Dynamics of Red Blood Cells and Fluid Vesicle in flows
Hiroshi Noguchi1 and Gerhard Gompper2
1Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
2Institut für Festkörperforschung, Forschungszentrum Jülich, 52425, Jülich, Germany
noguchi@issp.u-tokyo.ac.jp
Red blood cells and lipid vesicles exhibit rich behaviors in flows. We have studied their dynamics using a particle-based hydrodynamic simulation
method, multi-particle collision (MPC) dynamics. Several transitions of their shapes and dynamic modes are discovered. In simple shear flow, three
types of dynamic modes, tank-treading, tumbling, swinging, occur. They are coupled with shape deformation. In capillary flow, shape transition to parachute shape and alignments of cells are observed. These results show good agreement with experiments.

shear jump

Lipid vesicle in simple shear flow

discocyte(red-blood-cellshape)

0.2

0.5

1

prolate(rod-like)prolatelarge shear

00.5
stomatocyte

small shear020

tank-treading
prolatetumbling
buddedvesicle

θ/π
000

Stomatocyte to prolate

50t/τ100

Prolate to discocyte
Dashed lines: simple
theoretical model-0.5050t/ τ100

Budded vesicle to prolate(tumbling)(tank-treading)Dense system (L.J. McWhirter)

capillary flowmean distance between cells

Discocyte in random order

Isolated fluid vesicle
Parachute in single file alignment

slow flow.
γτ=0.92-0.5

40

time t /τ.
γτ=3.6800.50.5θ/πaspherecity αsp

0.4
α sp

α sp

1

fast flow

Slipper in zigzag alignment

Vesicle with shear elasticity

Discocyte

ParachuteSlipper

mean pressure gragient

fast flow

200c τ /Rvm
0 cap(a)shear-elasticvesicle
fluidvesicle
020040bending modulus

discocyte
to parachute(b)100

1000c τ /R
vm0 cap

slow flow/kBT

parachute
to discocyte
0500

1000

2R0 /kBT

shear modulus

Red blood cells
in glass capillarytsukada et al.
Microvasc. Res.61, 231 (2001).

Red blood cells
in microvessel
Skalak et al. Science 164, 717 (1969).

c∆Pves /Rcap/vmη0pressure drop per vesicle

Linear dependence of transition velocities vm.
2(a) fluid and shear-elastic vesicles at R0 /kBT=112.
(b) shear-elastic vesicles at /kBT=10.
discocyte

6parachute

4

shear-elasticvesicle2

fluid vesicle
00100

200

mean flow rate vmτ0/R cap

CONCLUSION
Simple shear flow [1-4]Fluid vesicles exhibit transitions of their shapes and dynamics modes.
Elongational transitions (from discocyte, stomatotye, or buded shape to prolate )and shrinking transition (prolate to discocyte) are found.

prolateCapillary flow [5-7]As flow velocity increases, shear-elastic vesicles transit from a nonaxisymmetric discocyte to an axisymmetric parachute shape, while fluid vesicles
transit from a discocyte to a prolate ellipsoid.
In dense suspensions, the hydrodynamic interacitions induce orderedalignmens: single-file parchute and two-file.
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[6] J. L. McWhirter, H. Noguchi, and G. Gompper, PNAS
[2] H. Noguchi and G. Gompper, Phys. Rev. E 72, 011901 (2005).
[3] H. Noguchi and G. Gompper, Phys. Rev. Lett. 98, 128103 (2007). 106, 6039 (2009).
[7] H. Noguchi, et al. EPL 89, 28002 (2010).
[4] H. Noguchi, J. Phys. Soc. Jpn. 78, 041007 (2009).