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. (c) 2005 Elsevier B.V. All rights reserved.