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STABILIZED, MULTISCALE, AND MULTIPHYSICS METHODS IN FLUID MECHANICS

The Deformation of a Vesicle in a Linear Shear Flow

[+] Author and Article Information
Shu Takagi1

Research Program for Computational Science, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japantakagish@riken.jp

Takeshi Yamada2

Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japanyuushi@fel.t.u-tokyo.ac.jp

Xiaobo Gong

Research Program for Computational Science, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japangong@riken.jp

Yoichiro Matsumoto

Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japanymats@mech.t.u-tokyo.ac.jp

1

1Corresponding author. Also at Department of Mechanical Engineering, The University of Tokyo.

2

2Present address: Hitachi Company, 7-2-1 Omika-cho, Hitachi 319-1221, Japan.

J. Appl. Mech 76(2), 021207 (Jan 15, 2009) (6 pages) doi:10.1115/1.3062966 History: Received February 29, 2008; Revised July 07, 2008; Published January 15, 2009

In this paper, we discuss the motion of a vesicle in a linear shear flow. It is known that deformable vesicles such as liposomes show the so-called tank-treading and tumbling motions depending on the viscosity ratio between the inside and outside of the vesicle, the swelling ratio, and so on. First, we have conducted numerical simulations on the tank-treading motion of a liposome in a linear shear flow and compared the results with other numerical and experimental results. It is confirmed that the inclination angle of the vesicle becomes smaller when the viscosity ratio becomes larger or the swelling ratio becomes smaller and that the present results show quantitatively good agreement with other results. Then, the effects of membrane modeling are discussed from the mechanics point of view. There are two types of modeling for the lipid bilayer biomembrane. One is a two-dimensional fluid membrane, which reflects the fluidity of the lipid molecules. The other is a hyperelastic membrane, which reflects the stiffness of cytoskeleton structure. Liposome is usually modeled as a fluid membrane and red blood cell (RBC) is modeled as a hyperelastic one. We discuss how these differences of membrane models affect the behaviors of vesicles under the presence of shear flow. It is shown that the hyperelastic membrane model for RBC shows a less inclination angle of tank-treading motion and early transition from tank-treading to tumbling.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

The behavior of deformable liposome in a simple shear flow (r is the viscosity ratio between the inside and outside of a liposome, and θi is the inclination angle)

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Figure 2

The initial configuration of a RBC in a linear shear flow

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Figure 4

Dependence of inclination angle θι of 3D tank-treading motion on viscosity ratio

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Figure 5

Dependence of inclination angle θι of tank-treading motion on swelling ratio (comparison of 2D and 3D results)

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Figure 6

Dependence of inclination angle θι of tank-treading motion on swelling ratio (rearrangement of 2D and 3D results)

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Figure 7

Comparison of the tank-treading shapes between experiments and the present simulations

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Figure 8

Comparison of the inclination angle with other results

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Figure 9

The motion of a RBC in a linear shear flow. (a) tank-treading motion: μin/μout=0.35, γ=950 1/s, and B=4.2×10−3 dyn/cm. (b) tumbling motion: μin/μout=6.2, γ=950 1/s, and B=4.2×10−3 dyn/cm.

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Figure 10

The effect of membrane model to the inclination angle of tank-treading motion

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Figure 3

Dependence of inclination angle θ of 2D tank-treading motion on viscosity ratio

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