Nonlinear propagation of ultrasounds in bubbly viscoelastic media: A study on the influence of the medium properties on the nonlinear parameter

Abstract

A mathematical model that describes nonlinear ultrasonic wave propagation in bubbly viscoelastic media is developed by coupling the acoustic wave equation with a modified Rayleigh–Plesset equation, formulated in terms of bubble volume variation and incorporating the linear Kelvin–Voigt viscoelastic model. This formulation enables direct analysis of the influence of viscoelastic properties under soft tissue conditions. The differential system is numerically solved to investigate the transition from linear to nonlinear regimes in representative viscoelastic fluids and media that vary in shear elasticity. Laws of harmonic amplitudes vs. excitation at the source are defined from their polynomial fits. They confirm this nonlinear trend and reveal the influence of elasticity. To quantify these effects, the nonlinear parameter $\beta$ is computed using a finite amplitude method. Our results show that increasing shear elasticity significantly attenuates nonlinear propagation and suppresses harmonic generation, with $\beta$ decreasing as the shear modulus increases. In contrast, viscosity exhibits only a minor influence within the range studied in this work. These findings demonstrate that $\beta$ is highly sensitive to the mechanical properties of the medium and can serve as an effective indicator to characterize the nonlinear acoustic response of bubbly viscoelastic media. The agreement with previous studies presents our new model as a valuable tool for the study of nonlinear ultrasound in bubbly soft tissues and materials.