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Dynamics of a non-spherical microcapsule with incompressible interface in shear flow

Published online by Cambridge University Press:  18 April 2011

P. M. VLAHOVSKA ,
Y.-N. YOUNG ,
G. DANKER  and
C. MISBAH
P. M. VLAHOVSKA*
Affiliation:
School of Engineering, Brown University, Providence, RI 02912, USA
Y.-N. YOUNG
Affiliation:
Department Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA
G. DANKER
Affiliation:
Laboratoire de Spectrométrie Physique, UMR, 140 avenue de la physique, Université Joseph Fourier and CNRS, 38402 Saint Martin d'Heres, France
C. MISBAH
Affiliation:
Laboratoire de Spectrométrie Physique, UMR, 140 avenue de la physique, Université Joseph Fourier and CNRS, 38402 Saint Martin d'Heres, France
*
†Email address for correspondence: [email protected]
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Abstract

We study the motion and deformation of a liquid capsule enclosed by a surface-incompressible membrane as a model of red blood cell dynamics in shear flow. Considering a slightly ellipsoidal initial shape, an analytical solution to the creeping-flow equations is obtained as a regular perturbation expansion in the excess area. The analysis takes into account the membrane fluidity, area-incompressibility and resistance to bending. The theory captures the observed transition from tumbling to swinging as the shear rate increases and clarifies the effect of capsule deformability. Near the transition, intermittent behaviour (swinging periodically interrupted by a tumble) is found only if the capsule deforms in the shear plane and does not undergo stretching or compression along the vorticity direction; the intermittency disappears if deformation along the vorticity direction occurs, i.e. if the capsule ‘breathes’. We report the phase diagram of capsule motions as a function of viscosity ratio, non-sphericity and dimensionless shear rate.

JFM classification

Biological Fluid Dynamics: Capsule/cell dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 221 - 247
Copyright
Copyright © Cambridge University Press 2011

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References

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