Acoustics of a Liquid with Droplets Covered by a Shell in the Presence of Phase Transitions
Д. А. Губайдуллин, K. A. Panin, Yu. V. Fedorov
Abstract
The modified Rayleigh–Lamb equation that takes into account radial oscillations of a liquid droplet covered by a viscoelastic shell and located in the viscoelastic medium is derived. At the center of the droplet there is a vapor bubble. The problem of heat- and mass transfer between the vapor, the liquid phase, the shell, and the carrying liquid is solved for small oscillations of inclusion. The energy equation is found. The dispersion relation is derived based on the obtained equations for radial oscillations of inclusion, the energy equation, and the well-known wave equation for a bubbly liquid. The dependences of the phase velocity and the attenuation coefficient on the perturbation frequency are constructed for a mixture of liquid with dodecafluoropentane C5F12 and octafluoropropane C3F8 droplets covered by a shell with vapor bubbles at the center. The effect of phase transitions, shell of inclusions, and elastic carrying phase on dynamics of acoustic waves is illustrated. In a particular case, the theory is compared with the well-known experimental data.