Determination of nonlinearity parameter B/A of liquids by comparison with solutions of the three-dimensional Westervelt equation

Abstract

Though nonlinear propagation depends upon the nonlinearity parameter B/A of the medium, it is often difficult to measure accurately. Thermodynamic methods often require high temperature and pressure excursions that can damage fragile molecules. Finite-amplitude methods often require unrealistic assumptions of ideal piston sources to account for diffraction effects. An alternative, described here, is to use the numerical solution of the three-dimensional Westervelt equation for weakly nonlinear fields (considering up to 10 s of harmonics of the fundamental frequency), and to match measured harmonic generation with that for simulated media. In particular, we follow Jafarzadeh et al. [Ultrasound Med. Biol. 47(3), 809–819 (2021)] to find that the nonlinearity parameter of a liquid can be recovered by determining the best match between measurements and simulations of media with different B/A values. Ideal piston sources with radial symmetry are not required, only a high-spatial-resolution hydrophone scan of the near-field source plane. Other techniques to determine the nonlinearity parameter by comparing propagation models with experiments, such as Richard et al. [New J. Phys. 22, 063021 (2020)], may improve on earlier measurement methods.