Journal
JOURNAL OF FLUID MECHANICS
Volume 678, Issue -, Pages 221-247Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2011.108
Keywords
capsule/cell dynamics
Categories
Funding
- NSF [CBET-0846247, CBET-0853673, DMS-0708977]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1009105] Funding Source: National Science Foundation
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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.
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