Acoustic properties of a two-fluid compressible mixture with micro-inertia

We study the propagation of acoustic waves in a mixture of two compressible components with micro-inertia. A special symmetric form of linearized governing equations is found permitting us to establish the stability of plane harmonic waves in the full region of flow parameters. It is shown that in non-viscous limit the dispersion relation has two real branches. One branch is defined for all disturbance frequencies, and the other one is defined only for frequencies greater than the resonance frequency. We prove that the group velocity attains its minimal value which is less than the sound speeds of each component. It is also shown that the Wood sound speed appears in our model in the limit of low frequencies only if the dissipation is taken into account. In the dissipation-free limit the equilibrium sound speed is always greater than the Wood speed.