Shape stability of an encapsulated microbubble undergoing translational motion

Abstract

Encapsulated microbubbles (EMBs) are associated with a variety of important diagnostic and therapeutic medical applications, including sonography, drug delivery, and sonoporation. The nonspherical oscillations, or shape modes, of EMBs strongly affect their stability and acoustic signature, and thus are an important factor in the design and utilization of EMBs. Under acoustic forcing, EMBs often translate with significant velocity, which can excite shape modes, yet few studies have addressed the effect of translation on the shape stability of EMBs. To investigate this phenomenon, an axisymmetric model is developed for the case of small shape oscillations. The exterior fluid is modeled as potential flow using an asymptotic analysis. Viscous effects within the thin boundary layer at the interface are included, owing to the no-slip boundary condition. In-plane stress and bending moment due to the encapsulation are incorporated into the model through the dynamic boundary condition at the interface. The evolution equations for radial oscillation, translation, and shape oscillation of an EMB are derived. These equations are solved numerically to analyze the shape mode stability of an EMB and a gas bubble subject to an acoustic, traveling plane wave. The findings demonstrate the counterintuitive result that translation more readily destabilizes an EMB than an uncoated gas bubble. The main factor responsible for mediating this translation-induced interfacial instability is the no-slip condition at the encapsulating membrane.