Acoustic waves in a mixture of fluids with capillary effects

Acoustic waves with long wave-lengths are studied in a mixture of compressible fluids when capillarity and viscosity are taken into account. Volume fractions are finite so that the interactions between the fluids are strong. The macroscopic description is obtained from the local description by using the homogenization process for periodic structures. As expected, the equivalent macroscopic medium behaves like a two-phase one, exhibiting a coupling between the two phases as well as added masses and dispersion. Two dilatational waves are displayed. The second one is shown to be mostly unstable.