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Title: A perturbation solution for long wavelength thermoacoustic propagation in dispersions
Authors: Harlen, O.G.
Holmes, M.J.
Pinfield, Valerie J.
Povey, Malcolm
Sleeman, B.D.
Keywords: Helmholtz equation
Ultrasound spectroscopy
Low frequency limit
Issue Date: 2010
Publisher: © Elsevier B.V.
Citation: HARLEN, O.G. ... et al., 2010. A perturbation solution for long wavelength thermoacoustic propagation in dispersions. Journal of Computational and Applied Mathematics, 234 (6), pp. 1996 - 2002.
Abstract: In thermoacoustic scattering the scattered field consists of a propagating acoustic wave together with a non-propagational “thermal” wave of much shorter wavelength. Although the scattered field may be obtained from a Rayleigh expansion, in cases where the particle radius is small compared with the acoustic wave length, these solutions are ill-conditioned. For this reason asymptotic or perturbation solutions are sought. In many situations the radius of the scatter is comparable to the length of the thermal wave. By exploiting the non-propagational character of the thermal field we obtain an asymptotic solution for long acoustic waves that is valid over a wide range of thermal wavelengths, on both sides of the thermal resonance condition. We show that this solution gives excellent agreement with both the full solution of the coupled Helmholtz equations and experimental measurements. This treatment provides a bridge between perturbation theory approximations in the long wavelength limit and high frequency solutions to the thermal field employing the geometric theory of diffraction.
Description: This article was published in the Journal of Computational and Applied Mathematics [© Elsevier B.V.] and the definitive version is available at: http://dx.doi.org/10.1016/j.cam.2009.08.101
Version: Accepted for publication
DOI: 10.1016/j.cam.2009.08.101
URI: https://dspace.lboro.ac.uk/2134/11131
Publisher Link: http://dx.doi.org/10.1016/j.cam.2009.08.101
ISSN: 0377-0427
Appears in Collections:Published Articles (Chemical Engineering)

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