S. Ilke Kaykanat

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.

This paper investigates the dynamics of an encapsulated bubble within a spherical liquid cell that is surrounded by an infinite elastic solid, aiming to enhance our understanding of bubble oscillations, which is crucial for targeted therapeutic release. The Carreau–Yasuda model is used for the surrounding liquid, and a nonlinear neo–Hookean hyperelastic model is used for the shell, replacing a simpler Newtonian liquid and linear shell models. This increased complexity is necessary to accurately capture bubble oscillations in a parameter range where both the non-Newtonian properties of liquid and the nonlinear behavior of the shell are critical. Resonance occurs when the acoustic field's driving frequency matches the natural frequency, thus, amplifying oscillations. The properties of the shell and elastic solid can dampen or amplify these oscillations, depending on their magnitudes and resonance frequency, making it essential to optimize these properties for balanced control and responsiveness in bubble oscillations. The parametric range for the bubble surface area and the wall liquid shear stress is determined for safe biomedical application. The maximum bubble surface area is 4000 μm2 and the maximum wall shear stress is 3000 Pa for the parameters given in this paper. The study also highlights that the damping effect of the power-law index varies with ultrasonic drive frequency, pressure amplitude, Carreau–Yasuda properties, and cavity size, which is not observed for Newtonian fluids.

The onset of non-spherical oscillations of a microbubble in an unbounded power–law liquid, important for biomedical ultrasound applications, is studied. Two sets of evolution equations are obtained from the equation of motion: a Rayleigh Plesset-type equation for the spherical oscillations and an equation for the non-spherical oscillations. The non-spherical oscillations are modeled using the perturbation method via the Legendre polynomials. Two kinds of instabilities, namely parametric and Rayleigh-Taylor instabilities, are investigated. A higher power–law index causes the damping of the oscillations for both spherical and non-spherical oscillations. The power–law index damping effect depends on the ultrasonic drive frequency. At natural frequency, the amplitude of the perturbations is high compared to the non-resonant cases. At a low consistency index, the damping effect of the power–law index decreases. Unlike Newtonian liquids, the viscosity of power–law liquids is affected by the frequency of the acoustic field, thereby affecting Rayleigh-Taylor instability.

Targeted drug delivery is proposed to reduce the toxic effects of conventional therapeutic methods. For that purpose, nanoparticles are loaded with drugs called nanocarriers and directed toward a specific site. However, biological barriers challenge the nanocarriers to convey the drug to the target site effectively. Different targeting strategies and nanoparticle designs are used to overcome these barriers. Ultrasound is a new, safe, and non-invasive drug targeting method, especially when combined with microbubbles. Microbubbles oscillate under the effect of the ultrasound, which increases the permeability of endothelium, hence, the drug uptake to the target site. Consequently, this new technique reduces the dose of the drug and avoids its side effects. This review aims to describe the biological barriers and the targeting types with the critical features of acoustically driven microbubbles focusing on biomedical applications. The theoretical part covers the historical developments in microbubble models for different conditions: microbubbles in an incompressible and compressible medium and bubbles encapsulated by a shell. The current state and the possible future directions are discussed.