Acoustics of a viscoelastic medium with encapsulated bubbles

Abstract

In this paper, a modified Rayleigh-Lamb equation is derived that takes into account the radial vibrations of a gas bubble coated with a viscoelastic shell and located in an elastic medium. For small oscillations of inclusion, the problem of heat exchange between a gas, a liquid phase, a viscoelastic shell, and an elastic medium is solved. The energy integral is determined. In the case of small disturbances, the dispersion relation is found from the Rayleigh-Lamb equations, energy, and the known wave equation for the bubbly medium. An analytical expression of the equilibrium speed of sound is written out and its dependence on the size of the viscoelastic shell and the disturbance frequency is established. An example of a mixture of polydimethylsiloxane with air bubbles coated with a rubber shell illustrates the influence of the elasticity of the carrier medium and the shell of the bubbles on the dependence of the phase velocity and attenuation coefficient on the perturbation frequency. For a mixture of water with air bubbles coated with a rubber shell, the influence of the dependences of the shear modulus and viscosity of butyl rubber on the frequency of disturbances at different temperature on the dispersion curves is shown. A comparison of the theory with experimental data is given.