Natural oscillations of a gas bubble in a liquid-filled cavity located in a viscoelastic medium

Abstract

The present study is motivated by cavitation phenomena that occur in the stems of trees. The internal pressure in tree conduits can drop down to significant negative values. This drop gives rise to cavitation bubbles, which undergo high-frequency eigenmodes. The aim of the present study is to determine the parameters of the bubble natural oscillations. To this end, a theory is developed that describes the pulsation of a spherical bubble located at the center of a spherical cavity surrounded by an infinite solid medium. It is assumed that the medium inside the bubble is a gas-vapor mixture, the cavity is filled with a compressible viscous liquid, and the medium surrounding the cavity behaves as a viscoelastic solid. The theoretical solution takes into account the outgoing acoustic wave produced by the bubble pulsation, the incoming wave caused by reflection from the liquid-solid boundary, and the outgoing wave propagating in the solid. A dispersion equation for the calculation of complex wavenumbers of the bubble eigenmodes is derived. Approximate analytical solutions to the dispersion equation are found. Numerical simulations are performed to reveal the effect of different physical parameters on the resonance frequency and the attenuation coefficient of the bubble oscillations.