Shape transitions of fluid vesicles and red blood cells in capillary flows

doi:10.1073/pnas.0504243102

Shape transitions of fluid vesicles and red blood cells in capillary flows

Hiroshi Noguchi† and
Gerhard Gompper

Institut für Festkörperforschung, Forschungszentrum Jülich, 52425 Jülich, Germany

Edited by Tom C. Lubensky, University of Pennsylvania, Philadelphia, PA (received for review May 23, 2005)

Abstract

The dynamics of fluid vesicles and red blood cells (RBCs) in cylindrical capillary flow is studied by using a three-dimensional mesoscopic simulation approach. As flow velocity increases, a model RBC is found to transit from a nonaxisymmetric discocyteto an axisymmetric parachute shape (coaxial with the flow axis), while a fluid vesicle is found to transit from a discocyte to a prolate ellipsoid. Both shape transitions reduce the flow resistance. The critical velocities of the shape transitions are linearly dependent on the bending rigidity and on the shear modulus of the membrane. Slipper-like shapes of the RBC model are observed around the transition velocities. Our results are in good agreement with experiments on RBCs.

Footnotes

↵ † To whom correspondence should be addressed. E-mail: hi.noguchi{at}fz-juelich.de.
Author contributions: H.N. and G.G. designed research, performed research, and wrote the paper.
This paper was submitted directly (Track II) to the PNAS office.
↵ ‡ This value differs by a factor of 4 from the result of ref. 35 because we employ a harmonic potential with a minimum at vanishing distance.
↵ § The pressure difference between front and rear end of a vesicle generates a solvent-density gradient, because the multiparticle collision dynamics fluid obeys a ideal-gas equation of state. The density exhibits a maximum at the dimple of the parachute shape in our simulations and is ≈50% higher than the average density at v _mτ/R _cap=218. To check whether this method causes any artifacts, we have simulated parachute-shaped elastic and fluid vesicles with a twice as large solvent density, ρ = 20m _s/a ³, where the relative density increase is only 25%. The peak of v _z in the annulus between the vesicle and the wall (see Fig. 5) is slightly lower, and ΔP _ves is ≈10% lower than for ρ = 10 m _s/a ³. Thus, we overestimate ΔP _ves by ≈10... 20%. Because the vesicle shapes are not changed, the effect on the vesicle dynamics should be very weak, however.