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Influence of membrane viscosity on capsule dynamics in shear flow

Published online by Cambridge University Press:  08 February 2013

Alireza Yazdani  and
Prosenjit Bagchi
Alireza Yazdani
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, The State University of New Jersey, Piscataway, NJ 08854, USA
Prosenjit Bagchi*
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, The State University of New Jersey, Piscataway, NJ 08854, USA
*
†Email address for correspondence: [email protected]
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Abstract

Most previous numerical studies on capsule dynamics in shear flow have ignored the role of membrane viscosity. Here we present a numerical method for large deformation of capsules using a Kelvin–Voigt viscoelastic model for the membrane. After introducing the model and the related numerical implementation, we present a comprehensive analysis of the influence of the membrane viscosity on buckling, deformation and dynamics. We observe that the membrane viscosity leads to buckling in the range of shear rate in which no buckling is observed for capsules with purely elastic membrane. For moderate to large shear rates, the wrinkles on the capsule surface appear in the same range of the membrane viscosity that was reported earlier for artificial capsules and red blood cells based on experimental measurements. In order to obtain stable shapes, it is necessary to introduce the bending stiffness. It is observed that the range of the bending stiffness required is also in the same range as that reported for the red blood cells, but considerably higher than that estimated for artificial capsules. Using the stable shapes obtained in the presence of bending stiffness, we analyse the influence of membrane viscosity on deformation, inclination and tank-treading frequency of initially spherical capsules. Membrane viscosity is observed to reduce the capsule deformation, and introduce a damped oscillation in time-dependent deformation and inclination. The time-averaged inclination angle shows a non-monotonic trend with an initial decrease reaching a minimum and a subsequent increase with increasing membrane viscosity. A similar non-monotonic trend is also observed in the tank-treading frequency. We then consider the influence of the membrane viscosity on the unsteady dynamics of an initially oblate capsule. The dynamics is observed to change from a swinging motion to a tumbling motion with increasing membrane viscosity. Further, a transient dynamics is also observed in which a capsule starts with one type of dynamics, but settles with a different dynamics over a long time.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Capsule/cell dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 718 , 10 March 2013 , pp. 569 - 595
Copyright
©2013 Cambridge University Press

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Yazdani and Bagchi supplementary movie

Formation and propagation of wrinkles on capsule surface at capillary number Ca = 0.6.

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Supplementary material: PDF

Yazdani and Bagchi supplementary material

Supplementary data

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Yazdani and Bagchi supplementary movie

Formation and propagation of wrinkles on capsule surface at Ca = 0.1.

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Video 1.2 MB