Study on the dynamics of a single cavitation bubble in a compressible spherical liquid confined by an elastic solid.

Cavitation bubbles within elastic solids are widespread phenomena in both natural environments and technological systems, yet their confinement-dependent dynamics remain not well understood. To systematically study the bubble behavior in these phenomena, we develop a coupled model to study the dynamical behavior of a single cavitation bubble within a spherically constrained compressible liquid domain, incorporating the first-order compressibility correction, within a finite-thickness elastic solid. Linear analysis reveals a fundamental inverse relationship between resonant frequency and inner radius of the elastic solid, which is agree with the experimental results obtained by Vincent when the outer radius of the elastic solid is greater than or equal to twice the inner radius. Linear analysis reveals that the bubble's resonant frequency exhibits a non-monotonic response to inner radius of elastic solid: it initially decreases and then increases as the ambient bubble radius decreases under a certain inner radius of elastic solid. Nonlinear simulations demonstrate that the first-order compressibility correction significantly suppresses the amplitude of bubble rebounces and enhances oscillation stability. Parametric studies reveal that the maximum bubble radius is influenced by the geometric and material properties of the elastic solid: it grows proportionally with the solid's inner radius, exhibits an inverse relationship with its outer radius, and increases as the bulk and shear moduli of the solid decrease. These findings analyze how geometric and material confinement parameters affect the dynamical behaviors of cavitation bubbles confined within elastic solids, thereby providing a theoretical foundation for enhancing ultrasound cavitation applications in confined environments, such as guiding the design of ultrasound contrast agent bubbles.