Size quantification of non-spherical bubbles by ultrasound

Abstract

Ultrasonic detection is an effective method to quantify bubbles in opaque liquid, and acoustic scattering model is the key in ultrasonic inversion technique. Classical scattering models are usually based on the spherical assumption and <em>ka</em> is much less than 1. However, these conditions are not always satisfied in practical applications. In this study, a quantitative strategy of ultrasonic inversion is proposed for non-spherical bubbles and <em>ka</em> deviation assumption. A series solution model for a spherical gas bubble is established without considering the <em>ka</em> constraint, and it was compared with the classical Medwin (<em>ka</em><<1) and Anderson (<em>ka</em>≈1) models. The difference in their scattering cross sections <em>σ<sub>bs</sub></em> is only at the higher order formants of scattering and so the fitted line can be used to solve the multi-valued problem between <em>σ<sub>bs</sub></em> and <em>ka</em>. For a non-spherical bubble, <em>σ<sub>bs</sub></em> is determined by the frequency domain backscattering signal and size is characterized by the equivalent radius<em> a</em><sup>*</sup>and the inversion is performed by fitted curve from series solution model. Ultrasonic quantitative results were examined by high-speed photography. Results show that bubble rises in a zigzag pattern and non-spherical bubbles, their scattering cross sections are measured by the frequency domain scattering signal obtained at a position of ultrasonic measurement and the equivalent radius is inverted by the series solution fitting curve. The deviation between the results and the actual results <em>r</em><sub>0</sub> is about 1mm(relative error less than 45%) when 9≤<em>kr</em><sub>0</sub>≤35. This method can be used for acoustic inversion of non-spherical bubbles in a certain range of measurement accuracy.