Modeling and Simulation of Parametric Nonlinear Focused Ultrasound in Three-Dimensional Bubbly Liquids with Axial Symmetry by a Finite-Element Model

Abstract

Tis 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 fnite-element method in an axisymmetric three-dimensional domain and the generalized-α method in the time domain. Te model solves a diferential system derived for the nonlinear interaction of acoustic waves and gas bubble oscillations. Te high nonlinearity and dispersion of the bubbly medium hugely afect the behavior of the fnite-amplitude waves. Tese characteristics are used here to generate frequency components of the signals that do not exist at the source through nonlinear mixing (parametric antenna). Te 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.