Control of acoustic cavitation yield by dual frequency sonication: A Lyapunov exponent analysis

The radius of a bubble, described by the Rayleigh-Plesset equation, demonstrates a completely nonlinear structure and exhibits chaotic behavior across a range of parameter values. In this paper, we first present the chaotic oscillations of a bubble subjected to varying system parameters, including frequency, amplitude, viscosity, and surface tension. Subsequently, we utilize the periodic perturbation method to regulate the bubble’s chaotic dynamics through numerical analysis and simulation. The appropriate values for the control parameters were determined based on previous laboratory results validated by bifurcation diagram. The proposed method has been evaluated using two simulation techniques, namely, bifurcation diagrams and numerical calculations of the Lyapunov exponent (LE). This study represents the first instance where the parameters of the acoustic cavitation controller are analytically calculated, and their effects have been confirmed. The findings indicate that the proposed method can significantly reduce and potentially eliminate system turbulence. The accuracy of the proposed method has been also investigated experimentally using two approaches: the area of aluminum foil destruction by ultrasound waves and the measurement of subharmonics which indicates the effectiveness of the proposed method.