Numerical modelling for the simulation of nonlinear ultrasound in liquids with gas bubbles

Abstract

Abstract Several numerical models have been developed in different configurations to simulate the behaviour of finite-amplitude ultrasound when interacting with tiny gas bubbles in a liquid. Since this interaction is highly nonlinear, specific models must be developed to understand the propagation of the waves in this kind of dispersive media for which their nonlinear and attenuation coefficients, as well as the sound speed, are extremely dependent on the ratio of the driven frequency to the bubble resonance. The bubble volume variation is mathematically modelled in the time domain through a Rayleigh-Plesset equation with terms up to the second order, whereas the time-dependent acoustic field relies on the wave equation in one or several dimensions. Both differential equations are coupled and auxiliary conditions are imposed. The differential systems are solved by the developed numerical models. In this paper we study in a three-dimensional resonator with axial symmetry how new harmonics obtained by nonlinear distortion can be enhanced by taking the nonlinear resonance effect into account, and we show that the generation of new frequency components by nonlinear frequency mixing exists. We also analyse the stable cavitation phenomenon in a three-dimensional focused field with axial symmetry by considering a nonlinear dependence of bubble generation in the liquid and the existence of primary Bjerknes forces.