Ultrasound-induced nonlinear oscillations of a spherical bubble in a gelatin gel

We experimentally observe and theoretically analyse oscillations of a spherical bubble in a gelatin gel under ultrasound irradiation to quantify viscoelastic effects on the nonlinear bubble dynamics. A bubble nucleus is generated by focusing a laser pulse into a 6 wt% gelatin gel supersaturated with dissolved air, which enables us to control the bubble radius at mechanical equilibrium via influx of the gas air into the bubble. Linearized and finite-amplitude oscillations of the bubble are driven by 28 kHz ultrasound and recorded by a high-speed camera; the resonance curves of the oscillation amplitude as a function of the equilibrium radius are constructed for different ultrasound intensities. First, the viscosity and shear modulus of the gel are obtained by fitting the resonance curve (for the lowest ultrasound intensity) to the linearized solution of the Rayleigh-Plesset model that accounts for the gel's nonlinear elasticity of neo-Hookean type and diffusive effects on the bubble dynamics. Next, finite-amplitude oscillations of the bubble are compared with the nonlinear Rayleigh-Plesset calculations. The comparison suggests a need to include the gel's elasticity in the calculations to more accurately reproduce the nonlinear bubble dynamics. Another important finding is that the so-called spring softening feature appears in the experimentally determined resonance curve as the oscillation amplitude increases, which can be predicted by the Rayleigh-Plesset model. Furthermore, our experiment with the highest ultrasound intensity shows non-spherical oscillation of mode 1 that does not appear in the case of water but can be predicted by shape instability theory.