Inertial migration of a 3D elastic capsule in a plane Poiseuille flow

The inertial migration of a three-dimensional (3D) elastic capsule in a plane Poiseuille flow has been simulated by using the penalty immersed boundary method. An improved front-tracking method was developed to take into account the difference between the viscosities of the interior and exterior fluids. The calculation domain was confined to the capsule boundary by employing the ray casting algorithm. The dynamic motions and the lateral equilibrium positions of the elastic capsules in moderate Reynolds number (Re) flows were examined as functions of the initial lateral position (y₀), Re, the aspect ratio (ε), the viscosity ratio (λ), the membrane stretching coefficient (ϕ), the bending coefficient (γ) and the initial roll angle (θ_x). Three dynamical motions were observed: tank-treading, swinging and tumbling. The initial behavior of the capsule is influenced by the initial lateral position (y₀), but the equilibrium position of the capsule is not affected by variation in y₀. The equilibrium position is determined by the balance between the wall effect and the shear gradient effect.