Propagation of acoustic waves in a visco-elastic two-phase system: influences of the liquid viscosity and the internal diffusion

The main purpose of the present paper is to present the mathematical expression for the frequency-dependent effective acoustic properties of a liquid–bubble mixture. Effects of the bubble resonance, the heat and mass transfer between the liquid and bubbles, and the viscoelasticity of the liquid are included in the expression. Several characteristic frequencies associated with these internal processes are represented by simple functions of the material and condition parameters. Using these expressions, the acoustic properties of bubbly magmas are calculated and analyzed. It is shown that the dispersion and attenuation of the pressure wave are particularly considerable in the frequency range lower than the characteristic frequency of the mass transfer and in the range near the characteristic frequency of the viscous response of the bubble radius. In the frequency range bounded by these two frequencies, the bubbly magma can be regarded as an elastic medium with the slow sound speed. The significance of such acoustic properties on resonance of a body of bubbly magma is demonstrated in a simple one-dimensional system.