Impact of a bubble–bubble interaction on nonlinear acoustic properties of pressure waves in a non-dilute bubbly liquid

Abstract

Bubble–bubble interactions have become important owing to their development for various applications using pressure waves and dense microbubbles. Although the acoustic properties of the nonlinear propagation of pressure waves in bubbly liquids are important to develop these applications, a physico-mathematical model incorporating the effects of bubble–bubble interaction has not yet been proposed in the framework of nonlinear acoustics for bubbly liquid. In this study, we theoretically investigate pressure wave propagation in a bubbly liquid, focusing on the effect of bubble–bubble interaction on the pressure wave behavior. Specifically, we aim to quantitatively assess the corresponding nonlinear, dissipation, and dispersion effects. By using a singular perturbation method for a set of averaged equations for bubbly liquids, we obtain a Korteweg–de Vries–Burgers equation as the second-order single nonlinear wave equation and discuss the magnitude of the effect of the bubble–bubble interaction. A comparison of the results with and without bubble–bubble interaction shows that the interaction increases the advection, nonlinear, dissipation, and dispersion effects of the pressure waves. Because these effects are greater at higher void fractions (i.e., denser bubbles), the present findings will be useful for both the physics and applications of non-dilute bubbly liquids.