Lateral migration of a two-dimensional vesicle in unbounded Poiseuille flow. - Archive ouverte HAL Access content directly
Journal Articles Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Year : 2008

Lateral migration of a two-dimensional vesicle in unbounded Poiseuille flow.

Badr Kaoui
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G. H. Ristow
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Isabelle Cantat
Walter Zimmermann
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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 toward the center of the Poiseuille flow. This is in a marked contrast with a result [L. G. Leal, Annu. 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 toward 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.

Dates and versions

hal-00674499 , version 1 (27-02-2012)

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Badr Kaoui, G. H. Ristow, Isabelle Cantat, Chaouqi Misbah, Walter Zimmermann. Lateral migration of a two-dimensional vesicle in unbounded Poiseuille flow.. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2008, 77 (2 Pt 1), pp.021903. ⟨10.1103/PhysRevE.77.021903⟩. ⟨hal-00674499⟩
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