On the propagation of harmonic acoustic waves in bubbly liquids

The propagation of harmonic acoustic waves in a half-space (i.e., x > 0) filled with a viscous, isothermal bubbly liquid is studied. The exact solution to this problem, which corresponds to the compressible Stokes' second problem for the van Wijngaarden-Eringen equation, is obtained and an in-depth analytical and numerical investigation is carried out. Specifically, high- and low-frequency asymptotic results are given for the attenuation coefficient, the wave number, as well as several other propagation parameters, and special/ limiting cases are noted. In addition, general features of the solution are illustrated via numerical computations. Most significantly, the analysis shows the following: (i) the attenuation coefficient and wave number are equal at the natural bubble frequency; (ii) the bubbly liquid exhibits anomalous dispersion; (iii) for high-frequencies, there exists a layer adjacent to x = 0 that oscillates virtually in phase with the boundary (driving) motion; (iv) for low-frequencies, there exists a layer adjacent to x = 0 that is essentially transparent to harmonic waves; (v) the penetration depth exhibits an absolute minimum. Published by Elsevier Ltd.