Inertial migration of an elastic capsule in a Poiseuille flow

Abstract

The inertial migration of a two-dimensional elastic capsule in a Poiseuille flow was studied over the Reynolds number range 1 ≤ Re ≤ 100. The lateral migration velocity, slip velocity, and the deformation and inclination angle of the capsule were investigated by varying the lateral position, Reynolds number, capsule-to-channel size ratio (λ), membrane stretching coefficient (ϕ), and membrane bending coefficient (γ). During the initial transient motion, the lateral migration velocity increased with increasing Re and λ, but decreased with increases in ϕ, γ, and the lateral distance from the wall. On the other hand, the deformation of the capsule increased and the inclination angle became smaller as Re, ϕ, γ, and the distance from the wall decreased. The initial behavior of the capsule was influenced by variation in the initial lateral position (y(0)), but the equilibrium position of the capsule was not affected by such variation. The balance between the wall effect and the shear gradient effect determined the equilibrium position. As Re increased, the equilibrium position initially shifted closer to the wall and then moved toward the channel center. A peak in the equilibrium position was observed near Re = 30 for λ = 0.1, and the peak shifted to higher Re as λ increased. Depending on the lateral migration velocity, the equilibrium position moved toward the centerline for larger λ, but moved toward the wall for larger ϕ and γ.