A Monte Carlo-based modeling for ultrasonic propagation through multiphase mixtures containing solid particles and bubbles

Ultrasonic attenuation methods offer non-invasive and low-cost measurements on particle size and concentration in multiphase flows, wherein the forward model plays a critical role as it theoretically interprets the underlying physical behavior and yields the sensitivity matrix for connecting particle characteristics and ultrasonic spectrum contents. In this study, a novel Monte Carlo model (MCM) is developed, specifically tailored for the multiphase system with spherical bubbles and elastic solid particles. Within this framework, the discrete phonons are introduced to represent continuous ultrasonic waves, whose behaviors are probed statistically, with the support of the rigorous theorem on ultrasonic scattering and absorption. Thus, the acoustic attenuation coefficient is accessed numerically by counting the phonon arriving at the sensor rather than the solution of the wave equation. A bubble–liquid two-phase system is investigated first, providing numerical validation with the classical ECAH model and the BL model at the bubble volume concentration within 10%. By introducing a concept of mixing ratio, the MCM is then extended to a three-phase system, namely an aqueous suspension containing both bubbles and solid particles, numerically evaluating the significant influences of the mixing of bubbles on the ultrasonic attenuation. This study provides a concise numerical model to characterize the bubbles and particles simultaneously in multiphase systems.