Influence of shell compressibility on the ultrasonic properties of polydispersed suspensions of nanometric encapsulated droplets

Abstract

Liquid droplets of nanometric size encapsulated by a polymer shell are envisioned for targeted drug delivery in therapeutic applications. Unlike standard micrometric gas-filled contrast agents used for medical imaging, these particles present a thick shell and a weakly compressible core. Hence, their dynamical behavior may be out of the range of validity of the models available for the description of encapsulated bubbles. In the present paper, a model for the ultrasound dispersion and absorption in a suspension of nanodroplets is proposed, accounting for both dilatational and translational motions of the particle. The radial motion is modeled by a generalized Rayleigh-Plesset-like equation which takes into account the compressibility of the viscoelastic shell, as well as the one of the core. The effect of the polydispersity of particles in size and shell thickness is introduced in the coupled balance equations which govern the motion of the particles in the surrounding fluid. Both effects of shell compressibility and polydispersity are quantified through the dispersion and absorption curves obtained on a wide ultrasonic frequency range. Finally, some results for larger gas-filled particles are also provided, revealing the limit of the role of the shell compressibility.