFGLZ17_724,
  author = {H. Ammari and B. Fitzpatrick and D. Gontier and H. Lee and H. Zhang},
  title = {Sub-wavelength focusing of acoustic waves in bubbly media},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2017-28},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2017/2017-28.pdf },
  year = {2017}
}

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