Abstract:

The theoretical results for the resonant backscattering form factor f ((theta)=(pi),k) versus wave number k for scattering from a submerged elastic shell filled with a bubbly fluid are presented using MATHEMATICA 2.2. The elastic shell is a castable urethane known as Smooth-On 775 which has a density of (rho)=1.03 g/cm[sup 3] and longitudinal and shear speeds of c[inf d]~1450 m/s, c[inf s]~70 m/s, respectively. The bubbly fluid is taken to be air bubbles of uniform radius (50 (mu)m) and spacing, suspended in a host liquid of castor oil, instead of water, due to its greater viscosity. Resonant scattering is compared over a range of volume void fractions 0<(beta)<0.01 for the frequency range 0--20 kHz. Shell inner radius b and thickness t are varied. Results are compared with an ``ideal'' spherical cloud of bubbly water. Comparisons are virtually identical for shells where b=5.08 cm and t=0.635 cm. The scattering theory by Ayres et al. [Int. J. Solids Struct. 23, 937--946 (1987)] is used, along with the theoretical model by K. W. Commander and A. Prosperetti [J. Acoust. Soc. Am. 85, 732--746 (1989)] for the complex sound speed and density in a bubbly medium.