Numerical prediction of ultrasonic attenuation in concentrated emulsions and suspensions using Monte Carlo method

For the study of predicting ultrasonic attenuation of mixed particles and probing the effect of interaction between neighboring particles, the Monte Carlo method was investigated to establish a submicron particle size characterization model in concentrated particulate two-phase system and serve as a probability and statistics technique to evaluate the underlying ultrasonic events during the ultrasound propagation. The numerical simulation method was proposed to predict the ultrasonic attenuation characteristics in the two-phase system of silica suspensions and corn oil-in-water emulsions with different particle sizes, ultrasonic frequencies and concentrations. Furthermore, an extension of the well-established single-particle theory of Epstein-Carhart and Allegra-Hawley (ECAH) was carried out, by incorporated in the couple phase model from a hydrodynamic point of view and effective hypothesis both accounted for the ultrasonic wave overlapping effect for the close proximity of particles. The simulation result shows agreement with the results of the ECAH model, the Lloyd & Berry (LB) model and the Waterman model in the dilute limitation, corresponding to glass beads and silica particles respectively. Afterwards, such a method was then applied into mixed particle system, where the mixed iron particles and glass beads with various ratios were set as examples for the purpose of predicting ultrasonic attenuation for the mixed particle systems. After comparing with the experimental results, it is shown that as a function of frequency, the variation of the ultrasonic attenuation coefficient with different mixing ratio manifests a nonlinear tendency. Also noteworthy is that the physical properties of particles play a dramatic impact in influencing ultrasonic attenuation. At higher concentrations, it was validated both in two-phase system of silica suspensions and corn oil-in-water emulsions that the attenuation predicted by Monte Carlo method agreed well with the experimental results of literature, yielding a theoretically increasing but less than linear expected attenuation with particle concentration. Particularly, the critical concentration of deviation from the linear change was obtained and interpreted using the thermal and viscous overlapping theory. The proposed Monte Carlo method presents a novel approach in calculating the attenuation in high particle volume concentration of more than 40% and provides a numerical modeling of particle size measurement in the complex particle-particle interaction condition.