A hybrid immersed boundary-lattice Boltzmann method solver for modeling encapsulated microbubbles

Encapsulated microbubbles (EMBs) have biomedical applications that include ultrasound imaging and targeted drug delivery. EMBs are modeled as a gas core surrounded by a thin, viscoelastic coating immersed in a viscous liquid, therefore, numerical simulation of their dynamic response to acoustic forcing is a complicated multiphase flow problem that involves fluid-structure interaction. Upon insonation, an EMB can undergo both spherical (volumetric) and nonspherical (shape) oscillations. In this study, we use a multicomponent multiphase lattice Boltzmann method (LBM) to solve for the fluid dynamics of the interior and exterior fluid phases and couple this with the immersed boundary (IB) method to account for the fluid-structure interaction between the fluid phases and the encapsulation. This hybrid IB-LBM solver explicitly solves for the bubble surface shape via tracking Lagrangian markers placed on the interface, and can account for nonspherical deformations. The force exerted on the surrounding fluids by the EMB coating is incorporated into the IB-LBM solver using a viscoelastic constitutive model. Simulations of the EMB response to step and sinusoidal variations in far-field pressure using the IB-LBM solver are validated against the modified Rayleigh-Plesset equation and other results in the scientific literature. The accuracy of the IB-LBM model is analyzed with respect to the stencil choice for the kernel function used for velocity interpolation and force spreading, and also with respect to the choice of time integration scheme for advecting the EMB surface.