Search

This paper presents the development of a numerical model able to track in time the behavior of nonlinear focused ultrasound when interacting with tiny gas bubbles in a liquid. Our goal here is to analyze the frequency components of the waves by developing a model that can easily be adapted to the geometrical restrictions and complexities that come out in several application frameworks (sonochemistry, medicine, and engineering). We thus model the behavior of nonlinear focused ultrasound propagating in a liquid with gas bubbles by means of the finite-element method in an axisymmetric three-dimensional domain and the generalized-α method in the time domain. The model solves a differential system derived for the nonlinear interaction of acoustic waves and gas bubble oscillations. The high nonlinearity and dispersion of the bubbly medium hugely affect the behavior of the finite-amplitude waves. These characteristics are used here to generate frequency components of the signals that do not exist at the source through nonlinear mixing (parametric antenna). The ability of the model to work with complex geometries, which is the main advantage of the method, is illustrated through the simulation of nonlinear focused ultrasound in a medium excited from two spherical sources in opposite directions.

This paper studies the nonlinear resonance of a cavity filled with a nonlinear biphasic medium made of a liquid and gas bubbles at a frequency generated by nonlinear frequency mixing. The analysis is performed through numerical simulations by mixing two source signals of frequencies well below the bubble resonance. The finite-volume and finite-difference based model developed in the time domain simulates the nonlinear interaction of ultrasound and bubble dynamics via the resolution of a differential system formed by the wave and Rayleigh–Plesset equations. Some numerical results, consistent with the literature, validate our procedure. Other results reveal the existence of a frequency shift of the cavity resonance at the difference-frequency component, which rises with pressure amplitude and evidences the global changes undergone by the bubbly medium under finite amplitudes. Finally, this work shows the enhancement of the amplitude of the difference-frequency component generated by parametric excitation using the nonlinear resonance shift, which is more pronounced when the second primary frequency is constant, the first one is varied to match the nonlinear resonance, and both have the same amplitude.