Lateral migration of a 2D vesicle in unbounded Poiseuille flow

TL;DR

This study numerically investigates how a 2D vesicle migrates across streamlines in unbounded Poiseuille flow, revealing a migration toward the flow center driven by flow deformation and vesicle shape changes.

Contribution

It demonstrates that vesicles migrate toward the flow center in Poiseuille flow, contrasting previous results for droplets, and provides scaling laws for migration velocity.

Findings

Vesicles migrate toward the flow center due to flow deformation.

Migration velocity increases with capillary number and plateaus at high values.

Plateau migration velocity depends on flow curvature.

Abstract

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.