Phase Transition in Acoustic Localization in a Soft Medium Permeated with Air Bubbles

Propagation of an acoustic wave in a soft medium permeated with air bubbles is theoretically investigated by using a self-consistent approach. The soft medium is assumed to be viscoelastic to estimate the effect of acoustic absorption on the acoustic localization in such a medium. The oscillation phases of bubbles are examined by employing a phase diagram method. A collective oscillation of the bubbles is observed once the acoustic localization occurs, which is known as a phenomenon of `phase transition', and such a phenomenon persists as we manually increase the viscosity factor of the soft medium. Therefore it is proven that the phenomenon of phase transition may serve as a unique criterion to effectively identify acoustic localization in a bubbly soft medium even in the presence of viscosity, and the directions of the phase vectors help to determine the extent of localization. This is of practical significance for experimental research studying the acoustic localization in such a medium, for which the presence of viscosity generally causes great ambiguity in distinguishing the effects of localization and acoustic absorption.