### Abstract

The effect of a tank-treading motion of the red cell membrane on a staggered "zipper"-type red cell flow in capillaries is examined, using a two-dimensional theoretical model. An approximately triangular cell with a thin flexible membrane enclosing a viscous fluid is adopted as a model of the red cell. The motion of model red cells arranged periodically along a two-dimensional channel in an idealized zipper-type arrangement is analyzed numerically by a finite element method applied to the Stokes equations for the flow both inside and outside the model cells. It is shown that, if the viscosity ratio of the internal fluid to the suspending fluid is lower than a critical value, there exists a stable zipper-type arrangement of cells. In that arrangement, the cells remain stationary relative to each other with the membrane tank-treading. In contrast, inhibiting tank-treading by increasing the viscosity ratio above the critical value induces a cyclic oscillatory motion of red cells. The critical viscosity ratio increases if the channel is narrowed or if the spacing between cells is reduced. The present results suggest that the membrane tank-treading tends to stabilize zipper-type arrangements of red cells in capillaries at high hematocrit.

Original language | English (US) |
---|---|

Pages (from-to) | 379-393 |

Number of pages | 15 |

Journal | Microvascular Research |

Volume | 40 |

Issue number | 3 |

DOIs | |

State | Published - 1990 |

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### ASJC Scopus subject areas

- Biochemistry
- Cardiology and Cardiovascular Medicine

### Cite this

*Microvascular Research*,

*40*(3), 379-393. https://doi.org/10.1016/0026-2862(90)90034-O

**Two-dimensional analysis of two-file flow of red cells along capillaries.** / Sugihara-Seki, M.; Secomb, Timothy W; Skalak, R.

Research output: Contribution to journal › Article

*Microvascular Research*, vol. 40, no. 3, pp. 379-393. https://doi.org/10.1016/0026-2862(90)90034-O

}

TY - JOUR

T1 - Two-dimensional analysis of two-file flow of red cells along capillaries

AU - Sugihara-Seki, M.

AU - Secomb, Timothy W

AU - Skalak, R.

PY - 1990

Y1 - 1990

N2 - The effect of a tank-treading motion of the red cell membrane on a staggered "zipper"-type red cell flow in capillaries is examined, using a two-dimensional theoretical model. An approximately triangular cell with a thin flexible membrane enclosing a viscous fluid is adopted as a model of the red cell. The motion of model red cells arranged periodically along a two-dimensional channel in an idealized zipper-type arrangement is analyzed numerically by a finite element method applied to the Stokes equations for the flow both inside and outside the model cells. It is shown that, if the viscosity ratio of the internal fluid to the suspending fluid is lower than a critical value, there exists a stable zipper-type arrangement of cells. In that arrangement, the cells remain stationary relative to each other with the membrane tank-treading. In contrast, inhibiting tank-treading by increasing the viscosity ratio above the critical value induces a cyclic oscillatory motion of red cells. The critical viscosity ratio increases if the channel is narrowed or if the spacing between cells is reduced. The present results suggest that the membrane tank-treading tends to stabilize zipper-type arrangements of red cells in capillaries at high hematocrit.

AB - The effect of a tank-treading motion of the red cell membrane on a staggered "zipper"-type red cell flow in capillaries is examined, using a two-dimensional theoretical model. An approximately triangular cell with a thin flexible membrane enclosing a viscous fluid is adopted as a model of the red cell. The motion of model red cells arranged periodically along a two-dimensional channel in an idealized zipper-type arrangement is analyzed numerically by a finite element method applied to the Stokes equations for the flow both inside and outside the model cells. It is shown that, if the viscosity ratio of the internal fluid to the suspending fluid is lower than a critical value, there exists a stable zipper-type arrangement of cells. In that arrangement, the cells remain stationary relative to each other with the membrane tank-treading. In contrast, inhibiting tank-treading by increasing the viscosity ratio above the critical value induces a cyclic oscillatory motion of red cells. The critical viscosity ratio increases if the channel is narrowed or if the spacing between cells is reduced. The present results suggest that the membrane tank-treading tends to stabilize zipper-type arrangements of red cells in capillaries at high hematocrit.

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UR - http://www.scopus.com/inward/citedby.url?scp=0025677215&partnerID=8YFLogxK

U2 - 10.1016/0026-2862(90)90034-O

DO - 10.1016/0026-2862(90)90034-O

M3 - Article

C2 - 2084502

AN - SCOPUS:0025677215

VL - 40

SP - 379

EP - 393

JO - Microvascular Research

JF - Microvascular Research

SN - 0026-2862

IS - 3

ER -