Numerical evaluation of the boundary layer approximation for sound attenuation by solid particles in water

Mercer, Douglas G. (1989) Numerical evaluation of the boundary layer approximation for sound attenuation by solid particles in water. Masters thesis, Memorial University of Newfoundland.

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Abstract

Sound scattering and attenuation by small solid spheres in viscous fluids at ultrasonic frequencies is investigated theoretically. The approach is based upon that of Allegra and Hawley [1972], and Pierce [1981], and involves separating the sound field into different modes, which include strongly damped thermal compression and viscous shear wave modes, in addition to the usual weakly damped acoustic modes. A simplification of the computational problem is then sought by obtaining approximate expressions for the (six) boundary conditions at the fluid-scatterer interface, through the use of a suitable boundary layer approximation. We find that the radial stress at the boundary in the fluid may be approximated as the dynamic pressure, and that the thermal waves generated at the boundary are purely radial to an excellent approximation. This result for the thermal waves implies that in a partial wave expansion of the attenuation, thermal effects only appear in the isotropic term, and higher order, nonisotropic terms may be treated in the viscous thermally non-conducting limit with high accuracy. Numerical results are compared to Allegra and Hawley's measurements for aqueous suspensions of polystyrene spheres, and reasonable agreement is obtained in the appropriate limit.

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