Lateral migration of a capsule in a parabolic flow

Red blood cells migrate to the center of the blood vessel in a process called axial migration, while other blood cells, such as white blood cells and platelets, are disproportionately found near the blood vessel wall. However, much is still unknown concerning the lateral migration of cells in the blood; the specific effect of hydrodynamic factors such as a wall or a shear gradient is still unclear. In this study, we investigate the lateral migration of a capsule using the boundary integral method, in order to compute exactly an infinite computational domain for an unbounded parabolic flow and a semi-infinite computational domain for a near-wall parabolic flow in the limit of Stokes flow. We show that the capsule lift velocity in an unbounded parabolic flow is linear with respect to the shear gradient, while the lift velocity in a near-wall parabolic flow is dependent on the distance to the wall. Then, using these relations, we give an estimation of the relative effect of the shear gradient as a function of channel width and distance between the capsule and the wall. This estimation can be used to determine cases in which the effect of the shear gradient or wall can be neglected; for example, the formation of the cell-free layer in blood vessels is determined to be unaffected by the magnitude of the shear gradient.