Transient wave propagation in bubbly liquids

A theoretical and numerical investigation of the propagation of one-dimensional waves in a bubbly liquid is presented. A variational formulation of the problem is used that yields both the linear-momentum equation and the equation that describes the oscillations of the bubbles. The compressibility of the liquid is taken into account in the formulation. The thermal dissipation is treated by solving the energy-balance equations simultaneously with the mechanical equations. Solutions are obtained by a finite-difference procedure and are compared to the experimental data of Kuznetsov et al. and Noordzij & van Wijngaarden. In some cases quite good agreement is obtained, but in others substantial errors are found. It is suggested that the observed discrepancies may be due to the breakup of the bubbles in the case of very large amplitude disturbances; the fact that the formulation does not include relative motion between the liquid and the bubbles; and possible non-planarity effects in the experiments.