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A Low Frequency Potential Scattering Description of Acoustic Propagation in Dispersions

O. G. Harlen, M. J. Holmes, M. J. W. Povey, Y. Qiu and B. D. Sleeman
SIAM Journal on Applied Mathematics
Vol. 61, No. 6 (Apr. - May, 2001), pp. 1906-1931
Stable URL: http://www.jstor.org/stable/3061878
Page Count: 26
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A Low Frequency Potential Scattering Description of Acoustic Propagation in Dispersions
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Abstract

Ultrasound spectroscopy is a new technique for studying particle size that has great potential due to its ability to size concentrated dispersions such as food emulsions. Successful particle sizing using spectroscopic techniques requires an accurate scattering theory. Single particle scattering theory, first developed by Rayleigh and refined by Epstein and Carhart, is an exact theory for an isolated particle suspended in a medium. The theory involves expansion of the scattered fields as a series of Hankel functions, which, when solved in the far field, give the scattering coefficients. However, the numerical solution for these coefficients is badly conditioned and as a result, it is not possible to guarantee under all circumstances accurate results for calculation of the scattering coefficients. It is also difficult to solve the scattering problem for shapes other than ellipsoids and to account for scattering by more than one particle. Herein is presented a low frequency, asymptotic approximation to single particle scattering theory that is accurate and is easily generalized to arbitrary shapes and to more than one particle. Kleinman [Arch. Rational Mech. Anal., 18 (1965), pp. 205-229] showed that it was possible to obtain an iterative solution to the Helmholtz equation outside a scatterer with Dirichlet boundary conditions and satisfying the radiation condition by solving a sequence of potential problems. In this paper we develop Kleinman's idea and apply it to the more complex problem of thermo-acoustic scattering. In this method, which we call "low frequency potential scattering theory"-LFPST for short, an asymptotic series solution is calculated by solving a sequence of coupled Poisson equations. We show that LFPST agrees with single particle scattering theory and experiment in the low frequency limit.

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