Abstract
Thermoacoustic scattering is a principal scattering mechanism in the ultrasonic characterisation of water-continuous colloids. Thermal effects are particularly important in highly concentrated systems, where non-propagational thermal fields surrounding the disperse particles overlap. For low concentrations, the single sphere solution of Epstein and Carhart has become a popular tool for determining the particle size distribution. However, for small particle sizes it suffers from ill-conditioning that can make the solution numerically unstable. This problem has been resolved, by Harlen et. al. (2001, SIAM Journal on Applied Mathematics, 61 1906-1931), who obtained an asymptotic solution for low concentrations that is valid when the particle diameter is small compared to the wavelength. In this paper we will use this asymptotic method to calculate the effects of multiple scattering that occur at higher concentrations. We use the addition translation theorem to calculate the effects of multiple scattering between a pair of spheres of different sizes and show how this affects the close-field scattering pattern.
Highlights
Ultrasonic techniques are becoming increasingly popular tools for characterising soft solids and colloids
In thermoacoustic scattering the scattered field is written as the sum of an acoustic and a thermal wave so that the velocity potential is given by eikcz + φ + ψ in the continuous phase and φ + ψ in the suspended phase, where eikcz is the incident plane wave, φ and φ are the Attenuation per wavelength αλ Thermal Wave Number and particle radius product k a scattered acoustic fields in the two phases and ψ and ψ the thermal fields
We show thermal field for the case of a 200nm and a 1 μm particle
Summary
Ultrasonic techniques are becoming increasingly popular tools for characterising soft solids and colloids. The acoustic field describing the scattered sound, with wavenumber kc, while the thermal field represents the temperature fluctuations near the droplet boundaries and has a complex wavenumber kT This thermal wave decays rapidly with distance and the inverse of |kT | represents the distance heat can diffuse over the period of the radiation. Lloyd and Berry [4] developed a method of including multiple scattering based on an infinite number of energy shells This method is only applied to the acoustic field and so does not consider the changes to the scattering from the overlap of the thermal fields between neighbouring droplets. This is used this to correct the far-field scatting pattern from which the attenuation is calculated. Which for the case of the experimental in figure (1) is approximately 18%
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