Abstract
In this study, an oscillator model of bubble-in-water is proposed to analyze the effective modulus of low-concentration bubbly water. We show that in a wide range of wave frequency the bubbly water acquires a negative effective modulus, while the effective density of the medium is still positive. These two properties imply the existence of a wide acoustic gap in which the propagation of acoustic waves in this medium is prohibited. The dispersion relation for the acoustic modes in this medium follows Lorentz type dispersion, which is of the same form as that of the phonon-polariton in an ionic crystal. Numerical results of the gap edge frequencies and the dispersion relation in the long-wavelength regime based on this effective theory are consistent with the sonic band results calculated with the plane-wave expansion method (PWEM). Our theory provides a simple mechanism for explaining the long-wavelength behavior of the bubbly water medium. Therefore, phenomena such as the high attenuation rate of sound or acoustic Anderson localization in bubbly water can be understood more intuitively. The effects of damping are also briefly discussed. This effective modulus theory may be generalized and applied to other bubble-in-soft-medium type sonic systems.
Highlights
Metamaterials are usually manmade structures designed to have some exotic properties that are rarely or never seen in natural materials
The metamaterial theory of bubbly water we developed in this paper is based on an oscillator model for a pulsating bubble in water
The purpose of this paper is to provide a simple theory to study the acoustic properties of bubbly water at low filling fraction and long wavelengths
Summary
Metamaterials are usually manmade structures designed to have some exotic properties that are rarely or never seen in natural materials. The structure of periodically arranged rubber-shelled metal spheres embedded in an epoxy background is an acoustic metamaterial with negative mass density for low frequency sound [2]. In both cases, the exotic wave properties are caused by the coupling of the propagating wave in the background medium to the local resonance mechanism in each cell. We will show in this paper that bubbly water can be treated as a natural metamaterial, and the resonance coupling of the pressure wave with the bubble pulsation results in a negative modulus of the medium, giving a low frequency gap.
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