A mathematical and numerical framework for bubble meta-screens

TL;DR

This paper develops a mathematical and numerical framework to analyze and design bubble meta-screens, revealing their resonant behavior and explaining super-absorption phenomena in acoustic wave propagation.

Contribution

It provides analytical formulas for Minnaert resonance and demonstrates how bubble parameters influence acoustic meta-screen behavior.

Findings

Resonance occurs at a wavelength much larger than bubble size.

The structure acts as an effective Neumann boundary at resonance.

Numerical simulations validate the analytical formulas.

Abstract

The aim of this paper is to provide a mathematical and numerical framework for the analysis and design of bubble meta-screens. An acoustic meta-screen is a thin sheet with patterned subwavelength structures, which nevertheless has a macroscopic effect on the acoustic wave propagation. In this paper, periodic subwavelength bubbles mounted on a reflective surface (with Dirichlet boundary condition) is considered. It is shown that the structure behaves as an equivalent surface with Neumann boundary condition at the Minnaert resonant frequency which corresponds to a wavelength much greater than the size of the bubbles. Analytical formula for this resonance is derived. Numerical simulations confirm its accuracy and show how it depends on the ratio between the periodicity of the lattice, the size of the bubble, and the distance from the reflective surface. The results of this paper formally explain the super-absorption behavior observed in [V. Leroy et al., Phys. Rev. B, 2015].