Numerical simulation of nonlinear ultrasonic standing waves in bubbly liquid

The purpose of this paper is to numerically predict the behavior of ultrasonic waves in a bubbly liquid inside a resonator by taking into account the nonlinearity and dissipation of the bubbles. The predictions are based on a one-dimensional nonlinear differential system written in acoustic pressure and bubble volume variation. Bubbles are the unique source for nonlinearity and dissipation. They are assumed to be spherical and all of the same size, and evenly dispersed in the liquid. Resonators of different lengths are considered. Nonlinear results obtained at high-amplitude excitations are compared to linear fields. Conclusion about acoustic pressure distributions, waveforms, and frequency content, as well as mean and rms pressures are given. It turns out that the dynamics of the air-bubbles present in water has some particular effects (nonlinearity, dispersion, dissipation) on the acoustic pressure field. This paper shows that the combination of these effects triggers a particular behavior of the nonlinear standing waves within the resonator.