Propagation of Nonlinear Acoustic Waves in the Suspension of Ultrasound Contrast Agents Part I: Equation for Counting Resonance Effects and Revealing Acoustic Localization

TL;DR

This paper derives a nonlinear equation to describe how acoustic waves propagate in bubbly liquids containing ultrasound contrast agents, focusing on resonance effects and acoustic localization phenomena.

Contribution

It introduces a new nonlinear PDE that captures resonance effects of microbubbles and explains acoustic localization in bubbly liquids.

Findings

Derivation of a nonlinear PDE for acoustic wave propagation near resonance.

The equation recovers classical results for finite amplitude waves.

Explicit interpretation of acoustic localization in bubbly liquids.

Abstract

The oscillations of ultrasound contrast agents are of particular importance to the understanding of the propagation of acoustic waves in the bubbly liquids (suspensions of ultrasound contrast agents). Acoustic waves propagating in bubbly liquids have been investigated extensively. Little has been dedicated to the resonance effects of the microbubbles on the propagating waves. Here a nonlinear partial differential equation for describing one-dimensional acoustic waves propagating near the resonance frequency of the microbubbles in bubbly liquids is obtained. The present equation recovers classical results for propagating acoustic waves with finite amplitudes in liquids and interprets the acoustic localization in bubbly liquids explicitly.