A computational study of flow of deformable capsules through inflating microvessels

Flow of deformable particles through compliant microvessels is encountered in biological and synthetic applications. Examples include flow of deformable blood cells, vesicles and capsules through small blood vessels and flexible microfluidic passages. Here we present a computational approach for modeling the flow of deformable capsules through inflating microtubes. The capsules are viscous drops surrounded by thin hyperelastic membranes. The tube wall is also taken to be thin and modeled as a hyperelastic membrane. A finite-element method is used for membrane mechanics, and a finite-volume/spectral method is used for the fluid motion. A diffuse-interface immersed-boundary method is used for the capsule/flow coupling while a hybrid of the sharp-interface (ghost-node) and diffuse-interface immersed-boundary methods for vessel/flow coupling. We find that a capsule can go through different phases of shape transition as it travels through the inflating tube, from bullet to parachute to complex multilobe shapes, unlike in a tube of constant cross-section. We further find that an initially single-file train of capsules becomes unstable and transforms into random capsule distribution as the tube inflates. A quantitative comparison of capsule dynamics in inflating versus rigid-walled tubes is presented.