On the propagation of transient acoustic waves in isothermal bubbly liquids

The dynamic propagation of acoustic waves in a half-space filled with a viscous, bubbly liquid is studied under van Wijngaarden's linear theory. The exact solution to this problem, which corresponds to the compressible Stokes' 1st problem for the van Wijngaarden–Eringen equation, is obtained and analyzed using integral transform methods. Specifically, the following results are obtained: (i) van Wijngaarden's theory is found to be ill-suited to describe air bubbles in water; (ii) At start-up, the behavior of the bubbly liquid is similar to that of a class of non-Newtonian fluids under shear; (iii) Bounds on the pressure field are established; (iv) For large time, the solution exhibits Taylor shock-like (i.e., nonlinear) behavior.