Lateral migration of a 3D elastic capsule in a Poiseuille flow

The lateral migration of a 3D elastic capsule undergoing large deformation in a 3D Poiseuille flow was explored at moderate Reynolds number (10$\le $Re$\le $100) as a function of the initial lateral position (y$_{0})$, Reynolds number (Re), aspect ratio ($\varepsilon )$, viscosity ratio ($\lambda )$, membrane stretching coefficient ($\varphi )$ and bending coefficient ($\gamma )$. Several numerical methods were used to simulate the problem: the immersed boundary method for fluid-structure interaction, the penalty method for volume conservation in the capsule and the front-tracking method for distinguishing the fluid in capsule from the fluid outside capsule. Three different types of capsule motions were observed: tank-treading (TT) motion, tumbling (TU) motion and swinging (SW) motion according to variations of $\varepsilon $ and Re. The initial behavior of the elastic capsule was influenced by the initial lateral position (y$_{0})$, but the equilibrium position and the dynamic motion of the capsule were not affected by such variations. The capsule had a strong tendency toward TU motion at higher values of Re, $\varphi $ and $\gamma $, whereas the capsule underwent TT or SW motion as the values of $\varepsilon $ and $\lambda $ increased.