Numerical modeling of an encapsulated microbubble using an immersed boundary-lattice Boltzmann method

Encapsulated microbubbles (EMBs) are 1-10 microns in diameter and are used for various biomedical applications, such as ultrasound imaging and intravenous drug delivery. EMBs have a thin encapsulating layer of lipid, protein or polymer to stabilize them against dissolution in the bloodstream. When an EMB is subjected to ultrasound, the high compressibility of its gas core leads to both spherical and nonspherical oscillations. Numerical modeling of an EMB is a challenging problem that requires accounting for fluid-structure interaction (FSI) between a thin viscoelastic solid layer, a viscous incompressible exterior liquid, and a compressible interior gas. In this work, a numerical method is presented for modeling nonspherical, axisymmetric EMBs that uses the lattice Boltzmann method (LBM) to solve the fluid dynamics of the liquid and gas phases and the immersed boundary (IB) method to account for the FSI between the encapsulation and surrounding fluids. The primary advantage of this hybrid IB-LBM is its front tracking feature, i.e., the shape of the bubble surface is directly determined without need for its reconstruction. Simulations of the IB-LBM of a spherical bubble subjected to acoustic forcing are validated against the Rayleigh-Plesset equation. In addition, the accuracy of the IB-LBM model is investigated with respect to the stencil choice for the kernel function used for velocity interpolation and force spreading and the choice of time integration scheme for advecting the bubble surface.