Acoustics of bubbles trapped in microgrooves: From isolated subwavelength resonators to superhydrophobic metasurfaces

Abstract

We study the acoustic response of flat-menisci bubbles trapped in the grooves of a microstructured hydrophobic substrate immersed in water. In the first part of the paper we consider a single bubble subjected to a normally incident plane wave. We use the method of matched asymptotic expansions, based on the smallness of the gas-to-liquid density ratio, to describe the near-field of the groove, where the compressibility of the liquid can be neglected, and an acoustic region, on the scale of the wavelength, which is much larger than the groove opening in the resonance regime of interest. We find that bubbles trapped in grooves support multiple subwavelength resonances, which are damped -radiatively -even in the absence of dissipation. Beyond the fundamental resonance, at which the pinned meniscus is approximately parabolic, we find a sequence of higher-order anti-resonance and resonance pairs; at the anti-resonances (whose frequencies are independent of the gas properties and groove size) the gas is idle and the scattering vanishes, while

Scattering of acoustic waves by a nonlinear resonant bubbly screen

“…Some extensions of the present work are easy, some others are more tricky. We have neglected the effects of surface tension and viscosity; as in Schnitzer et al (2019), this is partially justified by the large, dominant, radiative damping of the array. However, there are no particular difficulties in including them, as has been done in Caflisch et al (1985a,b), and there is little doubt that this will affect the Rayleigh-Plesset equation only.…”

“…The case of arrays of cylindrical bubbles involved in anechoic tiles, see e.g. Hladky-Hennion & Decarpigny (1991) and Sharma et al (2017), with a long or infinite length in one direction is slightly more involved but of interest; it requires us to use a different scaling adapted to the two-dimensional problem, as done in Schnitzer et al (2019). For this application, accounting in addition for a viscoelastic matrix rather than for a liquid may be quite involved depending on the considered viscoelastic model.…”

“…We have neglected the effects of surface tension and viscosity; as in Schnitzer et al. (2019), this is partially justified by the large, dominant, radiative damping of the array. However, there are no particular difficulties in including them, as has been done in Caflisch et al.…”

“…Leroy et al (2009) realized controlled experiments to study the transmission of ultrasound by a single layer of bubbles in water; Bretagne, Tourin & Leroy (2011) realized a bubble raft close to an interface with air or sandwiched in air and analysed the effects of such interfaces; Leroy et al (2015) demonstrate the ability of the metascreens to produce superabsorption and Lanoy et al (2018) obtain perfect absorption by critical coupling. Eventually an original metasurface has been recently proposed by Schnitzer, Brandão & Yariv (2019) with cylindrical bubbles trapped in the grooves of a microstuctured hydrophobic wall which is shown to be capable of supporting guided waves analogues to spoof plasmon waves.…”

“…(2018) obtain perfect absorption by critical coupling. Eventually an original metasurface has been recently proposed by Schnitzer, Brandão & Yariv (2019) with cylindrical bubbles trapped in the grooves of a microstuctured hydrophobic wall which is shown to be capable of supporting guided waves analogues to spoof plasmon waves.

Figure 1.The actual problem: a bubbly screen in the plane with spacing in both directions.

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