Spherical oscillations of encapsulated microbubbles: Effect of shell compressibility and anisotropy

We introduce a model that describes spherical oscillations of encapsulated microbubbles in an unbounded surrounding fluid. A Rayleigh–Plesset-like equation is derived by coupling the Navier–Stokes equation that describes fluid dynamics with the Navier equation that describes solid dynamics via the internal/external boundary conditions. While previous models were restricted to incompressible isotropic shells, the solid shell is modeled here as a compressible viscoelastic isotropic material and then generalized to an anisotropic material. The exact value of the resonance frequency is calculated analytically, and the damping constant is computed in the approximation of weak damping. A correction of the widely used Church model for incompressible shells is evidenced, and the effects of shell compressibility and anisotropy are discussed.