Bubbly Water as a Natural Metamaterial of Negative Bulk-Modulus

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.

Modeling ultrasonic metafluids: The significance of discrete oscillators

“…Metafluids are a special class of acoustic metamaterials, in which the inclusions are suspended in a host fluid. In existing practical realizations, the inclusions acting as micro-oscillators are typically symmetrically shaped or periodically arranged to achieve negative χ and ρ [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In such systems, monopolar resonances (breathing modes) affecting the compressibility of the system can be achieved relatively easily by the inclusion of bubble-like or vesicle-like objects [6][7][8][9][10][18][19][20][21].…”

“…In existing practical realizations, the inclusions acting as micro-oscillators are typically symmetrically shaped or periodically arranged to achieve negative χ and ρ [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In such systems, monopolar resonances (breathing modes) affecting the compressibility of the system can be achieved relatively easily by the inclusion of bubble-like or vesicle-like objects [6][7][8][9][10][18][19][20][21]. Such hollow (gas-filled) objects are highly compressible and, together with the effective mass load of the surrounding fluid, produce resonances at ultrasonic frequencies despite their small size.…”

Suspension of discrete microscopic oscillators as a model of an ultrasonic metafluid

“…In soft materials, various models have been investigated, mainly theoretically, from bubbles [19][20][21][22][23][24][25] and elastic spheres [26][27][28][29] suspended in liquids or soft solids, periodic fluid-solid [30,31] or hard sphere-soft matrix [32] composites. Scattering by monopolar resonances of single bubbles or pairs of bubbles has been rigorously treated in ref.…”

Sonic and Photonic Crystals

“…The gradient cavity, waveguide, switch, and spatial beam filtering with autocloned photonic crystals were studied and discussed [1][2][3][4][5][6]. The metamaterial of crystal structure can be found in [7][8][9][10], and the negative effects of those star-shaped structures were investigated and the applications in those studies were also discussed.…”