Effect of clustered bubbly liquids on linear-wave propagation

Abstract

The spatial distribution of bubble liquids strongly affect linear-wave propagation in bubbly liquids. The classical understanding suggests that using positional correlations of the bubbles, such as “hole correction” or Perkus-Yevick approximation, describes the spatial information of bubble clouds. However, bubbly liquids are observed experimentally with complex bubble ensembles that take the form of clusters, filaments, and clouds which cannot be intuitively described by these pair-correlation functions and need to be better clarified. To achieve this purpose, a three-dimensional random model, the Neyman-Scott point process, is proposed to describe bubbly liquids with clustering. Base on this method, we study the influence of such phenomenon on acoustic dispersion and attenuation relations. A formula for effective wavenumber in bubbly liquids is derived, based on self-consistent method. Comparing with the equation of Commander and Prosperetti [J. Acoust. Soc. Am. 85, 732 (1989)], our results show that the clustering can suppress peaks in the attenuation and the phase velocity as functions of the frequency. Further, we provide a numerical simulated method. A clustered bubbly liquid is simulated with strict mathematical method and the statistical informations are obtained through unbiased statistical approach. Through the results, we quantificationally analyze the influence of estimated value on predictions.