Translational motion and radial oscillations of two encapsulated bubbles in a viscoelastic medium subjected to an acoustic field

This paper investigates the coupled radial oscillations and translational motions of two encapsulated gas bubbles embedded in a viscoelastic medium. Each bubble comprises a gas core and a finite-thickness viscoelastic shell. The bubble shells and surrounding medium are modeled separately as Kelvin–Voigt-type viscoelastic mediums combining neo-Hookean elasticity with viscous dissipation. Resonance occurs when the driving frequency of the acoustic field matches the bubbles' natural frequency, which causes higher bubble oscillations. The material properties of both the shell and the surrounding medium can increase these oscillations, depending on their relation to the resonance frequency. The shell properties of each bubble significantly affect the surface area of the other bubble, which can be critical to determining the drug payload capacity and diffusion rate. Key parameters, such as acoustic pressure amplitude, initial bubble separation, and resonance, increase the bubble surface area. At resonance, the distance between the bubble centers reaches a minimum, which may cause bubbles to collapse. The bubbles can repel or attract each other depending on shell properties and bubble sizes. The velocity field of the surrounding medium is derived by expanding the velocity potential to the third order in the inverse bubble separation distance. This paper also examines the differences between simplified and higher-order models, highlighting that these differences become particularly pronounced near resonance. Finally, dual-frequency excitation allows bubble expansion and separation to be tuned by redistributing the pressure amplitudes while keeping their sum of squares fixed.