On what can or cannot influence the small amplitude oscillations of a gas bubble

The analysis presented in this paper concerns the impact of different physical quantities and conditions on the small amplitude oscillations of a single gas bubble immersed in a liquid, in the presence of an acoustic forcing pressure. Namely, effects related to the nature of the gas and its modeling, to the boundary conditions on the bubble wall, and to the size and shape of the bubble itself are studied and compared. The solutions are always determined analytically. The polytropic index and the damping coefficient are not assigned a priori but are determined from gas dynamics equations of Navier–Stokes–Fourier, and rational extended thermodynamics type. This preliminary approach facilitates the distinction between essential features and reasonable possible simplifications, also with a view to extending the model to nonlinear regimes. Furthermore, the results obtained could suggest how to prescribe the polytropic index more accurately when the gas dynamics in the bubble are reduced to a simple polytropic process.