A simplified predictive model for the minimum resonance frequency of high-void-fraction bubble clouds

To efficiently predict the minimum resonance frequency of high-void-fraction bubble clouds and enable porosity inversion, this paper develops a simplified model based on multiple scattering theory and effective medium theory, incorporating a mean-field approximation. The model depends solely on porosity and the average bubble radius. Using data obtained from COMSOL simulations and fitted with a rational 2D function, an explicit predictive formula is derived. The results show that the model performs well for fitting scenarios within the porosity range of 0.25%–25% and bubble radii of 1–3 mm. Without requiring detailed bubble size distribution or individual bubble sizes, the model enables rapid estimation of the resonance frequency of bubble clouds, providing an efficient computational tool for acoustic bubble monitoring and porosity inversion.