Mathematical models for the acoustic response of a solids-loaded encapsulated bubble

Abstract

A method of active acoustic resonance interference spectroscopy is introduced for estimation of bubble properties. A modified form of Rayleigh-Plesset equation for forced oscillation of either a single free bubble or elastic shell encapsulated microbubble with attached solids loading is solved by the regular perturbation method for steady oscillatory solutions as a result of small amplitude acoustic excitation by a point sinusoidal oscillator. A model for the total pressure field at an acoustic receiver in an incompressible liquid is then solved by the regular perturbation method. Closed-form analytical solutions are found for pressure power at the acoustic receiver as a function of the excitation frequency and strength; the properties of the bubble, liquid, and encapsulating shell; and the geometry of the active monitoring system. The receiver pressure power exhibits a maximum due to bubble resonance and a minimum due to destructive interference between source and bubble response pressure fields at higher excitation frequencies. The inverse problem is solved to derive unique closed-form analytical estimators for bubble equilibrium size, attached solids mass loading, and encapsulating layer dilatational viscosity as a function of the frequencies of the fundamental resonance maximum, interference minimum, second harmonic maximum total average acoustic power, monitoring system, and phase properties.

Controlled nanoparticle release from stable magnetic microbubble oscillations

“…We note that theoretically the mass loading from our NP shell is negligible. 28 Previous work also found that NP shell does not modify the acoustic properties of MMBs. 29 However, the resonant frequencies of MMBs with larger radii (435 μm) stabilized at approximately 50 kHz.…”