Bubblelike scatterer monolayers at solid–fluid interfaces: Effects on reflectivity

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Air-filled bubbles and bubblelike scatterers (balloons, very thin shells, and cavities in rubberlike layers) of radius a, in a liquid of sound velocity c, satisfy the compactness condition ka<1 at frequencies ω=kc in the neighborhood of their resonant ‘‘bubble’’ frequency ω0. One can therefore describe the scatter from a monolayer of such scatterers at an interface between two media using the generalized smoothed-boundary theory developed by this writer elsewhere [I. Tolstoy, J. Acoust. Soc. Am. 75, 1–22 (1984); 79, 666–672 (1986)] in which the scatterers are replaced by distributions of monopoles and dipoles. For bubblelike scatterers, and for ω≂ω0, the monopole contributions outweigh the dipole contributions by many orders of magnitude; there is then a layer of monopoles whose effective scattering cross sections near resonance are between 1012 (bubbles in water) and 106 (cavities in rubber) times that of a small hard sphere of the same radius. Such monolayers lead to major changes of reflectivity—which can be calculated rather simply, using plane distributions of scatterers, e.g., a square lattice of basis l on a hard wall, with or without taking into account monopole interaction through multiple scatter. In either case, the models predict the existence of kl values at which the wall/fluid interface becomes anechoic at or close to ω=ω0. Numerical examples are given for air-filled cavities in rubberlike materials next to a perfectly hard wall. In practice, anechoic conditions are approximated for a narrow band of frequencies ωA±Δω, ωA≂ω0, and Δω/ωA≂10−2 for soft rubber (FJ95) and ≂5×10−2 for harder rubbers [FJ65: using constants given by Gaunaurd et al., J. Acoust. Soc. Am. 65, 573–594 (1979)]. For given ωA, the effect is, in practice, less sensitive to spacing kl (departures of ±25% from the exact value are tolerable). Simple theoretical considerations suggest that similar anechoic conditions will be achieved for elastic plates with the same cavity distributions in an interfacial rubber layer. A constant ambient pressure is implicitly assumed throughout (horizontal interfaces and monolayers).