Modeling and parametric investigation of thick encapsulated microbubble's nonspherical oscillations

Numerous studies have been carried out in the past few decades to investigate the radial oscillations of encapsulated microbubbles (MBs). Nonspherical oscillations also have gained attention, being unavoidable in actual applications of these bubbles. The present paper is intended to describe the nature of resonance trends of such spherical and nonspherical modes of a thick encapsulated MB filled with air and suspended in water. The shell material is assumed to be linear viscoelastic and quasi-incompressible. The considered isotropic and spherically isotropic material parametric range is limited to thick polymer shelled MBs. For the case of an isotropic material, shell viscosity has a major influence on the fundamental modes with meridional wave number n = 0, 4, especially for thicker bubbles, unlike for the case of the spherically isotropic material case considered, where the viscosity has very little influence. For most of the parametric range, n = 2, 3 modes are underdamped and their frequency is found to be lower than the n = 0, 4 modes, for both material cases. An interesting case is found for a spherically isotropic quasi-incompressible material case, where the first few nonspherical mode resonances are very close to radial mode resonance frequency.