The migration of a suspended vesicle in an unbounded Poiseuille flow is
investigated numerically in the low Reynolds number limit. We consider the
situation without viscosity contrast between the interior of the vesicle and
the exterior. Using the boundary integral method we solve the corresponding
hydrodynamic flow equations and track explicitly the vesicle dynamics in two
dimensions. We find that the interplay between the nonlinear character of the
Poiseuille flow and the vesicle deformation causes a cross-streamline migration
of vesicles towards the center of the Poiseuille flow. This is in a marked
contrast with a result [L.G. Leal, Ann. Rev. Fluid Mech. 12,
435(1980)]according to which the droplet moves away from the center (provided
there is no viscosity contrast between the internal and the external fluids).
The migration velocity is found to increase with the local capillary number
(defined by the time scale of the vesicle relaxation towards its equilibrium
shape times the local shear rate), but reaches a plateau above a certain value
of the capillary number. This plateau value increases with the curvature of the
parabolic flow profile. We present scaling laws for the migration velocity.Comment: 11 pages with 4 figure