Investigation on the primary resonance of a cylindrical bubble in compressible liquid

In the present paper, the paramount characteristics of the resonance of cylindrical bubbles in a compressible liquid are theoretically investigated with multi-scale analysis. Considering the liquid's compressibility, a dimensionless equation of the cylindrical bubble wall motion is established for the primary resonance under a single-frequency acoustic field. Comparing with the numerical results, the present analytical solution is verified in terms of accuracy. The key parameters on the characteristics of primary resonance are further explored including the equilibrium bubble radius, dimensionless amplitude of the acoustic field, and other detuning parameters. The main conclusions are given as follows: (1) During primary resonance, three typical nonlinear phenomena are observed: multivalued solutions, jumps, and hysteresis phenomena. (2) The liquid's compressibility affects the intensity of acoustic waves emitted by the bubbles during primary resonance. The maximum pressure at the bubble interface in the incompressible liquid is higher than that in the compressible liquid. (3) In the amplitude–frequency curve, the unstable region of the compressible liquid is smaller and the peak is lower than in the incompressible liquid.